目前已经有好几个扩展解决方案被实际采用，但ZK-Rollup（Zero-Knowledge Rollup）技术始终被视为是扩容解决方案的最佳解答，原因究竟为何呢？

以太坊可扩展性问题

高昂的gasfees已经成为以太坊的主要问题，由于交易费用是以ETH支付，当资产价格上涨时，使用网络的成本也随之上升，ETH今年上涨了460%，这意味著以美元计算的交易成本也增加了460%。

另外，交易费用也取决于网络拥堵程度，由于目前的链上应用项目对以太坊区块空间有著极大的需求，但是区块空间是有限的，导致其网络很容易变得拥挤，使交易确认速度变慢及gasfee变高。

使用网络的高成本成为用户参与DeFi（去中心化金融）和NFT的阻碍，甚至失去参与DAO的机会，许多加密货币爱好者已经迁移到其他第一层区块链上，如Solana（SOL）和Avalanche（AVAX）。

网络

在过去的几年里，几个扩展解决方案已经被开发出来，以帮助缓解以太坊的网络拥堵及交易成本问题。

Polygon在2019年推出，可以说是第一个获得巨大吸引力的以太坊扩容解决方案，该网络使用一个名为Plasma的扩容方案。

它将交易从主要的以太坊区块链转移到一个专用的侧链，许多以太坊原生的DeFi应用已经在Polygon上推出，如Curve（CRV）和Aave（AAVE）。

虽然Polygon网络透过低交易成本成功吸引用户使用，但它常被质疑安全性和中心化问题，而被认为不是一个真正的扩展解决方案。

该网络使用其自身的节点验证者管理PoS共识机制，这意味著它不使用以太坊主网来验证交易。

根据截稿前的Polygonscan的数据，只有100个验证者管理Polygon网络，最大的验证节点地址占其整体网络验证区块的27%以上。

网络

Rollup扩展解決方案

网络

近期Rollup扩展解决方案在以太坊社群引起了一阵热议，Rollup方案顾名思义就是一种将计算数据“打包”并将有效性证明（Validity Proof）送回以太坊主网的方式。

这种做法可节省区块空间，进一步减少提交给主网的数据量，由于交易被捆绑在一起，Gasfee就能让许多用户分摊。

Rollup为用户提供了近乎即时的交易速度，可以将费用减少50到200倍，同时保持以太坊主网的安全性和去中心化。

目前Rollup方案的两种类型分别为：

Optimistic Rollup和Zero-Knowledge Rollup（ZK-Rollup）。

什麽是Optimistic Rollup？

网络

Optimistic Rollup方案假设发回主链的交易是合法的，只有当验证人能够透过提交诈欺证明（Fraud Proof）来证明交易是诈骗性的，交易才会被拒绝。

换句话说，Optimistic Rollups采取“在证明有罪之前是无罪的”的方法来验证交易。

目前Optimistic Rollup已经能看到实际采用情形，部分原因是开发者在该网络上开发应用程式较容易。

Optimistic Rollup可以直接支援完整的智能合约功能，开发人员可以使用以太坊的程式语言Solidity编写应用程式。

根据L2beat的数据显示，目前最大的Optimistic Rollup网络Arbitrum已经在DeFi应用当中吸引了超过25亿美元的总锁仓价值（TVL），它承载了以太坊上许多受欢迎的DeFi应用。

然而，由于Optimistic Rollup验证交易的方法，它们面临一些挑战，传送回以太坊主网的资金要经历长达一周的挑战期（Dispute Time Delay），这给用户带来了不便，并破坏了可组合性。

网络

虽然Optimistic Rollups已经改进了基于Plasma的解决方案。

如Polygon，但他们通常被认为是不如ZK-Rollups的，Optimistic Rollups提供高达77倍的可扩展性提升，而ZK-Rollups提供了高达500倍的提升，并且无挑战期。

什么是ZK-Rollup？

网络

ZK-Rollup方案在交易打包至主网时产生加密证明以证明交易是合法的，只有在加密证明被验证后，交易才会在以太坊上被接受，与Optimistic Rollup不同，ZK-Rollup采取了“在证明无罪之前有罪的”的验证方式。

然而，ZK-Rollup还没有达到与Optimistic Rollup同类产品相同的兼容性水平，因为ZK-Rollup在每笔交易中要伴随著有效性证明。

所以它们在技术发展上更难，目前ZK-Rollup的开发上已经能执行一些简单的任务，例如直接转帐和交易，虽然整合智能合约功能是有可能的，但比Optimistic Rollup更加困难。

就在今年，以太坊联合创始人Vitalik Buterin预测，开发完全可组合的ZK-Rollup将需要几年时间。

然而，开发人员已经提前完成了计划，几个ZK-Rollups项目正在准备部署解决方案，这些解决方案是兼具可组合性和互操作性，甚至能让多个Rollups互通。

ZK-Rollups的发展将允许以太坊主网和多个第2层网络之间共享通讯框架，网络可以共享流动性并克服第1层区块链面临的最大的采用挑战。

基于ZK-Rollup的网络将不需要为了让去中心化交易所上拥有高效率交易而争夺流动性，而是能够以合作的方式扩展以太坊。

ZK-Rollup还具有另一个独特的功能，越多人交易会使交易费用变得更便宜，发送一个批次的费用不会有太大的变化。

随著更多的交易被打包在一个批次中，交易成本可以在更多的用户中分摊，ZK-Rollups可以打包几乎无限量的交易。

因此当有足够的用户时，交易的gasfee可以减少到只要几分钱，这个功能被称为“有效性证明摊销（Validity Proof Amortization）”。

虽然以太坊仍然面临著可扩展性问题，但一些开发者已经在部署第二层ZK-Rollup网络，承诺在智能合约、其他第二层解决方案和以太坊虚拟机之间实现完全可组合性和兼容性。

