In the traditional AMM model, liquidity is distributed uniformly along the price curve between 0 and ∞. An LP in a traditional AMM can make huge impermanent loss due to asset price volatility and it may exceed the fees collected. AMMs do not have order books. The price of the assets in the pool is the ratio between them in the pool and the ratio continues to change. As the change becomes bigger, liquidity providers become more exposed to impermanent loss. Suppose, you have provided liquidity in the USDC/ETH pool in a 50:50 ratio. If ETH goes up in value, the pool will have to rely on arbitrageurs continually to ensure that the pool price reflects the market price for maintaining the same value of both tokens in the pool. In such a situation, profit from the token, that appreciated in value, is taken away from the liquidity provider. If you decide to withdraw your liquidity at that point, your impermanent loss becomes permanent. Often, we can see that an LP could have earned more just by HODLing rather than LPing.

Uniswap V3 tried to change the game with its concentrated liquidity. It was the first protocol that allowed liquidity to be allocated within a custom price range. In a concentrated liquidity, liquidity providers may concentrate their capital to smaller price intervals than (0, ∞). For example, in DAI/USDC pair, an LP may choose to allocate capital solely to the 0.99 - 1.01 range. In a concentrated liquidity pool, LPs may have many different positions that create individualized price curves to reflect the preferences of each LP. While this is an effective way to decrease impermanent loss but you can earn trading fees only if the market price is within your selected range. The problem with concentrated liquidity is that it needs a more active presence from LP. In a volatile market, you need to reset the price ranges frequently to optimize returns. If the price moves outside the range, the capital efficiency effectively becomes zero. Again, continuous monitoring of such LP position is a big problem and moving the liquidity to a new range costs gas fees.

Maverick AMM solves that problem by natively automating the movement of concentrated liquidity. It maximizes capital efficiency by automating the reconcentration of liquidity as price moves. If you are an LP provider on Maverick, you can select from a variety of liquidity-shifting modes that do the work of monitoring prices and reconcentrating liquidity for them. Let us simplify this. Suppose, you want to provide your liquidity in the USDC-ETH pair and you are very bullish about ETH. You have a directional belief that ETH is going to move up in the long run and that is why you want to collect trading fees while increasing your ETH amount. There is no AMM in the market that can support your directional belief. In Maverick AMM, you can make a bet on the price movement of a particular token.

Maverick TVL is $19.66m now – from Defillama

Liquidity providers on Maverick can choose to follow the price of an asset in a single direction and can effectively bet on the price trajectory of a specific token. This looks a bit like the single-sided liquidity strategy on a concentrated liquidity pool. To understand it better, let us explore the three scenarios when you provide liquidity with a concentrated liquidity pool:

1. Current price is within your target price range

2. Current price < your target price range

3. Current price > your target price range

For the second and third cases, only one of the two tokens is required to provide LP. It allows single-side deposits. Here, your position does not earn fees or be used in trades until the market price moves into your range. Maverick brings innovation here. Let us remember your USDC-ETH pair and your bullishness about ETH. When ETH price moves up, your selected AMM mode of Maverick will automatically reconcentrate liquidity to follow it, in order to capture more fees. If you make a correct bet on price direction, you can use this mode to enjoy re-concentrated liquidity around the price as it moves in your desired direction without experiencing any impermanent loss.

Maverick AMM’s core philosophy is centered around Automated Liquidity Placement (ALP). This is a proprietary feature of Maverick. The goal of ALP is to provide better capital control for LPs and improve capital efficiency. It fills the gap between price belief and the tools available to bet for the price belief in an AMM model. The beauty of Maverick AMM is that you can select a range and specify how that liquidity should move as the price moves. The smart contract of Maverick AMM will natively shift your liquidity (maybe with each swap) so that your LP can remain capital efficient on a continuous basis.

Like any other AMM DEX, LPs supply liquidity to a pool on Maverick so that the traders can trade. LPs earn trading fees from the swaps made by traders. Each pool is defined by three parameters: Pair of assets, Bin width, and Fee rate. LPs can freely choose the pools. Generally, an LP supplies quantities of both tokens but a ‘single-sided liquidity’ provision is also there. When LPs supply liquidity, they need to select how the liquidity will be distributed across a price range. The smallest unit of the price range is called ‘bin’ and LPs can choose to stake liquidity in one or more bins. Maverick is a permissionless AMM and anybody can deploy a pool. The widths of the bins are variable and pool deployers set it when they deploy pools. During pool deployment, fee tier is also selected. There are 4 liquidity modes in Maverick AMM:

Select mode option during liquidity supply in Maverick - Screenshot from DAPP

Mode Right: Liquidity moves with price as the price increases but there is no movement when the price decreases. Consider the USDC-ETH pool. If you are bullish about ETH, you will select Mode Right and add liquidity to the left of the current active bin.

Mode Left: Liquidity moves with price as the price decreases but there is no movement when the price increases. Consider the USDC-ETH pool. If you are bearish about ETH, you will select Mode Left and add liquidity to the right of the current active bin.

Mode Both: Liquidity moves with price in both directions. This mode allows you to add liquidity to the current active bin and to either of the bins immediately to the left or right of the active bin. It is designed to generate maximum trading fees by keeping all your provided liquidity concentrated close to the price.

Mode Static: It allows adding liquidity without engaging any of Maverick AMM’s liquidity-shifting mechanisms. It is very much like established Range AMM and less capital efficient.

[

Source – 4 liquidity modes of Maverick

The flexible market-making of Maverick is an innovation that allows users to select different positions in a single pool. The best thing is that these positions can be parameterized as per the need of the user. Customizability is a popular feature of TradFi and DeFi needs it for better user adoption. Maverick has the potential to take LPing to a new level by bringing a new class of market participants. In maximum AMM models, the fee is held separately from the liquidity in the pool. Maverick excels here too. The fee income is auto-reinvested to the bin where it is collected, which increases capital efficiency even more. So far, so good! But what about decentralization? A protocol like Maverick needs to be truly decentralized in order to be sustainable over the long term. This is why the team wants Maverick to be community-owned down the line. The decentralization roadmap is already in progress, and MAV, the governance token of Maverick, is supposed to be launched soon. Be sure to keep an eye out for Maverick's upcoming surprises!

Follow Maverick on Twitter and Medium. Join their vibrant Discord if you have queries. The audit reports of Maverick are available here. DYOR before investing your money. This article was first published here.

What Is a Chief Executive Officer (CEO)?

A chief executive officer (CEO) is the highest-ranking executive in a company. Broadly speaking, a chief executive officer’s primary responsibilities include making major corporate decisions, managing the overall operations and resources of a company, acting as the main point of communication between the board of directors and corporate operations. In many cases, the chief executive officer serves as the public face of the company. 

The CEO is elected by the board and its shareholders. They report to the chair and the board, who are appointed by shareholders. 

The Cboe Volatility Index (VIX) is a real-time index that represents the market’s expectations for the relative strength of near-term price changes of the S&P 500 Index (SPX). Because it is derived from the prices of SPX index options with near-term expiration dates, it generates a 30-day forward projection of volatility. Volatility, or how fast prices change, is often seen as a way to gauge market sentiment, and in particular the degree of fear among market participants.

The index is more commonly known by its ticker symbol and is often referred to simply as “the VIX.” It was created by the Cboe Options Exchange (Cboe) and is maintained by Cboe Global Markets. It is an important index in the world of trading and investment because it provides a quantifiable measure of market risk and investors’ sentiments.

KEY TAKEAWAYS

• The Cboe Volatility Index, or VIX, is a real-time market index representing the market’s expectations for volatility over the coming 30 days.

• Investors use the VIX to measure the level of risk, fear, or stress in the market when making investment decisions.

• Traders can also trade the VIX using a variety of options and exchange-traded products, or they can use VIX values to price derivatives.

• The VIX generally rises when stocks fall, and declines when stocks rise.

How Does the Cboe Volatility Index (VIX) Work?

The VIX attempts to measure the magnitude of price movements of the S&P 500 (i.e., its volatility). The more dramatic the price swings are in the index, the higher the level of volatility, and vice versa. In addition to being an index to measure volatility, traders can also trade VIX futures, options, and ETFs to hedge or speculate on volatility changes in the index.

In general, volatility can be measured using two different methods. The first method is based on historical volatility, using statistical calculations on previous prices over a specific time period. This process involves computing various statistical numbers, like mean (average), variance, and finally, the standard deviation on the historical price data sets.

The second method, which the VIX uses, involves inferring its value as implied by options prices.1 Options are derivative instruments whose price depends upon the probability of a particular stock’s current price moving enough to reach a particular level (called the strike price or exercise price).

Since the possibility of such price moves happening within the given time frame is represented by the volatility factor, various option pricing methods (like the Black-Scholes model) include volatility as an integral input parameter. Since option prices are available in the open market, they can be used to derive the volatility of the underlying security. Such volatility, as implied by or inferred from market prices, is called forward-looking implied volatility (IV).

Extending Volatility to Market Level

The VIX was the first benchmark index introduced by Cboe to measure the market’s expectation of future volatility. Being a forward-looking index, it is constructed using the implied volatilities on S&P 500 index options and represents the market’s expectation of 30-day future volatility of the S&P 500 Index, which is considered the leading indicator of the broad U.S. stock market.1

Introduced in 1993, the VIX is now an established and globally recognized gauge of U.S. equity market volatility. It is calculated in real-time based on the live prices of the S&P 500 Index. Calculations are performed and values are relayed from 3 a.m. to 9:15 a.m., and from 9:30 a.m. to 4:15 p.m. EST. Cboe began the dissemination of the VIX outside of U.S. trading hours in April 2016.2

Calculation of VIX Values

VIX values are calculated using the Cboe-traded standard SPX options, which expire on the third Friday of each month, and the weekly SPX options, which expire on all other Fridays. Only SPX options are considered whose expiry period lies within more than 23 days and less than 37 days.3

While the formula is mathematically complex, it theoretically works as follows: It estimates the expected volatility of the S&P 500 Index by aggregating the weighted prices of multiple SPX puts and calls over a wide range of strike prices.4 All such qualifying options should have valid nonzero bid and ask prices that represent the market perception of which options’ strike prices will be hit by the underlying stocks during the remaining time to expiry.