ZK-Rollup的类型

网络

目前有两种不同类型的ZK-Rollup被用于以太坊的扩展解决方案中，第一种是最被广泛使用的类型ZK-SNARKs，全名为简洁的非交互式知识论证（Succinctnon-interactive arguments of knowledge），也是第一个被发现的零知识证明类型。

专注于隐私保护的区块链项目Zcash（ZEC）早在2016年就采用ZK-SNARKs，该技术构成了ZK-Rollup大部分开发者的资料库和代码，并被认为是以太坊扩展项目的一个强有力的选择。

但SNARKs有一个缺陷，它们需要一个初始创建事件的密钥，这些密钥用于创建交易所需的证明，如果可信设置事件中的密钥没有被销毁，它们可以被用来凭空创造新的代币或伪造交易。

目前备受瞩目的SNARK扩展解决方案是Matter Lab的zkSync，该项目于2020年6月启动。

在其目前的迭代中宣称每秒可处理2000笔交易，并希望在未来实现更高的吞吐量，该平台开始致力于在兼容EVM的环境中部署智能合约，推出了zkEVM测试网。

zkSync目前著重于让Ethereum主网的过渡尽可能容易，那些想在zkEVM上开发的人可以使用以太坊语言Solidity编写智能合约。

Matter Labs最近在a16z领投的B轮融资中筹集了5000万美元，以帮助zkSync的发展，此外，该公司已与几个以太坊DeFi应用合作，如Curve、Aave和1inch。

另一种ZK-Rollup方案为STARKs，全名为可扩展的透明知识论证（Scalable transparent arguments of knowledge），STARKs比SNARKs更有优势。

因为STARKs完全依赖哈希函数，不需要可信的设置，这意味着STARKs在理论上比SNARKs更安全。

StarkWare是第一家使用STARKs来扩展以太坊的公司，是目前开发基于STARK技术的主要推动者。

该公司的两位联合创始人EliBen-Sasson和Michael Riabzev共同发明了这项技术。

StarkWare为基于STARK的ZK-Rollups创造了一种图灵完备的编程语言，称为Cairo，“StarkEx协议”是以Cairo语言创造的第一个产品。

StarkEx是一种针对特定应用的扩展解决方案，目前正被几个以太坊项目使用，包括dYdX、ImmutableX、Sorare和DeversiFi。

StarkWare即将发布的StarkNet是一个无权限的ZK-Rollup网络，可以让开发者直接在第二层建构并启动应用程式。

StarkNet的目标是成为一个真正去中心化的多应用扩展解决方案。

网络

ZK-Rollup即将改变加密货币社群使用以太坊的方式，随著zkSync和StarkNet等高速、低成本网络的实现。

更多以太坊主网上的交易将被外包至第二层，这应该会让以太坊更接近其成为一个可扩展、安全和去中心化的区块链网络的愿景。

随着网络的不断升级，我们认为网络计算和收取费用的方式也相应地更新。我们在这里提出了一个初步的费用计算和收费方法，目的是随着 StarkNet 的发展对其进行完善。了解这些参数有助于构建者在设计他们的 StarkNet dApp 时更好地进行规划。

StarkNet 的交易成本

通常来说，一笔交易的成本由几个因素决定：

1. 数据 —— 发送至 L1 的数据量：

   1.1 状态差异信息

   1.2 L2 → L1 信息的数量

   1.3 已消耗的 L1 → L2 信息

   这些数据都会在不同的 StarkNet L1 交易中以 call data 的形式发送到 L1。

2. 计算成本 —— 这是针对跟踪步骤 (trace steps) 的计费，包括操作系统 (OS) 步骤 (如系统调用)。包括：

   • L1 证明验证

   • L2 计算成本 (SHARP)

3. 存储成本：在交易执行期间需要进行多少读/写操作。

4. 交易的 L2 网络传输成本：它的调用数据和发出的事件。

目前的费用机制

概括来讲，目前的解决方案是让用户/应用程序使用定序者 (Sequencer) 来估算接受 “交易” 所需要花费的成本：

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用户要求一个新的服务 ("gas 估算服务，estimate gas service") 来估算在当前状态下运行给定 “交易” 所需的费用。该服务根据下文中的公式进行估算。这项服务由 Sequencer 公开。在内部，它将尝试根据当前的 StarkNet 状态估算处理该交易所消耗的资源。

正如下文所解释的，这个估算值将是交易成本的首个粗略的近似值。费用本身将以 ETH (支付货币) 来指定，而 gas 价格作为估算服务的参数提供。

在这一点上，用户可以选择是否接受所估算的费用，或标记更高/更低的费用。然后，用户确定其愿意支付的费用并进行签名，这个签名也作为交易的一部分被发送到 Sequencer 中，以便执行这笔交易并添加到未来的区块中。

成本公式

对于费用的首个近似值，我们考虑了服务提供商 (sequencer 定序者 + prover 证明者) 支付的一些外部成本，如用于数据和计算的 L1 gas (上述的第 1 和 2.1 项)。计算的费用可能包括一个加价，以补偿 L1 gas 成本的波动。在这一点上，我们忽略了证明创建、存储操作和网络的 L2 成本 (上述的第 2.2、3、4 项)。