For detailed calculations with an example, one can refer to the section “The VIX Index Calculation: Step-by-Step” of the VIX white paper.

Evolution of the VIX

During its origin in 1993, VIX was calculated as a weighted measure of the implied volatility of eight S&P 100 at-the-money put and call options, when the derivatives market had limited activity and was in its growing stages.5

As the derivatives markets matured, 10 years later, in 2003, the Cboe teamed up with Goldman Sachs and updated the methodology to calculate VIX differently. It then started using a wider set of options based on the broader S&P 500 Index, an expansion that allows for a more accurate view of investors’ expectations of future market volatility. A methodology was adopted that remains in effect and is also used for calculating various other variants of the volatility index.2

VIX vs. S&P 500 Price

Volatility value, investors’ fear, and VIX values all move up when the market is falling. The reverse is true when the market advances—the index values, fear, and volatility decline.

The price action of the S&P 500 and the VIX often shows inverse price action: when the S&P falls sharply, the VIX rises—and vice versa.

As a rule of thumb, VIX values greater than 30 are generally linked to large volatility resulting from increased uncertainty, risk, and investors’ fear. VIX values below 20 generally correspond to stable, stress-free periods in the markets.

How to Trade the VIX

The VIX has paved the way for using volatility as a tradable asset, albeit through derivative products. Cboe launched the first VIX-based exchange-traded futures contract in March 2004, followed by the launch of VIX options in February 2006.2

Such VIX-linked instruments allow pure volatility exposure and have created a new asset class. Active traders, large institutional investors, and hedge fund managers use the VIX-linked securities for portfolio diversification, as historical data demonstrates a strong negative correlation of volatility to the stock market returns—that is, when stock returns go down, volatility rises, and vice versa.

Like all indexes, one cannot buy the VIX directly. Instead, investors can take a position in VIX through futures or options contracts, or through VIX-based exchange traded products (ETPs). For example, the ProShares VIX Short-Term Futures ETF (VIXY) and the iPath Series B S&P 500 VIX Short-Term Futures ETN (VXXB) are two such offerings that track a certain VIX-variant index and take positions in linked futures contracts.

Active traders who employ their own trading strategies and advanced algorithms use VIX values to price the derivatives, which are based on high beta stocks. Beta represents how much a particular stock price can move with respect to the move in a broader market index. For instance, a stock having a beta of +1.5 indicates that it is theoretically 50% more volatile than the market. Traders making bets through options of such high beta stocks utilize the VIX volatility values in appropriate proportion to correctly price their options trades.

Following the popularity of the VIX, the Cboe now offers several other variants for measuring broad market volatility. Examples include the Cboe Short-Term Volatility Index (VIX9D), which reflects the nine-day expected volatility of the S&P 500 Index; the Cboe S&P 500 3-Month Volatility Index (VIX3M); and the Cboe S&P 500 6-Month Volatility Index (VIX6M). Products based on other market indexes include the Nasdaq-100 Volatility Index (VXN); the Cboe DJIA Volatility Index (VXD); and the Cboe Russell 2000 Volatility Index (RVX).6

Options and futures based on VIX products are available for trading on Cboe and CFE platforms, respectively.

What Does the VIX Tell Us?

The Cboe Volatility Index (VIX) signals the level of fear or stress in the stock market—using the S&P 500 index as a proxy for the broad market—and hence is widely known as the “Fear Index.” The higher the VIX, the greater the level of fear and uncertainty in the market, with levels above 30 indicating tremendous uncertainty.

How Can an Investor Trade the VIX?

Like all indices, the VIX cannot be bought directly. However, the VIX can be traded through futures contracts and exchange traded funds (ETFs) and exchange traded notes (ETNs) that own these futures contracts.

Does the Level of the VIX Affect Option Premiums and Prices?

Yes, it does. Volatility is one of the primary factors that affect stock and index options’ prices and premiums. As the VIX is the most widely watched measure of broad market volatility, it has a substantial impact on option prices or premiums. A higher VIX means higher prices for options (i.e., more expensive option premiums) while a lower VIX means lower option prices or cheaper premiums.

How Can I Use the VIX Level to Hedge Downside Risk?

Downside risk can be adequately hedged by buying put options, the price of which depend on market volatility. Astute investors tend to buy options when the VIX is relatively low and put premiums are cheap. Such protective puts will generally get expensive when the market is sliding; therefore, like insurance, it’s best to buy them when the need for such protection is not obvious (i.e., when investors perceive the risk of market downside to be low).

What Is a Normal Value for the VIX?

The long-run average of the VIX has been around 21.4 High levels of the VIX (normally when it is above 30) can point to increased volatility and fear in the market, often associated with a bear market.

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TESLA INC

AAPL

APPLE INC

NKE

NIKE INC

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AMAZON.COM, INC

WMT

WALMART INC

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$

SELECT A PURCHASE DATE

              2 years ago                      5 years ago                      10 years ago         

CALCULATE

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Volatility is a statistical measure of the dispersion of returns for a given security or market index. In most cases, the higher the volatility, the riskier the security. Volatility is often measured as either the standard deviation or variance between returns from that same security or market index.

In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a "volatile" market. An asset's volatility is a key factor when pricing options contracts.

KEY TAKEAWAYS

• Volatility represents how large an asset's prices swing around the mean price—it is a statistical measure of its dispersion of returns.

• There are several ways to measure volatility, including beta coefficients, option pricing models, and standard deviations of returns.

• Volatile assets are often considered riskier than less volatile assets because the price is expected to be less predictable.

• Volatility is an important variable for calculating options prices.

Understanding Volatility

Volatility often refers to the amount of uncertainty or risk related to the size of changes in a security's value. A higher volatility means that a security's value can potentially be spread out over a larger range of values. This means that the price of the security can change dramatically over a short time period in either direction. A lower volatility means that a security's value does not fluctuate dramatically, and tends to be more steady.

One way to measure an asset's variation is to quantify the daily returns (percent move on a daily basis) of the asset. Historical volatility is based on historical prices and represents the degree of variability in the returns of an asset. This number is without a unit and is expressed as a percentage.

While variance captures the dispersion of returns around the mean of an asset in general, volatility is a measure of that variance bounded by a specific period of time. Thus, we can report daily volatility, weekly, monthly, or annualized volatility. It is, therefore, useful to think of volatility as the annualized standard deviation.

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TESLA INC

AAPL

APPLE INC

NKE

NIKE INC

AMZN

AMAZON.COM, INC

WMT

WALMART INC

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$

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              2 years ago                      5 years ago                      10 years ago         

CALCULATE

How to Calculate Volatility

Volatility is often calculated using variance and standard deviation. The standard deviation is the square root of the variance. 

For simplicity, let's assume we have monthly stock closing prices of $1 through $10. For example, month one is $1, month two is $2, and so on. To calculate variance, follow the five steps below.

1. Find the mean of the data set. This means adding each value and then dividing it by the number of values. If we add, $1, plus $2, plus $3, all the way to up to $10, we get $55. This is divided by 10 because we have 10 numbers in our data set. This provides a mean, or average price, of $5.50.

2. Calculate the difference between each data value and the mean. This is often called deviation. For example, we take $10 - $5.50 = $4.50, then $9 - $5.50 = $3.50. This continues all the way down to the first data value of $1. Negative numbers are allowed. Since we need each value, these calculations are frequently done in a spreadsheet.

3. Square the deviations. This will eliminate negative values.

4. Add the squared deviations together. In our example, this equals 82.5.

5. Divide the sum of the squared deviations (82.5) by the number of data values.

In this case, the resulting variance is $8.25. The square root is taken to get the standard deviation. This equals $2.87. This is a measure of risk and shows how values are spread out around the average price. It gives traders an idea of how far the price may deviate from the average.

Investopedia / Sabrina Jiang

If prices are randomly sampled from a normal distribution, then about 68% of all data values will fall within one standard deviation. Ninety-five percent of data values will fall within two standard deviations (2 x 2.87 in our example), and 99.7% of all values will fall within three standard deviations (3 x 2.87). In this case, the values of $1 to $10 are not randomly distributed on a bell curve; rather. they are uniformly distributed. Therefore, the expected 68%–95%º–99.7% percentages do not hold. Despite this limitation, traders frequently use standard deviation, as price returns data sets often resemble more of a normal (bell curve) distribution than in the given example.

Other Measures of Volatility

One measure of the relative volatility of a particular stock to the market is its beta (β). A beta approximates the overall volatility of a security's returns against the returns of a relevant benchmark (usually the S&P 500 is used). For example, a stock with a beta value of 1.1 has historically moved 110% for every 100% move in the benchmark, based on price level.

Conversely, a stock with a beta of .9 has historically moved 90% for every 100% move in the underlying index.

Market volatility can also be seen through the VIX or Volatility Index. The VIX was created by the Chicago Board Options Exchange as a measure to gauge the 30-day expected volatility of the U.S. stock market derived from real-time quote prices of S&P 500 call and put options.1 It is effectively a gauge of future bets investors and traders are making on the direction of the markets or individual securities. A high reading on the VIX implies a risky market.