因此，在这个阶段，计算费用的公式将是：

其中:

1. gas_price 是服务中配置的 gas 价格，每 gas 单位使用多少 ETH。这个价格以后可以通过 API 查询。

2. gas_per_byte 是存储调用数据时单个字节的 gas 成本，目前为每个字节 16 gas。

3. ♯(msgs) 是交易从 L2 到 L1 发送的信息数量。

4. bytes_per_msg 是消息的字节数。当然，每个消息的字节数都可以不同，所以我们可以使用所有消息的平均消息字节大小。

   额外的 5000 gas 是用来更新一个内部计数器的。

5. ♯(state_dif f_items) 是该交易所做的状态差异的数量。

   2⋅31 分别代表每次存储写入时需写入两个字段元素，每个字段元素由 31 个字节组成。

6. gas_per_step 是 (L1 上) 单步验证的一个常数定价。

   stepstxn 是该函数执行的步骤数。

注意：该交易费成本的大头在于 L1 数据部分。这包括状态差异和消息。换句话说，与在 L1 上发布数据的成本相比，计算成本可以忽略不计。 (gas_per_step << gas_per_byte)

未来的计划

这个机制在未来可能会有几种变化。

首先，我们希望进行一些优化以减少成本。具体来说，当几笔交易共享相同的证明时，它们也共享一些开销，因此会降低生产区块和验证的成本。在这种情况下，可以对原始交易的估算费用进行一些削减。

引入 volition 用于数据可用性 (即链下数据可用性)，从而可以提供另一个节约成本的方式，我们希望将其纳入成本估算的因素。为基于 L2 的数据所做的存储修改可能会产生不同的成本。

当网络变得去中心化时，我们会采用其他机制和市场设计，其中细节目前正在研究中。一个例子是使用 “费用拍卖” 模式 —— 用户可以使用不同成本组成的某种线性组合进行付费，并允许 sequencer 挑选付费最高的交易。

最后，引入费用抽象将允许网络参与者使用 ETH 以外的代币进行付费。

ECN的翻译工作旨在为中国以太坊社区传递优质资讯和学习资源，文章版权归原作者所有，转载须注明原文出处以及ethereum.cn，若需长期转载，请联系eth@ecn.co进行授权。

But why is Starknet for gaming when other L2s are available? State Channel (Ex- Celer Network) allows two or more parties to conduct multiple transactions off-chain, without the need for each transaction to be broadcast to the entire network but the adoption curve is very poor. Plasma (Ex – Polygon) allows specific assets to be transferred between the Ethereum mainnet and the sidechin but the mainchain does not secure such a sidechain. Optimistic Rollups (Ex - Arbitrum and Optimism) are adaptive but the withdrawal of funds takes up to 7 days. zkRollups (Ex - zkSync) generalizes computation with zero-knowledge and provides instant withdrawal while being quite fast and secure but the use case is limited to DEXs.

Starknet powered by Validium technology is more promising as it is a hybrid of State Channel, Plasma & zkRollup. It is fast, secure and provides a better user experience. The usage of ‘zero-knowledge’ eliminates the chances of cheating by bad actors and makes the protocol highly decentralized. It is also engineered for scalability, ensuring that it can accommodate exponential growth without sacrificing security and decentralization. STARKS rely on minimal, time-tested cryptographic assumptions, provides quantum security and eliminates the need for a trusted setup. The potential of trustless Web3 gaming can be captured with ease on Starknet.

Cairo, the programming language for blockchain developers to build applications on the StarkNet, is the first Turing-complete language for creating provable programs for general computation. It is optimal for harnessing the benefits of algebraic proof systems and ensuring efficient computation and verification processes. The best thing about Starknet is that it is designed to be future-proof. This Starknet roadmap of 2023 describes how the upcoming Starknet v0.12.0 will incorporate significant improvements in throughput and latency and in v0.13.0, the transaction costs will be reduced dramatically. All these will be beneficial for gaming DAPPs.

Ethereum’s EIP-4844 (Shard Blob Transaction) is expected in Q4 of 2023. Starknet will get tremendous benefits from it as soon as possible, in addition to the introduction of Volition (off-chain data availability). There will be a dramatic reduction in the cost of data. Volition will allow developers to build Starknet applications with a hybrid Data Availability (DA) mode: both on-chain and off-chain data. In Starknet v0.15.0, proof will attest to the integrity of one or more Starknet blocks. This will fix the block interval, and improve Starknet’s UX. Gaming is a computation-heavy exercise and the users expect a good experience. The Web2 gaming DAPPs just need to get their blockchain moments to be onboarded into Web3 and only Starknet can help them to shine.

Capital is a broad term that can describe anything that confers value or benefit to its owners, such as a factory and its machinery, intellectual property like patents, or the financial assets of a business or an individual. While money itself may be construed as capital, capital is more often associated with cash that is being put to work for productive or investment purposes.

In general, capital is a critical component of running a business from day to day and financing its future growth. Business capital may derive from the operations of the business or be raised from debt or equity financing. When budgeting, businesses of all kinds typically focus on three types of capital: working capital, equity capital, and debt capital. A business in the financial industry identifies trading capital as a fourth component.

KEY TAKEAWAYS

• The capital of a business is the money it has available to pay for its day-to-day operations and to fund its future growth.

• The four major types of capital include working capital, debt, equity, and trading capital. Trading capital is used by brokerages and other financial institutions.

• Any debt capital is offset by a debt liability on the balance sheet.

• The capital structure of a company determines what mix of these types of capital it uses to fund its business.

• Economists look at the capital of a family, a business, or an entire economy to evaluate how efficiently it is using its resources.

Capital

Understanding Capital

From the economists' perspective, capital is key to the functioning of any unit, whether that unit is a family, a small business, a large corporation, or an entire economy.

Capital assets can be found on either the current or long-term portion of the balance sheet. These assets may include cash, cash equivalents, and marketable securities as well as manufacturing equipment, production facilities, and storage facilities.

In the broadest sense, capital can be a measurement of wealth and a resource for increasing wealth. Individuals hold capital and capital assets as part of their net worth. Companies have capital structures that define the mix of debt capital, equity capital, and working capital for daily expenditures that they use.

Capital is typically cash or liquid assets being held or obtained for expenditures. In a broader sense, the term may be expanded to include all of a company’s assets that have monetary value, such as its equipment, real estate, and inventory. But when it comes to budgeting, capital is cash flow.

In general, capital can be a measurement of wealth and also a resource that provides for increasing wealth through direct investment or capital project investments. Individuals hold capital and capital assets as part of their net worth. Companies have capital structures that include debt capital, equity capital, and working capital for daily expenditures.

How individuals and companies finance their working capital and invest their obtained capital is critical for their prosperity.

A 10-K is a comprehensive report filed annually by a publicly-traded company about its financial performance and is required by the U.S. Securities and Exchange Commission (SEC). The report contains much more detail than a company's annual report, which is sent to its shareholders before an annual meeting to elect company directors.1

Some of the information a company is required to document in the 10-K includes its history, organizational structure, financial statements, earnings per share, subsidiaries, executive compensation, and any other relevant data.2

The SEC requires this report to keep investors aware of a company's financial condition and to allow them to have enough information before they buy or sell shares in the corporation, or before investing in the firm’s corporate bonds.2

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10-K

Understanding 10-Ks

Because of the depth and nature of the information they contain, 10-Ks are fairly long and tend to be complicated. But investors need to understand that this is one of the most comprehensive and most important documents a public company can publish on a yearly basis. The more information they can gather from the 10-K, the more they can understand the company.

The government requires companies to publish 10-K forms so investors have fundamental information about companies so they can make informed investment decisions. This form gives a clearer picture of everything a company does and what kinds of risks it faces.

Investors in the know are aware that 10-Ks can also be retrieved by using the company search function through the SEC's EDGAR database.3

The 10-K includes five distinct sections:

• Business. This provides an overview of the company’s main operations, including its products and services (i.e., how it makes money).

• Risk factors. These outline any and all risks the company faces or may face in the future. The risks are typically listed in order of importance.

• Selected financial data. This section details specific financial information about the company over the last five years. This section presents more of a near-term view of the company’s recent performance.

• Management’s discussion and analysis of financial condition and results of operations. Also known as MD&A, this gives the company an opportunity to explain its business results from the previous fiscal year. This section is where the company can tell its story in its own words.

• Financial statements and supplementary data. This includes the company’s audited financial statements including the income statement, balance sheets, and statement of cash flows. A letter from the company’s independent auditor certifying the scope of their review is also included in this section.4

A 10-K filing also includes signed letters from the company’s chief executive officer and chief financial officer. In it, the executives swear under oath that the information included in the 10-K is accurate.2 These letters became a requirement after several high-profile cases involving accounting fraud following the dot-com bust.5

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

NKE

NIKE 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

Where to Find a 10-K

Notably, 10-K filings are public information and readily available through a number of sources. In fact, the vast majority of companies include them in the Investor Relations section of their website. The information included in a 10-K can be difficult to move through, but the more familiar investors become with the layout and the type of information included, it will likely become easier to identify the most important details.

The January Effect is a perceived seasonal increase in stock prices during the month of January. Analysts generally attribute this rally to an increase in buying, which follows the drop in price that typically happens in December when investors, engaging in tax-loss harvesting to offset realized capital gains, prompt a sell-off.

Another possible explanation is that investors use year-end cash bonuses to purchase investments the following month. While this market anomaly has been identified in the past, the January effect seems to have largely disappeared as its presence became known.

KEY TAKEAWAYS

• The January Effect is the perceived seasonal tendency for stocks to rise in that month.

• Since 1938, 29 out of 30 years of gains seen in January-February resulted in average yearly S&P 500 advances of 20%.1

• The January Effect is theorized to occur when investors sell winners to incur year-end capital gains taxes in December and use those funds to speculate on weaker performers.

• Like other market anomalies and calendar effects, the January Effect is considered by some to be evidence against the efficient markets hypothesis.

Understanding the January Effect

The January Effect is a hypothesis, and like all calendar-related effects, suggests that the markets as a whole are inefficient, as efficient markets would naturally make this effect non-existent. The January Effect seems to affect small caps more than mid or large caps because they are less liquid.

Since the beginning of the 20th century, the data suggests that these asset classes have outperformed the overall market in January, especially toward the middle of the month. Investment banker Sidney Wachtel first noticed this effect in 1942.2 This historical trend, however, has been less pronounced in recent years because the markets seem to have adjusted for it.

Another reason analysts consider the January Effect less important as of 2021 is that more people are using tax-sheltered retirement plans and therefore have no reason to sell at the end of the year for a tax loss.

January Effect Explanations

Beyond tax-loss harvesting and repurchases, as well as investors putting cash bonuses into the market, another explanation for the January Effect has to do with investor psychology. Some investors believe that January is the best month to begin an investment program or perhaps are following through on a New Year's resolution to begin investing for the future.