A variable in option pricing formulas showing the extent to which the return of the underlying asset will fluctuate between now and the option's expiration. Volatility, as expressed as a percentage coefficient within option-pricing formulas, arises from daily trading activities. How volatility is measured will affect the value of the coefficient used.

Volatility is also used to price options contracts using models like Black-Scholes or binomial tree models. More volatile underlying assets will translate to higher options premiums because with volatility there is a greater probability that the options will end up in-the-money at expiration. Options traders try to predict an asset's future volatility, so the price of an option in the market reflects its implied volatility.

Real-World Example of Volatility

Suppose that an investor is building a retirement portfolio. Since she is retiring within the next few years, she's seeking stocks with low volatility and steady returns. She considers two companies:

1. Microsoft Corporation (MSFT), as of August 2021, has a beta coefficient of .78, which makes it slightly less volatile than the S&P 500 index.2

2. As of August 2021, Shopify Inc. (SHOP) has a beta coefficient of 1.45, making it significantly more volatile than the S&P 500 index.3

The investor would likely choose Microsoft Corporation for their portfolio, since it has less volatility and more predictable short-term value.

Implied Volatility vs. Historical Volatility

Implied volatility (IV), also known as projected volatility, is one of the most important metrics for options traders. As the name suggests, it allows them to make a determination of just how volatile the market will be going forward. This concept also gives traders a way to calculate probability. One important point to note is that it shouldn't be considered science, so it doesn't provide a forecast of how the market will move in the future.

Unlike historical volatility, implied volatility comes from the price of an option itself and represents volatility expectations for the future. Because it is implied, traders cannot use past performance as an indicator of future performance. Instead, they have to estimate the potential of the option in the market.

Also referred to as statistical volatility, historical volatility (HV) gauges the fluctuations of underlying securities by measuring price changes over predetermined periods of time. It is the less prevalent metric compared to implied volatility because it isn't forward-looking.

When there is a rise in historical volatility, a security's price will also move more than normal. At this time, there is an expectation that something will or has changed. If the historical volatility is dropping, on the other hand, it means any uncertainty has been eliminated, so things return to the way they were.

This calculation may be based on intraday changes, but often measures movements based on the change from one closing price to the next. Depending on the intended duration of the options trade, historical volatility can be measured in increments ranging anywhere from 10 to 180 trading days.

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Yacht insurance is an insurance policy that provides indemnity liability coverage for a sailing vessel. It includes liability coverage for bodily injury or damage to the property of others and damage to personal property on the vessel. Depending on the insurance provider, this insurance could also include gas delivery, towing, and assistance if your yacht gets stranded.

KEY TAKEAWAYS

• Yacht insurance provides indemnity liability coverage for a sailing vessel.

• It has two principal parts: hull insurance and protection and indemnity (P&I) insurance.

• While there is no legal agreed upon length that separates a yacht from a pleasure boat, generally it is considered to be somewhere between 27 and 30 feet.

Understanding Yacht Insurance

Some companies specialize in providing coverage for antique and classic boats. You can choose between an actual cash value or agreed value policy. The former is cheaper but factors in depreciation and market value, so your payout will be less.12 Some policies include discounts based on your boating education, safety features, and whether you have a hybrid or electric boat. Some companies also offer a package deal that decreases the rate on a yacht insurance policy if you purchase additional policies, such as for your home or car.3

Boats are defined as vessels under 197 feet long, while ships are 197 feet long or longer. There is no agreed upon length for a yacht, but they are generally considered to be at least 30 feet long. A vessel under 27 feet is considered a pleasure boat.4 

Although there isn't a standard definition of what the size of a yacht is, we can see that there is a general agreement within a range. With that being said, this general range falls within class 2 and class 3 of the Federal boat classification system.5

For its own purposes, the National Boat Owners Association marks the dividing line at 27 feet. Most yacht coverage is broader and more specialized than pleasure boat coverage, because larger vessels travel farther and are exposed to greater risks.2

Yacht insurance is broader and more specialized than pleasure boat coverage, due to the fact that a yacht can sail farther and thus runs greater risks.

A yacht insurance deductible, the amount of money you must pay out of your own pocket before your insurance kicks in, is usually a percentage of the insured value. A 1% deductible, for example, means that a boat insured for $100,000 would have a $1,000 deductible. Most lenders allow a maximum deductible of 2% of the insured value.6

Generally, yacht insurance coverage does not include wear and tear, gradual deterioration, marine life, marring, denting, scratching, animal damage, osmosis, blistering, electrolysis, manufacturer’s defects, defects in design, and ice and freezing.7

Two Parts of Yacht Insurance

There are two principal sections of a yacht insurance policy.

Hull insurance

Hull insurance is an all-risk, direct damage coverage that includes an agreed amount of hull coverage. That amount is settled on when the policy is written, and in the case of a total loss it will be paid out in full.8 In addition, there is replacement cost coverage on partial losses, though sails, canvas, batteries, outboards, and sometimes outdrives are not include and instead are subject to depreciation.9

Protection and indemnity (P&I)

Protection and indemnity (P&I) insurance is the broadest of all liability coverages, and because maritime law is particular, you will need coverages that are designed for those exposures. Longshore and harbor workers’ coverage and Jones Act coverage (for the yacht’s crew) are included and important, because your losses in these areas could run into six figures. P&I will cover any judgements against you and also pays for your defense in admiralty courts.910

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The Sharpe ratio was developed by Nobel laureate William F. Sharpe and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Volatility is a measure of the price fluctuations of an asset or portfolio.

KEY TAKEAWAYS

• The Sharpe ratio adjusts a portfolio’s past performance—or expected future performance—for the excess risk that was taken by the investor.

• A high Sharpe ratio is good when compared to similar portfolios or funds with lower returns.

• The Sharpe ratio has several weaknesses, including an assumption that investment returns are normally distributed.

0 seconds of 1 minute, 49 secondsVolume 75%

1:49

Sharpe Ratio

Formula and Calculation of Sharpe Ratio

\begin{aligned} &\textit{Sharpe Ratio} = \frac{R_p - R_f}{\sigma_p}\\ &\textbf{where:}\\ &R_{p}=\text{return of portfolio}\\ &R_{f} = \text{risk-free rate}\\ &\sigma_p = \text{standard deviation of the portfolio's excess return}\\ \end{aligned}​Sharpe Ratio=σp​Rp​−Rf​​where:Rp​=return of portfolioRf​=risk-free rateσp​=standard deviation of the portfolio’s excess return​

The Sharpe ratio is calculated as follows:

1. Subtract the risk-free rate from the return of the portfolio. The risk-free rate could be a U.S. Treasury rate or yield, such as the one-year or two-year Treasury yield.

2. Divide the result by the standard deviation of the portfolio’s excess return. The standard deviation helps to show how much the portfolio's return deviates from the expected return. The standard deviation also sheds light on the portfolio's volatility.

What the Sharpe Ratio Can Tell You

Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities. The risk-free rate of return is the return of an investment with zero risks, meaning it's the return investors could expect for taking no risk. The yield for a U.S. Treasury bond, for example, could be used as the risk-free rate.

Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.

The Sharpe ratio is one of the most widely used methods for calculating risk-adjusted return. Modern Portfolio Theory (MPT) states that adding assets to a diversified portfolio that has low correlations can decrease portfolio risk without sacrificing return.

Adding diversification should increase the Sharpe ratio compared to similar portfolios with a lower level of diversification. For this to be true, investors must also accept the assumption that risk is equal to volatility, which is not unreasonable but may be too narrow to be applied to all investments.

The Sharpe ratio can be used to evaluate a portfolio’s past performance (ex-post) where actual returns are used in the formula. Alternatively, an investor could use expected portfolio performance and the expected risk-free rate to calculate an estimated Sharpe ratio (ex-ante).

The Sharpe ratio can also help explain whether a portfolio's excess returns are due to smart investment decisions or a result of too much risk. Although one portfolio or fund can enjoy higher returns than its peers, it is only a good investment if those higher returns do not come with an excess of additional risk.

The greater a portfolio's Sharpe ratio, the better its risk-adjusted performance. If the analysis results in a negative Sharpe ratio, it either means the risk-free rate is greater than the portfolio’s return, or the portfolio's return is expected to be negative. In either case, a negative Sharpe ratio does not convey any useful meaning.

Example of How to Use Sharpe Ratio

The Sharpe ratio is often used to compare the change in overall risk-return characteristics when a new asset or asset class is added to a portfolio.

For example, an investor is considering adding a hedge fund allocation to their existing portfolio that is currently split between stocks and bonds and has returned 15% over the last year. The current risk-free rate is 3.5%, and the volatility of the portfolio’s returns was 12%, which makes the Sharpe ratio of 95.8%, or (15% - 3.5%) divided by 12%.

The investor believes that adding the hedge fund to the portfolio will lower the expected return to 11% for the coming year, but also expects the portfolio’s volatility to drop to 7%. They assume that the risk-free rate will remain the same over the coming year.

Using the same formula, with the estimated future numbers, the investor finds the portfolio has the expected Sharpe ratio of 107%, or (11% - 3.5%) divided by 7%.

Here, the investor has shown that although the hedge fund investment is lowering the absolute return of the portfolio, it has improved its performance on a risk-adjusted basis. If the addition of the new investment lowered the Sharpe ratio, it should not be added to the portfolio. This example assumes that the Sharpe ratio based on past performance can be fairly compared to expected future performance.

The Difference Between Sharpe Ratio and Sortino Ratio

A variation of the Sharpe ratio is the Sortino ratio, which removes the effects of upward price movements on standard deviation to focus on the distribution of returns that are below the target or required return.