Others have pontificated that mutual fund managers purchase stocks of top performers at the end of the year and eliminate questionable losers for appearance sake in their year-end reports, an activity known as "window dressing." This is unlikely, however, as the buying and selling would primarily affect large caps.

Year-end sell-offs also attract buyers interested in the lower prices, knowing the dips are not based on company fundamentals. On a large scale, this can drive prices higher in January.

Studies and Criticism

An ex-Director from the Vanguard Group, Burton Malkiel, the author of A Random Walk Down Wall Street, has criticized the January Effect, stating that seasonal anomalies such as it don't provide investors with any reliable opportunities. He also suggests that the January Effect is so small that the transaction costs needed to exploit it essentially make it unprofitable. It's also been suggested that too many people now time for the January Effect so that it becomes priced into the market, nullifying it all together.3

Other researchers have found that January Effect still exists, but only for smaller-cap stocks, owing to a lack of liquidity and interest from investors.4

What Is the January Effect in the Stock Market?

The January Effect is a purported market anomaly whereby stock prices tend to regularly rise in the first month of the year. Actual evidence of the January Effect is small, with many scholars arguing that it does not really exist.

Can You Make Money Exploiting the January Effect?

Unlikely. Even if the January Effect were real (it's probably not) and markets were to rise uncharacteristically each January, the fact that people may try to exploit can undermine its fruition.

Gamma is the rate of change in an option's delta per 1-point move in the underlying asset's price. Gamma is an important measure of the convexity of a derivative's value, in relation to the underlying. A delta hedge strategy seeks to reduce gamma in order to maintain a hedge over a wider price range. A consequence of reducing gamma, however, is that alpha will also be reduced.

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Gamma

Basics of Gamma

Gamma is the first derivative of delta and is used when trying to gauge the price movement of an option, relative to the amount it is in or out of the money. In that same regard, gamma is the second derivative of an option's price with respect to the underlying's price. When the option being measured is deep in or out-of-the-money, gamma is small. When the option is near or at the money, gamma is at its largest. All options that are a long position have a positive gamma, while all short options have a negative gamma.

Gamma Behavior

Since an option's delta measure is only valid for short period of time, gamma gives traders a more precise picture of how the option's delta will change over time as the underlying price changes. Delta is how much the option price changes in respect to a change in the underlying asset's price.

As an analogy to physics, the delta of an option is its "speed," while the gamma of an option is its "acceleration."

Gamma decreases, approaching zero, as an option gets deeper in the money and delta approaches one. Gamma also approaches zero the deeper an option gets out-of-the-money. Gamma is at its highest when the price is at-the-money.

The calculation of gamma is complex and requires financial software or spreadsheets to find a precise value. However, the following demonstrates an approximate calculation of gamma. Consider a call option on an underlying stock that currently has a delta of 0.4. If the stock value increases by $1, the option will increase in value by $0.40, and its delta will also change. After the $1 increase, assume the option's delta is now 0.53. The 0.13 difference in deltas can be considered an approximate value of gamma.

Gamma is an important metric because it corrects for convexity issues when engaging in hedging strategies. Some portfolio managers or traders may be involved with portfolios of such large values that even more precision is needed when engaged in hedging. A third-order derivative named "color" can be used. Color measures the rate of change of gamma and is important for maintaining a gamma-hedged portfolio.

KEY TAKEAWAYS

• Gamma is the rate of change for an option’s delta based on a single-point move in the delta’s price.

• Gamma is at its highest when an option is at the money, and is at its lowest when it is further away from the money.

Example of Gamma

Suppose a stock is trading at $10 and its option has a delta of 0.5 and a gamma of 0.1. Then, for every 10 percent move in the stock’s price, the delta will be adjusted by a corresponding 10 percent. This means that a $1 increase will mean that the option’s delta will increase to 0.6. Likewise, a 10 percent decrease will result in corresponding decline in delta to 0.4.

The harmonic mean is a type of numerical average. It is calculated by dividing the number of observations by the reciprocal of each number in the series. Thus, the harmonic mean is the reciprocal of the arithmetic mean of the reciprocals.

The harmonic mean of 1, 4, and 4 is: 

\frac{3}{\left(\frac{1}{1}\ +\ \frac{1}{4}\ +\ \frac{1}{4}\right)}\ =\ \frac{3}{1.5}\ =\ 2(11​ + 41​ + 41​)3​ = 1.53​ = 2

The reciprocal of a number n is simply 1 / n.

The Basics of a Harmonic Mean

The harmonic mean helps to find multiplicative or divisor relationships between fractions without worrying about common denominators. Harmonic means are often used in averaging things like rates (e.g., the average travel speed given a duration of several trips).

The weighted harmonic mean is used in finance to average multiples like the price-earnings ratio because it gives equal weight to each data point. Using a weighted arithmetic mean to average these ratios would give greater weight to high data points than low data points because price-earnings ratios aren't price-normalized while the earnings are equalized.

The harmonic mean is the weighted harmonic mean, where the weights are equal to 1. The weighted harmonic mean of x1, x2, x3 with the corresponding weights w1, w2, w3 is given as:

\displaystyle{\frac{\sum^n_{i=1}w_i}{\sum^n_{i=1}\frac{w_i}{x_i}}}∑i=1n​xi​wi​​∑i=1n​wi​​

KEY TAKEAWAYS

• The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals.

• Harmonic means are used in finance to average data like price multiples.