The Sortino ratio also replaces the risk-free rate with the required return in the numerator of the formula, making the formula the return of the portfolio less the required return, divided by the distribution of returns below the target or required return.

Another variation of the Sharpe ratio is the Treynor Ratio that uses a portfolio’s beta or correlation with the rest of the market. Beta is a measure of an investment's volatility and risk as compared to the overall market.

The goal of the Treynor ratio is to determine whether an investor is being compensated for taking additional risk above the inherent risk of the market. The Treynor ratio formula is the return of the portfolio, minus the risk-free rate, divided by the portfolio’s beta.

Limitations of Using Sharpe Ratio

The Sharpe ratio uses the standard deviation of returns in the denominator as its proxy of total portfolio risk, which assumes that returns are normally distributed. A normal distribution of data is like rolling a pair of dice. We know that over many rolls, the most common result from the dice will be seven, and the least common results will be two and twelve.

However, returns in the financial markets are skewed away from the average because of a large number of surprising drops or spikes in prices. Additionally, the standard deviation assumes that price movements in either direction are equally risky.

The Sharpe ratio can be manipulated by portfolio managers seeking to boost their apparent risk-adjusted returns history. This can be done by lengthening the measurement interval. This will result in a lower estimate of volatility. For example, the annualized standard deviation of daily returns is generally higher than that of weekly returns which is, in turn, higher than that of monthly returns.

Choosing a period for the analysis with the best potential Sharpe ratio, rather than a neutral look-back period, is another way to cherry-pick the data that will distort the risk-adjusted returns.

Alison Czinkota / Investopedia

What is a Good Sharpe Ratio?

Sharpe ratios above 1.0 are generally considered “good," as this would suggest that the portfolio is offering excess returns relative to its volatility. Having said that, investors will often compare the Sharpe ratio of a portfolio relative to its peers. Therefore, a portfolio with a Sharpe ratio of 1.0 might be considered inadequate if the competitors in its peer group have an average Sharpe ratio above 1.0.

How is the Sharpe Ratio Calculated?

To calculate the Sharpe ratio, investors first subtract the risk-free rate from the portfolio’s rate of return, often using U.S. Treasury bond yields as a proxy for the risk-free rate of return. Then, they divide the result by the standard deviation of the portfolio’s excess return. Note that, in using the standard deviation, this formula implicitly assumes that the portfolio’s returns are normally distributed, which may not in fact be the case.

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The Q ratio, also known as Tobin's Q, equals the market value of a company divided by its assets' replacement cost. Thus, equilibrium is when market value equals replacement cost. At its most basic level, the Q Ratio expresses the relationship between market valuation and intrinsic value. In other words, it is a means of estimating whether a given business or market is overvalued or undervalued.

KEY TAKEAWAYS

• The Q ratio was popularized by Nobel Laureate James Tobin and invented in 1966 by Nicholas Kaldor.

• The Q ratio, also known as Tobin's Q, measures whether a firm or an aggregate market is relatively over- or undervalued.

• It relies on the concepts of market value and replacement value.

• The simplified Q ratio is the equity market value divided by equity book value.

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Q Ratio

Formula and Calculation of the Q Ratio

\text{Tobin's Q}=\frac{\text{Total Market Value of Firm}}{\text{Total Asset Value of Firm}}Tobin’s Q=Total Asset Value of FirmTotal Market Value of Firm​

The Q ratio is calculated as the market value of a company divided by the replacement value of the firm's assets. Since the replacement cost of total assets is difficult to estimate, another version of the formula is often used by analysts to estimate Tobin's Q ratio. It is as follows:

\text{Tobin's Q} = \frac{\text{Equity Market Value + Liabilities Market Value}}{\text{Equity Book Value + Liabilities Book Value}}Tobin’s Q=Equity Book Value + Liabilities Book ValueEquity Market Value + Liabilities Market Value​

Often, the assumption is made the market value of liabilities and the book value of a company's liabilities are equivalent, since market value typically does not account for a firm's liabilities. This provides a simplified version of the Tobin's Q ratio as the following:

\text{Tobin's Q} = \frac{\text{Equity Market Value}}{\text{Equity Book Value}}Tobin’s Q=Equity Book ValueEquity Market Value​

What the Q Ratio Can Tell You

The Tobin's Q ratio is a quotient popularized by James Tobin of Yale University, Nobel laureate in economics, who hypothesized that the combined market value of all the companies on the stock market should be about equal to their replacement costs.

While Tobin is often attributed as its creator, this ratio was first proposed in an academic publication by economist Nicholas Kaldor in 1966. In earlier texts, the ratio is sometimes referred to as "Kaldor's v."

A low Q ratio—between 0 and 1—means that the cost to replace a firm's assets is greater than the value of its stock. This implies that the stock is undervalued. Conversely, a high Q (greater than 1) implies that a firm's stock is more expensive than the replacement cost of its assets, which implies that the stock is overvalued.

This measure of stock valuation is the driving factor behind investment decisions in Tobin's Q ratio. When applied to the market as a whole, we can gauge whether an entire market is relatively overbought or undervalued; we can represent this relationship as follows:

\text{Q Ratio (Market)} = \frac{\text{Market Capitalization of all Companies}}{\text{Replacement Value of all Companies}}Q Ratio (Market)=Replacement Value of all CompaniesMarket Capitalization of all Companies​

For either a firm or a market, a ratio greater than one would theoretically indicate that the market or company is overvalued. A ratio that is less than one would imply that it is undervalued.

Underlying these simple equations is an equally simple intuition regarding the relationship between price and value. In essence, Tobin’s Q Ratio asserts that a business (or a market) is worth what it costs to replace. The cost necessary to replace the business (or market) is its replacement value.

It might seem logical that fair market value would be a Q ratio of 1.0. But, that has not historically been the case. Prior to 1995 (for data as far back as 1945), the U.S. Q ratio never reached 1.0. During the first quarter of 2000, the Q ratio hit 2.15, while in the first quarter of 2009 it was 0.66. As of the second quarter of 2020, the Q ratio was 2.12.1

Replacement Value and the Q Ratio

Replacement value (or replacement cost) refers to the cost of replacing an existing asset based on its current market price. For example, the replacement value of a one-terabyte hard drive might be just $50 today, even if we paid $500 for the same storage space a few years ago.

In this scenario, ascertaining the replacement value would be easy because there is a robust market for hard drives from which to examine prices. To determine what a one-terabyte hard drive is worth, we would simply need to determine what it would cost to buy a one-terabyte hard drive (of comparable quality and specifications) from one of the many different suppliers on the market. In many cases, however, the replacement value of assets can prove much more elusive than this.

For instance, consider a business that owns complicated software tailor-made for its operations. Because of its highly specialized nature, there may not be any comparable alternatives available on the market. Unlike our previous example, we could not simply check to see how much similar software is selling for, because sufficiently similar software would not exist. It would thus be difficult, if not impossible, to render an objective estimate of the software’s replacement value.

Similar circumstances present themselves in a variety of business contexts, from complex industrial machinery and obscure financial assets to intangible assets such as goodwill. Due to the inherent difficulty of determining the replacement value of these and similar assets, many investors do not regard Tobin’s Q Ratio to be a reliable tool for valuing individual companies.

Example of How to Use the Q-Ratio

The formula for Tobin's Q ratio takes the total market value of the firm and divides it by the total asset value of the firm. For example, assume that a company has $35 million in assets. It also has 10 million shares outstanding that are trading for $4 a share. In this example, the Tobin's Q ratio would be:

\text{Tobin's Q Ratio} = \frac{\text{Total Market Value of Firm}}{\text{Total Asset Value of Firm}} = \frac{\$40,000,000}{\$35,000,000}= 1.14Tobin’s Q Ratio=Total Asset Value of FirmTotal Market Value of Firm​=$35,000,000$40,000,000​=1.14

Since the ratio is greater than 1.0, the market value exceeds the replacement value and so we could say the firm is overvalued and might be a sale.

An undervalued company, one with a ratio of less than one, would be attractive to corporate raiders or potential purchasers, as they may want to purchase the firm instead of creating a similar company. This would likely result in increased interest in the company, which would increase its stock price, which in turn increase its Tobin's Q ratio.

As for overvalued companies, those with a ratio higher than one, they may see increased competition. A ratio higher than one indicates that a firm is earning a rate higher than its replacement cost, which would cause individuals or other companies to create similar types of businesses to capture some of the profits. This would lower the existing firm's market shares, reduce its market price and cause its Tobin's Q ratio to fall.

Limitations of Using the Q Ratio

Tobin's Q is still used in practice, but others have since found that fundamentals predict investment results much better than the Q ratio, including the rate of profit—either for a company or the average rate of profit for a nation's economy.

Others, like Doug Henwood in his book Wall Street: How It Works and For Whom, find that the Q ratio fails to accurately predict investment outcomes over an important time period. The data for Tobin's original (1977) paper covered the years 1960 to 1974, a period for which Q seemed to explain investment pretty well. But looking at other time periods, the Q fails to predict over- or undervalued markets or firms. While the Q and the investment seemed to move together for the first half of the 1970s, the Q collapsed during the bearish stock markets of the late 1970s, even as investment in assets rose.

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Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. NPV is used in capital budgeting and investment planning to analyze the profitability of a projected investment or project. NPV is the result of calculations used to find today’s value of a future stream of payments.

KEY TAKEAWAYS

• Net present value, or NPV, is used to calculate the current total value of a future stream of payments.

• If the NPV of a project or investment is positive, it means that the discounted present value of all future cash flows related to that project or investment will be positive, and therefore attractive.

• To calculate NPV, you need to estimate future cash flows for each period and determine the correct discount rate.

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Understanding Net Present Value

Net Present Value (NPV) Formula

\begin{aligned} &NPV = \sum_{t = 1}^n \frac { R_t }{ (1 + i)^t } \\ &\textbf{where:} \\ &R_t=\text{Net cash inflow-outflows during a single period }t \\ &i=\text{Discount rate or return that could be earned in} \\ &\text{alternative investments} \\ &t=\text{Number of timer periods} \\ \end{aligned}​NPV=t=1∑n​(1+i)tRt​​where:Rt​=Net cash inflow-outflows during a single period ti=Discount rate or return that could be earned inalternative investmentst=Number of timer periods​

If you are unfamiliar with summation notation—here is an easier way to remember the concept of NPV:

\begin{aligned} &\textit{NPV} = \text{TVECF} - \text{TVIC} \\ &\textbf{where:} \\ &\text{TVECF} = \text{Today's value of the expected cash flows} \\ &\text{TVIC} = \text{Today's value of invested cash} \\ \end{aligned}​NPV=TVECF−TVICwhere:TVECF=Today’s value of the expected cash flowsTVIC=Today’s value of invested cash​

What Net Present Value Can Tell You

NPV accounts for the time value of money and can be used to compare similar investment alternatives.1 The NPV relies on a discount rate that may be derived from the cost of the capital required to invest, and any project or investment with a negative NPV should be avoided.1 One important drawback of NPV analysis is that it makes assumptions about future events that may not be reliable.

NPV looks to assess the profitability of a given investment on the basis that a dollar in the future is not worth the same as a dollar today. Money loses value over time due to inflation. However, a dollar today can be invested and earn a return, making its future value possibly higher than a dollar received at the same point in the future.

NPV seeks to determine the present value of an investment's future cash flows above the investment's initial cost. The discount rate element of the NPV formula discounts the future cash flows to the present-day value. If subtracting the initial cost of the investment from the sum of the cash flows in the present day is positive, then the investment is worthwhile.2

For example, an investor could receive $100 today or a year from now. Most investors would not be willing to postpone receiving $100 today. However, what if an investor could choose to receive $100 today or $105 in one year? The 5% rate of return (RoR) for waiting one year might be worthwhile for an investor unless another investment could yield a rate greater than 5% over the same period.

If an investor knew they could earn 8% from a relatively safe investment over the next year, they would choose to receive $100 today and not the $105 in a year, with the 5% rate of return. In this case, 8% would be the discount rate.

Positive vs. Negative NPV

A positive NPV indicates that the projected earnings generated by a project or investment—in present dollars—exceeds the anticipated costs, also in present dollars. It is assumed that an investment with a positive NPV will be profitable.

An investment with a negative NPV will result in a net loss. This concept is the basis for the Net Present Value Rule, which dictates that only investments with positive NPV values should be considered.

Calculating Net Present Value

Money in the present is worth more than the same amount in the future due to inflation and possible earnings from alternative investments that could be made during the intervening time. In other words, a dollar earned in the future won’t be worth as much as one earned in the present. The discount rate element of the NPV formula is a way to account for this.

For example, assume that an investor could choose a $100 payment today or in a year. A rational investor would not be willing to postpone payment. However, what if an investor could choose to receive $100 today or $105 in a year? If the payer was reliable, that extra 5% may be worth the wait, but only if there wasn’t anything else the investors could do with the $100 that would earn more than 5%.

An investor might be willing to wait a year to earn an extra 5%, but that may not be acceptable for all investors. In this case, the 5% is the discount rate, which will vary depending on the investor. If an investor knew they could earn 8% from a relatively safe investment over the next year, they would not be willing to postpone payment for 5%. In this case, the investor’s discount rate is 8%.

A company may determine the discount rate using the expected return of other projects with a similar level of risk or the cost of borrowing the money needed to finance the project. For example, a company may avoid a project that is expected to return 10% per year if it costs 12% to finance the project or an alternative project is expected to return 14% per year.

Imagine a company can invest in equipment that will cost $1,000,000 and is expected to generate $25,000 a month in revenue for five years. The company has the capital available for the equipment and could alternatively invest it in the stock market for an expected return of 8% per year. The managers feel that buying the equipment or investing in the stock market are similar risks.

NPV can be calculated using tables, spreadsheets (for example, Excel), or financial calculators.

Steps for Net Present Value

There are two key steps for calculating NPV:

Step 1: NPV of the initial investment

Because the equipment is paid for upfront, this is the first cash flow included in the calculation. No elapsed time needs to be accounted for, so today’s outflow of $1,000,000 doesn’t need to be discounted.

• Identify the number of periods (t): The equipment is expected to generate monthly cash flow and last for five years, which means there will be 60 cash flows and 60 periods included in the calculation.

• Identify the discount rate (i): The alternative investment is expected to pay 8% per year. However, because the equipment generates a monthly stream of cash flows, the annual discount rate needs to be turned into a periodic or monthly rate. Using the following formula, we find that the periodic rate is 0.64%.

\text{Periodic Rate} = (( 1 + 0.08)^{\frac{1}{12}}) - 1 = 0.64\%Periodic Rate=((1+0.08)121​)−1=0.64%

Step 2: NPV of future cash flows

Assume the monthly cash flows are earned at the end of the month, with the first payment arriving exactly one month after the equipment has been purchased. This is a future payment, so it needs to be adjusted for the time value of money. An investor can perform this calculation easily with a spreadsheet or calculator. To illustrate the concept, the first five payments are displayed in the table below.

Image by Sabrina Jiang © Investopedia 2020

The full calculation of the present value is equal to the present value of all 60 future cash flows, minus the $1,000,000 investment. The calculation could be more complicated if the equipment was expected to have any value left at the end of its life, but in this example, it is assumed to be worthless.

NPV = -\$1,000,000 + \sum_{t = 1}^{60} \frac{25,000_{60}}{(1 + 0.0064)^{60}}NPV=−$1,000,000+∑t=160​(1+0.0064)6025,00060​​

That formula can be simplified to the following calculation:

NPV = -\$1,000,000 + \$1,242,322.82 = \$242,322.82NPV=−$1,000,000+$1,242,322.82=$242,322.82

In this case, the NPV is positive; the equipment should be purchased. If the present value of these cash flows had been negative because the discount rate was larger, or the net cash flows were smaller, the investment should have been avoided.

Limitations of Net Present Value

Gauging an investment’s profitability with NPV relies heavily on assumptions and estimates, so there can be substantial room for error. Estimated factors include investment costs, discount rate, and projected returns. A project may often require unforeseen expenditures to get off the ground or may require additional expenditures at the project’s end.

Net Present Value vs. Payback Period

The payback period, or “payback method,” is a simpler alternative to NPV. The payback method calculates how long it will take for the original investment to be repaid. A drawback is that this method fails to account for the time value of money. For this reason, payback periods calculated for longer investments have a greater potential for inaccuracy.

Moreover, the payback period is strictly limited to the amount of time required to earn back initial investment costs. It is possible that the investment’s rate of return could experience sharp movements. Comparisons using payback periods do not account for the long-term profitability of alternative investments.

NPV vs. Internal Rate of Return (IRR)

The internal rate of return (IRR) is very similar to NPV except that the discount rate is the rate that reduces the NPV of an investment to zero. This method is used to compare projects with different lifespans or amounts of required capital.

For example, IRR could be used to compare the anticipated profitability of a three-year project that requires a $50,000 investment with that of a 10-year project that requires a $200,000 investment. Although the IRR is useful, it is usually considered inferior to NPV because it makes too many assumptions about reinvestment risk and capital allocation.

What Does the Net Present Value Mean?

Net present value (NPV) is a financial metric that seeks to capture the total value of a potential investment opportunity. The idea behind NPV is to project all of the future cash inflows and outflows associated with an investment, discount all those future cash flows to the present day, and then add them together. The resulting number after adding all the positive and negative cash flows together is the investment’s NPV. A positive NPV means that, after accounting for the time value of money, you will make money if you proceed with the investment.

What Is the Difference Between NPV and IRR?

NPV and IRR are closely related concepts, in that the IRR of an investment is the discount rate that would cause that investment to have an NPV of zero. Another way of thinking about this is that NPV and IRR are trying to answer two separate but related questions. For NPV, the question is, “What is the total amount of money I will make if I proceed with this investment, after taking into account the time value of money?” For IRR, the question is, “If I proceed with this investment, what would be the equivalent annual rate of return that I would receive?”

What Is a Good NPV?

In theory, an NPV is “good” if it is greater than zero.2 After all, the NPV calculation already takes into account factors such as the investor’s cost of capital, opportunity cost, and risk tolerance through the discount rate. And the future cash flows of the project, together with the time value of money, are also captured. Therefore, even an NPV of $1 should theoretically qualify as “good.” In practice, however, many investors will insist on certain NPV thresholds, such as $10,000 or greater, to provide themselves with an additional margin of safety.

Why Are Future Cash Flows Discounted?

NPV uses discounted cash flows due to the time value of money (TMV). The time value of money is the concept that money you have now is worth more than the identical sum in the future due to its potential earning capacity through investment and other factors such as inflation expectations. The rate used to account for time, or the discount rate, will depend on the type of analysis undertaken. Individuals should use the opportunity cost of putting their money to work elsewhere as an appropriate discount rate—simply put, it’s the rate of return the investor could earn in the marketplace on an investment of comparable size and risk.

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The knowledge economy is a system of consumption and production that is based on intellectual capital. In particular, it refers to the ability to capitalize on scientific discoveries and applied research.