• Harmonic means can also be used by market technicians to identify patterns such as Fibonacci sequences.

Harmonic Mean Versus Arithmetic Mean and Geometric Mean

Other ways to calculate averages include the simple arithmetic mean and the geometric mean. An arithmetic average is the sum of a series of numbers divided by the count of that series of numbers. If you were asked to find the class (arithmetic) average of test scores, you would simply add up all the test scores of the students, and then divide that sum by the number of students. For example, if five students took an exam and their scores were 60%, 70%, 80%, 90%, and 100%, the arithmetic class average would be 80%.

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.

The harmonic mean is best used for fractions such as rates or multiples.

Example of the Harmonic Mean

As an example, take two firms. One has a market capitalization of $100 billion and earnings of $4 billion (P/E of 25) and one with a market capitalization of $1 billion and earnings of $4 million (P/E of 250). In an index made of the two stocks, with 10% invested in the first and 90% invested in the second, the P/E ratio of the index is: 

\begin{aligned}&\text{Using the WAM:\ P/E}\ =\ 0.1 \times25+0.9\times250\ =\ 227.5\\\\&\text{Using the WHM:\ P/E}\ =\ \frac{0.1\ +\ 0.9}{\frac{0.1}{25}\ +\ \frac{0.9}{250}}\ \approx\ 131.6\\&\textbf{where:}\\&\text{WAM}=\text{weighted arithmetic mean}\\&\text{P/E}=\text{price-to-earnings ratio}\\&\text{WHM}=\text{weighted harmonic mean}\end{aligned}​Using the WAM: P/E = 0.1×25+0.9×250 = 227.5Using the WHM: P/E = 250.1​ + 2500.9​0.1 + 0.9​ ≈ 131.6where:WAM=weighted arithmetic meanP/E=price-to-earnings ratioWHM=weighted harmonic mean​

A leverage ratio is any one of several financial measurements that look at how much capital comes in the form of debt (loans) or assesses the ability of a company to meet its financial obligations. The leverage ratio category is important because companies rely on a mixture of equity and debt to finance their operations, and knowing the amount of debt held by a company is useful in evaluating whether it can pay off its debts as they come due. Several common leverage ratios are discussed below.

KEY TAKEAWAYS

• A leverage ratio is any one of several financial measurements that assesses the ability of a company to meet its financial obligations.

• A leverage ratio may also be used to measure a company's mix of operating expenses to get an idea of how changes in output will affect operating income. 

• Common leverage ratios include the debt-equity ratio, equity multiplier, degree of financial leverage, and consumer leverage ratio.

• Banks have regulatory oversight on the level of leverage they are can hold.

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Understanding The Leverage Ratio

What Does a Leverage Ratio Tell You?

Too much debt can be dangerous for a company and its investors. However, if a company's operations can generate a higher rate of return than the interest rate on its loans, then the debt may help to fuel growth. Uncontrolled debt levels can lead to credit downgrades or worse. On the other hand, too few debts can also raise questions. A reluctance or inability to borrow may be a sign that operating margins are tight.

There are several different ratios that may be categorized as a leverage ratio, but the main factors considered are debt, equity, assets, and interest expenses.

A leverage ratio may also be used to measure a company's mix of operating expenses to get an idea of how changes in output will affect operating income. Fixed and variable costs are the two types of operating costs; depending on the company and the industry, the mix will differ. 

Finally, the consumer leverage ratio refers to the level of consumer debt compared to disposable income and is used in economic analysis and by policymakers.

Banks and Leverage Ratios

Banks are among the most leveraged institutions in the United States. The combination of fractional-reserve banking and Federal Deposit Insurance Corporation (FDIC) protection has produced a banking environment with limited lending risks.

To compensate for this, three separate regulatory bodies, the FDIC, the Federal Reserve, and the Comptroller of the Currency, review and restrict the leverage ratios for American banks.1 This means they restrict how much money a bank can lend relative to how much capital the bank devotes to its own assets. The level of capital is important because banks can "write down" the capital portion of their assets if total asset values drop. Assets financed by debt cannot be written down because the bank's bondholders and depositors are owed those funds.

Banking regulations for leverage ratios are complicated. The Federal Reserve created guidelines for bank holding companies, although these restrictions vary depending on the rating assigned to the bank. In general, banks that experience rapid growth or face operational or financial difficulties are required to maintain higher leverage ratios.2

There are several forms of capital requirements and minimum reserve placed on American banks through the FDIC and the Comptroller of the Currency that indirectly impacts leverage ratios. The level of scrutiny paid to leverage ratios has increased since the Great Recession of 2007 to 2009 when banks that were "too big to fail" were a calling card to make banks more solvent. These restrictions naturally limit the number of loans made because it is more difficult and more expensive for a bank to raise capital than it is to borrow funds. Higher capital requirements can reduce dividends or dilute share value if more shares are issued.

For banks, the tier 1 leverage ratio is most commonly used by regulators.

Leverage Ratios for Evaluating Solvency and Capital Structure

Perhaps the most well known financial leverage ratio is the debt-to-equity ratio.

The Debt-to-Equity (D/E) Ratio

This is expressed as:

\text{Debt-to-Equity Ratio} = \frac{\text{Total Liabilities}}{\text{Total Shareholders' Equity}}Debt-to-Equity Ratio=Total Shareholders’ EquityTotal Liabilities​

For example, United Parcel Service's long-term debt for the quarter ending December 2019 was $21.8 billion. United Parcel Service's total stockholders' equity for the ending December 2019 was $3.3 billion. The company's D/E for the quarter was 8.62. That is considered high.3

A high debt/equity ratio generally indicates that a company has been aggressive in financing its growth with debt. This can result in volatile earnings as a result of the additional interest expense. If the company's interest expense grows too high, it may increase the company's chances of a default or bankruptcy.