The knowledge economy represents a large share of the activity in most highly developed economies. In a knowledge economy, a significant component of value may consist of intangible assets such as the value of its workers' knowledge or intellectual property.

KEY TAKEAWAYS

• The knowledge economy describes the contemporary commercialization of science and academic scholarship.

• In the knowledge economy, innovation based on research is commodified via patents and other forms of intellectual property.

• The knowledge economy lies at the intersection of private entrepreneurship, academia, and government-sponsored research.

• Knowledge-related industries represent a large share of the activity in most highly developed countries.

• A knowledge economy depends on skilled labor and education, strong communications networks, and institutional structures that incentivize innovation.

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Click Play to Learn What the Knowledge Economy Is

Understanding the Knowledge Economy

Developing economies tend to be heavily focused on agriculture and manufacturing, while highly developed countries have a larger share of service-related activities. This includes knowledge-based economic activities such as research, technical support, and consulting.

The knowledge economy is the marketplace for the production and sale of scientific and engineering discoveries. This knowledge can be commodified in the form of patents or other intellectual property protections. The producers of such information, such as scientific experts and research labs, are also considered part of the knowledge economy.

The Bayh-Dole Act of 1980 was a major turning point in the treatment of intellectual property in the U.S. because it allowed universities to retain title to inventions or discoveries made with federal R&D funding and to negotiate exclusive licenses.1

Thanks to globalization, the world economy has become more knowledge-based, bringing with it the best practices from each country's economy. Also, knowledge-based factors create an interconnected and global economy where human expertise and trade secrets are considered important economic resources.

However, it is important to note that generally accepted accounting principles (GAAP) do not allow companies to include these assets on their balance sheets.

The modern commercialization of academic research and basic science has its roots in governments seeking military advantage.

Knowledge Economy and Human Capital

The knowledge economy addresses how education and knowledge—that is, "human capital"— can serve as a productive asset or business product to be sold and exported to yield profits for individuals, businesses, and the economy.

This component of the economy relies greatly on intellectual capabilities instead of natural resources or physical contributions. In the knowledge economy, products, and services that are based on intellectual expertise advance technical and scientific fields, encouraging innovation in the economy as a whole.

The World Bank defines knowledge economies according to four pillars:

1. Institutional structures that provide incentives for entrepreneurship and the use of knowledge

2. Availability of skilled labor and a good education system

3. Access to information and communication technology (ICT) infrastructures

4. A vibrant innovation landscape that includes academia, the private sector, and civil society.2

Example of a Knowledge Economy

Academic institutions, companies engaging in research and development (R&D), programmers developing new software and search engines for data, and health workers using digital data to improve treatments are all components of a knowledge economy.

These economy brokers pass on the results of their research to workers in more traditional fields, such as farmers who use software applications and digital solutions to manage their crops better, advanced technological-based medical procedures such as robot-assistant surgeries, or schools that provide digital study aids and online courses for students.

How Big Is the Knowledge Economy?

Because it is not a clearly-defined category such as manufacturing, it is difficult to put an exact price tag on the global knowledge economy. However, it is possible to gain a rough estimate by gauging some of the major components of the knowledge economy. In the United States, the total intellectual property market is worth $6.6 trillion, according to the U.S. Chamber of Commerce, and IP-intensive industries account for over a third of GDP. The market size of the country's higher education institutions accounts for an additional $568 billion.34

What Are the Most Valuable Skills in the Knowledge Economy?

While higher education and technical training are obvious assets, communication and teamwork are also essential skills for a knowledge-based economy, according to the Organization for Economic Cooperation and Development. Since it is unlikely that any single knowledge worker can generate groundbreaking innovations alone, these interpersonal and workplace competencies are essential to surviving in a knowledge-based workplace.5

Which Country Has the Biggest Knowledge Economy?

The factors of a knowledge economy are measured by the United Nations Development Program's Global Knowledge Index, which replaced the World Bank Knowledge Economy Index after 2012. This metric scores each country based on "enabling factors" for the knowledge economy, such as education levels, technical and vocational training, innovation, and communications technology. According to the latest issue, Switzerland is the top-ranked knowledge economy with a total score of 71.5%. The next two are Sweden and the United States with scores of 70.0 each.6

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The Internal Revenue Service (IRS) is a U.S. government agency responsible for the collection of taxes and enforcement of tax laws (such as the wash sale rule).1 Established in 1862 by then-President Abraham Lincoln, the agency operates under the authority of the U.S. Department of the Treasury, and its primary purpose is the collection of individual income taxes and employment taxes. The IRS also handles corporate, gift, excise, and estate taxes.23

As of November 2021, the head of the IRS is Commissioner Charles P. Rettig, who was nominated to the post by then-President Donald Trump in 2018.4 He oversees a workforce of about 80,000 and a budget of more than $11 billion.5 A graduate of New York University, Rettig is the first commissioner since the 1990s to come to the job from a career in tax law rather than business management.6

KEY TAKEAWAYS

• Founded in 1862, the Internal Revenue Service (IRS) is a U.S. federal agency responsible for the collection of taxes and enforcement of tax laws.

• Most of the work of the IRS involves income taxes, both corporate and individual; it processed nearly 240 million tax returns in 2020.

• More than 94% of tax returns were filed electronically in 2020.

• After peaking in 2010, IRS audits have been on the decline each year.

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How Powerful Is The IRS?

How the Internal Revenue Service Works

Headquartered in Washington, D.C., the IRS services the taxation of all American individuals and companies. For fiscal year (FY) 2020 (Oct. 1, 2019, through Sept. 30, 2020), it processed more than 240 million income tax returns and other forms. During that period, the IRS collected more than $3.5 trillion in revenue and issued more than $736 billion in tax refunds (which included $268 billion in economic impact payments due to the COVID-19 pandemic).7

Individuals and corporations have the option to file income tax returns electronically, thanks to computer technology, software programs, and secure internet connections. The number of income tax returns that use e-file has grown steadily since the IRS began the program, and the overwhelming majority are now filed this way. During FY 2020, nearly 94.3% of all individual returns made use of the e-file option.8 By comparison, only about 40 million out of nearly 131 million returns, or nearly 31%, used it in 2001.9

As of October 2021, just over 112 million taxpayers received their refunds through direct deposit rather than by a traditional paper check, and the average direct-deposited amount was $2,851.10

Although the IRS recommends filing tax returns electronically, it does not endorse any particular platform or filing software.11

The IRS and Audits

As part of its enforcement mission, the IRS audits a select portion of income tax returns every year. For FY 2020, the agency audited 509,917 tax returns. This number breaks down to 0.63% of individual income tax returns and 1.0% of corporate tax returns. Around 72.6% of IRS audits occurred through correspondence, while 27.4% happened in the field.12 

After rising to a peak in 2010, the number of audits has dropped steadily each year.12 The amount of funding set aside for tax enforcement has declined by about 30% from 2010 to 2020, which indicates that even fewer audits should occur.13

Reasons for an IRS audit vary, but some factors may increase the odds of an examination. Chief among them is higher income.14 In 2020, the audit rate for all individual income tax returns was 0.63%. However, for someone who made more than $10 million, it was 9.8%.12

Running your own business also carries greater risks. Individuals making $200,000 to $1 million in 2018 who didn’t file Schedule C (the form for the self-employed) had a 0.6% chance of being audited, vs. 1.4%—basically double—for those who did.15

Other red flags for an audit include failing to declare the right amount of income, claiming a higher-than-normal amount of deductions (especially business-related ones), making disproportionately large charitable donations compared to income, and claiming rental real estate losses.16 No single factor determines who does or does not face an IRS audit each year.17

How to Interface with the IRS

By mail

There are numerous ways to contact the IRS. If you are filing a tax return by mail, your state of residence and whether or not you are expecting a tax refund will determine the address that you should use. There is a list on the IRS website.18 If you are sending an application or a payment, there is also a list on the IRS website of mailing addresses depending on your purpose.19

By phone or online

Individuals who want assistance can phone (800) 829-1040, Monday through Friday, 7 a.m. to 7 p.m. Eastern time (ET), and there are other toll-free numbers for businesses and other purposes.20 However, it can take some doing to reach an actual person. CPA Amy Northard has helpfully decoded the process on her blog, and it involves a lengthy series of responses you must make to automated questions. Investopedia has vetted it for accuracy.20 For online assistance for a variety of questions, use the Interactive Tax Assistant on the IRS website.21

In person

You can also set up an in-person appointment by phone at your local IRS office.22 The IRS website has a locator page into which you merely type your ZIP code to get the office location and phone number.23

Paying Your Taxes

You can pay your taxes to the IRS through an electronic transfer of funds from your bank account or by using a debit or credit card. Other methods include a same-day bank wire or an electronic funds withdrawal at the time that you e-file your return. If you are a business, or if you are making a large payment, you can use the Electronic Federal Tax Paying System, but you must first enroll in it.24

If you are not paying electronically, you have other options. You can mail in a personal check, cashier’s check, or money order. Make it payable to “U.S. Treasury,” and be sure that it contains the following information:25

• Your name and address

• Daytime phone number

• Social Security number (the SSN shown first if it’s a joint return) or employer identification number

• Tax year

• Related tax form or notice number

You may pay in cash if you wish, you may, but never send cash through the mail. Instead, make an in-person appointment at an IRS Taxpayer Assistance Center by calling (844) 545-5640, Monday through Friday, 7 a.m. to 7 p.m. ET. You should call 30 to 60 days before the day when you want to pay.26

You can also pay cash at one of the IRS Retail Partners: 7-Eleven, ACE Cash Express, Casey’s General Stores, CVS Pharmacy, Family Dollar, Dollar General, Walgreens, Pilot Flying J, Speedway, Kum & Go, Stripes, Royal Farms, GoMart, and Kwik Trip. This involves first getting a payment code sent to you by the IRS via email, which you must present when making your payment. There is a limit of $1,000 per payment.27

When was the IRS first established?

The IRS was established in 1862 by then-President Abraham Lincoln, who instituted an income tax to pay for the Civil War. The tax was repealed in 1872, revived in 1894, and declared unconstitutional by the U.S. Supreme Court in 1895. In 1913, the 16th Amendment to the U.S. Constitution reinstated the federal income tax.28

What is the best way to file my tax return?

It’s best to file your taxes electronically, which 94.3% of taxpayers did in 2020. You can still file a paper return by mail, but doing so will delay your receipt of any refund.

How can I pay my taxes?

The most popular way to pay your taxes is by electronic transfer, either directly from your bank account or through a debit or credit card. However, you can also pay by check or money order, and you can even pay in person—using cash if you wish.

How likely is it that the IRS will audit my taxes?

In 2020, the audit rate for individual tax returns was 0.63%. However, your chances go up if you make big bucks. The 2020 rate for people making $10 million or more was 9.8%. However, no one single factor determines whether or not the IRS will audit you.

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The geometric mean is the average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio. It is technically defined as "the nth root product of n numbers." The geometric mean must be used when working with percentages, which are derived from values, while the standard arithmetic mean works with the values themselves.

KEY TAKEAWAYS

• The geometric mean is the average rate of return of a set of values calculated using the products of the terms.

• Geometric mean is most appropriate for series that exhibit serial correlation—this is especially true for investment portfolios.

• Most returns in finance are correlated, including yields on bonds, stock returns, and market risk premiums.

• For volatile numbers, the geometric average provides a far more accurate measurement of the true return by taking into account year-over-year compounding that smooths the average.

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1:23

Geometric Mean

The Formula for Geometric Mean

\begin{aligned} &\mu _{\text{geometric}} = [(1+R _1)(1+R _2)\ldots(1+R _n)]^{1/n} - 1\\ &\textbf{where:}\\ &\bullet R_1\ldots R_n \text{ are the returns of an asset (or other}\\ &\text{observations for averaging)}. \end{aligned}​μgeometric​=[(1+R1​)(1+R2​)…(1+Rn​)]1/n−1where:∙R1​…Rn​ are the returns of an asset (or otherobservations for averaging).​

Understanding the Geometric Mean

The geometric mean, sometimes referred to as compounded annual growth rate or time-weighted rate of return, is the average rate of return of a set of values calculated using the products of the terms. What does that mean? Geometric mean takes several values and multiplies them together and sets them to the 1/nth power.

The geometric mean is an important tool for calculating portfolio performance for many reasons, but one of the most significant is it takes into account the effects of compounding.

For example, the geometric mean calculation can be easily understood with simple numbers, such as 2 and 8. If you multiply 2 and 8, then take the square root (the ½ power since there are only 2 numbers), the answer is 4. However, when there are many numbers, it is more difficult to calculate unless a calculator or computer program is used.

The longer the time horizon, the more critical compounding becomes, and the more appropriate the use of geometric mean.

The main benefit of using the geometric mean is the actual amounts invested do not need to be known; the calculation focuses entirely on the return figures themselves and presents an "apples-to-apples" comparison when looking at two investment options over more than one time period. Geometric means will always be slightly smaller than the arithmetic mean, which is a simple average.1

How to Calculate the Geometric Mean

To calculate compounding interest using the geometric mean of an investment's return, an investor needs to first calculate the interest in year one, which is $10,000 multiplied by 10%, or $1,000. In year two, the new principal amount is $11,000, and 10% of $11,000 is $1,100. The new principal amount is now $11,000 plus $1,100, or $12,100.

In year three, the new principal amount is $12,100, and 10% of $12,100 is $1,210. At the end of 25 years, the $10,000 turns into $108,347.06, which is $98,347.05 more than the original investment. The shortcut is to multiply the current principal by one plus the interest rate, and then raise the factor to the number of years compounded. The calculation is $10,000 × (1+0.1) 25 = $108,347.06.

Example of Geometric Mean

If you have $10,000 and get paid 10% interest on that $10,000 every year for 25 years, the amount of interest is $1,000 every year for 25 years, or $25,000. However, this does not take the interest into consideration. That is, the calculation assumes you only get paid interest on the original $10,000, not the $1,000 added to it every year. If the investor gets paid interest on the interest, it is referred to as compounding interest, which is calculated using the geometric mean.

Using the geometric mean allows analysts to calculate the return on an investment that gets paid interest on interest. This is one reason portfolio managers advise clients to reinvest dividends and earnings.

The geometric mean is also used for present value and future value cash flow formulas. The geometric mean return is specifically used for investments that offer a compounding return. Going back to the example above, instead of only making $25,000 on a simple interest investment, the investor makes $108,347.06 on a compounding interest investment.

Simple interest or return is represented by the arithmetic mean, while compounding interest or return is represented by the geometric mean.

How Do You Find the Geometric Mean in Excel?

The shortcut to calculating the geometric mean in Excel is “=GEOMEAN.” Specifically, enter the function into a cell and then list the numbers (or cells containing the numbers) that you would like to calculate the geometric mean for. 

Can You Calculate Geometric Mean With Negative Values?

You cannot—it is impossible to calculate a geometric mean that includes negative numbers.

How Do You Find the Geometric Mean Between Two Numbers?

To calculate the geometric mean of two numbers, you would multiply the numbers together and take the square root of the result.

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The dividend yield, expressed as a percentage, is a financial ratio (dividend/price) that shows how much a company pays out in dividends each year relative to its stock price.

The reciprocal of the dividend yield is the price/dividend ratio.

KEY TAKEAWAYS

• The dividend yield—displayed as a percentage—is the amount of money a company pays shareholders for owning a share of its stock divided by its current stock price.

• Mature companies are the most likely to pay dividends.

• Companies in the utility and consumer staple industries often having higher dividend yields. 

• Real estate investment trusts (REITs), master limited partnerships (MLPs), and business development companies (BDCs) pay higher than average dividends; however, the dividends from these companies are taxed at a higher rate. 

• It's important for investors to keep in mind that higher dividend yields do not always indicate attractive investment opportunities because the dividend yield of a stock may be elevated as the result of a declining stock price.

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Introduction To Dividend Yields

Understanding the Dividend Yield

The dividend yield is an estimate of the dividend-only return of a stock investment. Assuming the dividend is not raised or lowered, the yield will rise when the price of the stock falls. And conversely, it will fall when the price of the stock rises. Because dividend yields change relative to the stock price, it can often look unusually high for stocks that are falling in value quickly.

New companies that are relatively small, but still growing quickly, may pay a lower average dividend than mature companies in the same sectors. In general, mature companies that aren't growing very quickly pay the highest dividend yields. Consumer non-cyclical stocks that market staple items or utilities are examples of entire sectors that pay the highest average yield.

Although the dividend yield among technology stocks is lower than average, the same general rule that applies to mature companies also applies to the technology sector. For example, as of June 2021, Qualcomm Incorporated (QCOM), an established telecommunications equipment manufacturer, had a trailing twelve months (TTM) dividend of $2.63.1 Using its current price of $144.41 on August 17, 2021, its dividend yield would be 1.82%.2 Meanwhile, Square, Inc. (SQ), a relatively newer mobile payments processor, pays no dividends at all.3

In some cases, the dividend yield may not provide that much information about what kind of dividend the company pays. For example, the average dividend yield in the market is very high amongst real estate investment trusts (REITs). However, those are the yields from ordinary dividends, which are different than qualified dividends in that the former is taxed as regular income while the latter is taxed as capital gains.4

Along with REITs, master limited partnerships (MLPs) and business development companies (BDCs) typically have very high dividend yields. The structure of these companies is such that the U.S. Treasury requires them to pass on the majority of their income to their shareholders.56 This is referred to as a "pass-through" process, and it means that the company doesn't have to pay income taxes on profits that it distributes as dividends. However, the shareholder has to treat the dividend payments as ordinary income and pay taxes on them. Dividends from these types of companies (MLPs and BDCs) do not qualify for capital gains tax treatment.78

While the higher tax liability on dividends from ordinary companies lowers the effective yield the investor has earned, even when adjusted for taxes, REITs, MLPs, and BDCs still pay dividends with a higher-than-average yield.

Calculating the Dividend Yield

The formula for dividend yield is as follows:

How to calculate dividend yield. Investopedia 

The dividend yield can be calculated from the last full year's financial report. This is acceptable during the first few months after the company has released its annual report; however, the longer it has been since the annual report, the less relevant that data is for investors. Alternatively, investors can also add the last four quarters of dividends, which captures the trailing 12 months of dividend data. Using a trailing dividend number is acceptable, but it can make the yield too high or too low if the dividend has recently been cut or raised.

Because dividends are paid quarterly, many investors will take the last quarterly dividend, multiply it by four, and use the product as the annual dividend for the yield calculation. This approach will reflect any recent changes in the dividend, but not all companies pay an even quarterly dividend. Some firms, especially outside the U.S., pay a small quarterly dividend with a large annual dividend. If the dividend calculation is performed after the large dividend distribution, it will give an inflated yield.

Finally, some companies pay a dividend more frequently than quarterly. A monthly dividend could result in a dividend yield calculation that is too low. When deciding how to calculate the dividend yield, an investor should look at the history of dividend payments to decide which method will give the most accurate results.