Typically, a D/E ratio greater than 2.0 indicates a risky scenario for an investor; however, this yardstick can vary by industry. Businesses that require large capital expenditures (CapEx), such as utility and manufacturing companies, may need to secure more loans than other companies. It's a good idea to measure a firm's leverage ratios against past performance and with companies operating in the same industry to better understand the data. Fedex has a D/E ratio of 1.78, so there is cause for concern where UPS is concerned. However, most analysts consider that UPS earns enough cash to cover its debts.

The Equity Multiplier

The equity multiplier is similar, but replaces debt with assets in the numerator: 

\text{Equity Multiplier} = \frac{\text{Total Assets}}{\text{Total Equity}}Equity Multiplier=Total EquityTotal Assets​

For example, assume that Macy's (NYSE: M) has assets valued at $19.85 billion and stockholder equity of $4.32 billion. The equity multiplier would be:

\$19.85 \text{ billion} \div \$4.32 \text{ billion} = 4.59$19.85 billion÷$4.32 billion=4.59

Although debt is not specifically referenced in the formula, it is an underlying factor given that total assets includes debt.

Remember that Total Assets = Total Debt + Total shareholders' Equity. The company's high ratio of 4.59 means that assets are mostly funded with debt than equity. From the equity multiplier calculation, Macy's assets are financed with $15.53 billion in liabilities.

The equity multiplier is a component of the DuPont analysis for calculating return on equity (ROE):       

\begin{aligned} &\text{DuPont analysis} = NPM \times AT \times EM\\ &\textbf{where:}\\ &NPM=\text{net profit margin}\\ &AT=\text{asset turnover}\\ &EM=\text{equity multiplier}\\ \end{aligned}​DuPont analysis=NPM×AT×EMwhere:NPM=net profit marginAT=asset turnoverEM=equity multiplier​

The Debt-to-Capitalization Ratio

An indicator that measures the amount of debt in a company’s capital structure is the debt-to-capitalization ratio, which measures a company’s financial leverage. It is calculated as:

\begin{aligned} &\text{Total debt to capitalization} = \frac{(SD + LD)}{(SD + LD + SE)}\\ &\textbf{where:}\\ &SD=\text{short-term debt}\\ &LD=\text{long-term debt}\\ &SE=\text{shareholders' equity}\\ \end{aligned}​Total debt to capitalization=(SD+LD+SE)(SD+LD)​where:SD=short-term debtLD=long-term debtSE=shareholders’ equity​

In this ratio, operating leases are capitalized and equity includes both common and preferred shares. Instead of using long-term debt, an analyst may decide to use total debt to measure the debt used in a firm's capital structure. The formula, in this case, would include minority interest and preferred shares in the denominator.

Degree of Financial Leverage

Degree of financial leverage (DFL) is a ratio that measures the sensitivity of a company’s earnings per share (EPS) to fluctuations in its operating income, as a result of changes in its capital structure. It measures the percentage change in EPS for a unit change in earnings before interest and taxes (EBIT) and is represented as:

\begin{aligned} &DFL = \frac{\% \text{ change in }EPS}{\% \text{ change in }EBIT} \\ &\textbf{where:}\\ &EPS=\text{earnings per share}\\ &EBIT=\text{earnings before interest and taxes}\\ \end{aligned}​DFL=% change in EBIT% change in EPS​where:EPS=earnings per shareEBIT=earnings before interest and taxes​

DFL can alternatively be represented by the equation below:

DFL = \frac{EBIT}{EBIT - \text{interest}}DFL=EBIT−interestEBIT​

This ratio indicates that the higher the degree of financial leverage, the more volatile earnings will be. Since interest is usually a fixed expense, leverage magnifies returns and EPS. This is good when operating income is rising, but it can be a problem when operating income is under pressure.

The Consumer Leverage Ratio

The consumer leverage ratio is used to quantify the amount of debt the average American consumer has relative to their disposable income.

Some economists have stated that the rapid increase in consumer debt levels has been a contributing factor to corporate earnings growth over the past few decades. Others blamed the high level of consumer debt as a major cause of the great recession.

\text{Consumer leverage ratio} = \frac{\text{Total household debt}}{\text{Disposable personal income}}Consumer leverage ratio=Disposable personal incomeTotal household debt​

Understanding how debt amplifies returns is the key to understanding leverage. Debt is not necessarily a bad thing, particularly if the debt is taken on to invest in projects that will generate positive returns. Leverage can thus multiply returns, although it can also magnify losses if returns turn out to be negative.

The Debt-To-Capital Ratio

The debt-to-capital ratio is a measurement of a company's financial leverage. It is one of the more meaningful debt ratios because it focuses on the relationship of debt liabilities as a component of a company's total capital base. Debt includes all short-term and long-term obligations. Capital includes the company's debt and shareholders' equity.

This ratio is used to evaluate a firm's financial structure and how it is financing operations. Typically, if a company has a high debt-to-capital ratio compared to its peers, it may have a higher default risk due to the effect the debt has on its operations. The oil industry seems to have about a 40% debt-to-capital threshold. Above that level, debt costs increase considerably.