Advantages of Dividend Yields

Historical evidence suggests that a focus on dividends may amplify returns rather than slow them down. For example, according to analysts at Hartford Funds, since 1970, 84% of the total returns from the S&P 500 are from dividends. This assumption is based on the fact that investors are likely to reinvest their dividends back into the S&P 500, which then compounds their ability to earn more dividends in the future.9

For example, suppose an investor buys $10,000 worth of a stock with a dividend yield of 4% at a rate of a $100 share price. This investor owns 100 shares that all pay a dividend of $4 per share (100 x $4 = $400 total). Assume that the investor uses the $400 in dividends to purchase four more shares. The price would be adjusted on the ex-dividend date by $4 per share to $96 per share. Reinvesting would purchase 4.16 shares; dividend reinvestment programs allow for fractional share purchases. If nothing else changes, the next year the investor will have 104.16 shares worth $10,416. This amount can be reinvested into more shares once a dividend is declared, thus compounding gains similar to a savings account.

Disadvantages of Dividend Yields

While high dividend yields are attractive, it's possible they may be at the expense of the potential growth of the company. It can be assumed that every dollar a company is paying in dividends to its shareholders is a dollar that the company is not reinvesting to grow and generate more capital gains. Even without earning any dividends, shareholders have the potential to earn higher returns if the value of their stock increases while they hold it as a result of company growth.

It's not recommended that investors evaluate a stock based on its dividend yield alone. Dividend data can be old or based on erroneous information. Many companies have a very high yield as their stock is falling. If a company's stock experiences enough of a decline, they may reduce the amount of their dividend, or eliminate it altogether.

Investors should exercise caution when evaluating a company that looks distressed and has a higher-than-average dividend yield. Because the stock's price is the denominator of the dividend yield equation, a strong downtrend can increase the quotient of the calculation dramatically.

For example, General Electric Company's (GE) manufacturing and energy divisions began underperforming from 2015 through 2018, and the stock's price fell as earnings declined. The dividend yield jumped from 3% to more than 5% as the price dropped.10 As you can see in the following chart, the decline in the share price and eventual cut to the dividend offset any benefit of the high dividend yield.

Dividend Yield vs. Dividend Payout Ratio

When comparing measures of corporate dividends, it's important to note that the dividend yield tells you what the simple rate of return is in the form of cash dividends to shareholders. However, the dividend payout ratio represents how much of a company's net earnings are paid out as dividends. While the dividend yield is the more commonly used term, many believe the dividend payout ratio is a better indicator of a company's ability to distribute dividends consistently in the future. The dividend payout ratio is highly connected to a company's cash flow.

The dividend yield shows how much a company has paid out in dividends over the course of a year. The yield is presented as a percentage, not as an actual dollar amount. This makes it easier to see how much return the shareholder can expect to receive per dollar they have invested.

What if you had started investing years ago?

Find out what a hypothetical investment would be worth today.

SELECT A STOCK

TSLA

TESLA INC

AAPL

APPLE INC

COKE

COCA-COLA CONSOLIDATED INC

AMZN

AMAZON.COM, INC

WMT

WALMART INC

SELECT INVESTMENT AMOUNT

$

SELECT A PURCHASE DATE

              2 years ago                      5 years ago                      10 years ago         

CALCULATE

Example of Dividend Yield

Suppose Company A’s stock is trading at $20 and pays annual dividends of $1 per share to its shareholders. Suppose that Company B's stock is trading at $40 and also pays an annual dividend of $1 per share. 

This means Company A's dividend yield is 5% ($1 / $20), while Company B's dividend yield is only 2.5% ($1 / $40). Assuming all other factors are equivalent, an investor looking to use their portfolio to supplement their income would likely prefer Company A over Company B because it has double the dividend yield.

What Does the Dividend Yield Tell You?

The dividend yield is a financial ratio that tells you the percentage of a company’s share price that it pays out in dividends each year. For example, if a company has a $20 share price and pays a dividend of $1 per year, its dividend yield would be 5%. If a company’s dividend yield has been steadily increasing, this could be because they are increasing their dividend, because their share price is declining, or both. Depending on the circumstances, this may be seen as either a positive or a negative sign by investors.

Is a High Dividend Yield Good?

Yield-oriented investors will generally look for companies that offer high dividend yields, but it is important to dig deeper in order to understand the circumstances leading to the high yield. One approach taken by investors is to focus on companies that have a long track record of maintaining or raising their dividends, while also verifying that those companies have the underlying financial strength to continue paying dividends well into the future. To do so, investors can refer to other metrics such as the current ratio and the dividend payout ratio.

Why Is Dividend Yield Important?

Some investors, such as retirees, are heavily reliant on dividends for their income. For these investors, the dividend yield of their portfolio could have a meaningful effect on their personal finances, making it very important for these investors to select dividend-paying companies with long track records and clear financial strength. For other investors, dividend yield may be less significant, such as for younger investors who are more interested in growth companies that can retain their earnings and use them to finance their growth.

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Berkshire Hathaway is a holding company for a multitude of businesses, including GEICO and Fruit of the Loom. It's run by chair and CEO Warren Buffett. Berkshire Hathaway is headquartered in Omaha, Nebraska. Originally, it was a company comprised of a group of textile milling plants.

Buffett assumed control of the struggling New England company in 1965. Since that time, Berkshire has grown to be one of the largest companies in the world, based on market capitalization.

KEY TAKEAWAYS

• Berkshire Hathaway is a massive holding company that's been run by famed value investor Warren Buffett since the 1960s.

• Berkshire Hathaway has a market capitalization of close to $700 billion.

• Its class A shares (BRK.A) are among the most expensive in the stock market.

• It owns a variety of well-known private businesses and significant minority interests in public companies, such as Apple.

• Greg Abel is the heir apparent to Berkshire CEO Warren Buffett who, in his nineties, has yet to announce any plans to step down.

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How Warren Buffett Made Berkshire a Winner

Understanding Berkshire Hathaway

Warren Buffett became the controlling shareholder of Berkshire Hathaway in the mid-1960s and began a progressive strategy of diverting cash flows from the core business into other investments. As of May 2022, Berkshire Hathaway had a market capitalization of close to $700 billion, making it one of the largest publicly traded companies worldwide.1

Berkshire Hathaway has a long history of operating success and smart investments. The company currently is the seventh-largest public company in the world in terms of market capitalization.1 Berkshire's stock trades on the New York Stock Exchange as two classes—A shares and B shares. Class A shares closed at $471,670 per share on May 17, 2022.2

3,641,613%

The overall return of Berkshire Hathaway’s stock from 1965 to 2021. During this same period, the S&P 500 returned 30,209%.3

Insurance subsidiaries represent a large part of Berkshire Hathaway's holdings. However, the company also manages hundreds of diverse businesses all over the world. These include Duracell, International Dairy Queen, Pampered Chef, Fruit of the Loom, NetJets, and GEICO, among others.4

In addition to owning private companies, Berkshire also has a large investment portfolio of stocks in major public companies, such as Apple (AAPL), Bank of America (BAC), and United Parcel Service (UPS).5 As of the first quarter of 2022, Berkshire's public market equity portfolio was valued at more than $363 billion.6

Early in his career, Buffett came across the novel idea to use the float from his insurance subsidiaries to invest elsewhere. He focused on selecting stock that would be held for the long term.

Buffett has long eschewed a diversified stock portfolio in favor of trusted investments that would be over-weighted in order to leverage the anticipated return. Over time, Buffett’s investing prowess became so renowned that Berkshire Hathaway's annual shareholder meetings are now a mecca for value investing proponents. They're also the target of intense media scrutiny.

Special Considerations

From 1965 to 2021, the compounded annual gain of Berkshire Hathaway’s stock was just shy of twice that of the S&P 500 index. Berkshire’s stock generated an annualized 20.1% over that period, while the S&P 500’s annualized gain was 10.5%.3

Succession has always been a hot topic for Berkshire. The big question is whether Buffett’s replacement can continue the streak of outperforming the market. This becomes even more pressing when you consider that Buffett turned 91 years old in August of 2021.

In 2010, Buffett announced that he would be succeeded at Berkshire Hathaway by a team comprised of one CEO and two to four investment managers.

In 2011, it was announced that hedge fund managers Todd Combs and Ted Weschler would be two of those managers. In 2018, the company put Ajit Jain in charge of all of the insurance operations and made Greg Abel the manager of all other (noninsurance) operations. Both men seemed likely candidates for Buffett's heir apparent.

Buffet has not announced any retirement plans. Still, it's good that the question of succession has been answered, considering the advanced age of the Oracle of Omaha.

On May 1, 2021, vice chair of Berkshire Hathaway, Charlie Munger, unofficially announced that Warren Buffett would be succeeded as CEO by Greg Abel when Buffett eventually steps down. Abel's official title is CEO of Berkshire Hathaway Energy and vice chair in charge of noninsurance operations.

Who Is Warren Buffett?

Warren Buffett is a well-known business owner and investor. He's renowned not only for the jaw-dropping success of Berkshire Hathaway, the holding company of which he's been in charge since 1964. Buffett is also celebrated for his winning approach to investing, which has created great wealth for many shareholders. His frugal lifestyle, despite being one of the world's wealthiest individuals, and his easy-going manner have earned him fans across the globe.

What Is Value Investing?

Value investing refers to investing in a security with an intrinsic value that's greater than its market value. The idea is that the undervalued security's market value should increase to meet its intrinsic value. Warren Buffett is one example of an investor whose focus on value investing has led to incredible success.

What Is a Class A Share?

Class A shares of common stock usually give shareholders a greater amount of voting rights than Class B and other classes of stock. They're often held by a company's executives and some members of management so that those in charge of the company can retain control of it in various situations, such as a hostile takeover attempt.

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