The Debt-To-EBITDA Leverage Ratio

The debt-to-EBITDA leverage ratio measures a company's ability to pay off its incurred debt. Commonly used by credit agencies, this ratio determines the probability of defaulting on issued debt. Since oil and gas companies typically have a lot of debt on their balance sheets, this ratio is useful in determining how many years of EBITDA would be required to pay back all the debt. Typically, it can be alarming if the ratio is over 3, but this can vary depending on the industry.

The Debt-To-EBITDAX Ratio

Another variation of the debt-to-EBITDA ratio is the debt-to-EBITDAX ratio, which is similar, except EBITDAX is EBITDA before exploration costs for successful efforts companies. This ratio is commonly used in the United States to normalize different accounting treatments for exploration expenses (the full cost method versus the successful efforts method).

Exploration costs are typically found in the financial statements as exploration, abandonment, and dry hole costs. Other noncash expenses that should be added back in are impairments, accretion of asset retirement obligations, and deferred taxes.

The Interest Coverage Ratio

Another leverage ratio concerned with interest payments is the interest coverage ratio. One problem with only reviewing the total debt liabilities for a company is they do not tell you anything about the company's ability to service the debt. This is exactly what the interest coverage ratio aims to fix.

This ratio, which equals operating income divided by interest expenses, showcases the company's ability to make interest payments. Generally, a ratio of 3.0 or higher is desirable, although this varies from industry to industry.

The Fixed-Charge Coverage Ratio

Times interest earned (TIE), also known as a fixed-charge coverage ratio, is a variation of the interest coverage ratio. This leverage ratio attempts to highlight cash flow relative to interest owed on long-term liabilities.

To calculate this ratio, find the company's earnings before interest and taxes (EBIT), then divide by the interest expense of long-term debts. Use pre-tax earnings because interest is tax-deductible; the full amount of earnings can eventually be used to pay interest. Again, higher numbers are more favorable.

Net worth is the value of the assets a person or corporation owns, minus the liabilities they owe. It is an important metric to gauge a company's health, providing a useful snapshot of its current financial position.

KEY TAKEAWAYS

• Net worth is a quantitative concept that measures the value of an entity and can apply to individuals, corporations, sectors, and even countries.

• Net worth provides a snapshot of an entity's current financial position.

• In business, net worth is also known as book value or shareholders' equity.

• People with substantial net worth are called high-net-worth individuals (HNWI).

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What is Net Worth?

Understanding Net Worth

Net worth is calculated by subtracting all liabilities from assets. An asset is anything owned that has monetary value, while liabilities are obligations that deplete resources, such as loans, accounts payable (AP), and mortgages.

Net worth can be described as either positive or negative, with the former meaning that assets exceed liabilities and the latter that liabilities exceed assets. Positive and increasing net worth indicates good financial health. Decreasing net worth, on the other hand, is cause for concern as it might signal a decrease in assets relative to liabilities.

The best way to improve net worth is to either reduce liabilities while assets stay constant or rise, or increase assets while liabilities either stay constant or fall.

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

NKE

NIKE 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

Types of Net Worth

Net worth can be applied to individuals, companies, sectors, and even countries.

Net Worth in Business

In business, net worth is also known as book value or shareholders' equity. The balance sheet is also known as a net worth statement. The value of a company's equity equals the difference between the value of total assets and total liabilities. Note that the values on a company's balance sheet highlight historical costs or book values, not current market values.

Lenders scrutinize a business's net worth to determine if it is financially healthy. If total liabilities exceed total assets, a creditor may not be too confident in a company's ability to repay its loans.

A consistently profitable company will register a rising net worth or book value as long as these earnings are not fully distributed to shareholders as dividends. For a public company, a rising book value will often be accompanied by an increase in the value of its stock price.

Net Worth in Personal Finance

An individual's net worth is simply the value that is left after subtracting liabilities from assets.

Examples of liabilities, otherwise known as debt, include mortgages, credit card balances, student loans, and car loans. An individual's assets, meanwhile, include checking and savings account balances, the value of securities such as stocks or bonds, real property value, the market value of an automobile, et al. Whatever is left after selling all assets and paying off personal debt is the net worth.

Note that the value of personal net worth includes the current market value of assets and the current debt costs.

People with a substantial net worth are known as high net worth individuals (HNWI) and form the prime market for wealth managers and investment counselors. Investors with a net worth, excluding their primary residence, of at least $1 million—either alone or together with their spouse—are "accredited investors" in the eyes of the Securities and Exchange Commission (SEC), and, therefore, permitted to invest in unregistered securities offerings.

Example of Net Worth

Consider a couple with the following assets:

• Primary residence valued at $250,000,

• An investment portfolio with a market value of $100,000,

• Automobiles and other assets valued at $25,000.

Liabilities include:

• An outstanding mortgage balance of $100,000

• A car loan of $10,000

The couple's net worth would, therefore, be calculated as:

[$250,000 + $100,000 + $25,000] - [$100,000 + $10,000] = $265,000

Assume that five years later, the couple's financial position changes: the residence value is $225,000, investment portfolio $120,000, savings $20,000, automobile and other assets $15,000; mortgage loan balance $80,000, and car loan $0 because it was paid off. Based on these new figures, the net worth five years later would be:

[$225,000 + $120,000 + $20,000 + $15,000] - $80,000 = $300,000.

The couple's net worth has gone up by $35,000, despite the decrease in the value of their residence and car. As we can see above, these declines were more than offset by increases in other assets, in this case, the investment portfolio and savings, as well as a drop in liabilities owed.

Special Considerations

Negative Net Worth

A negative net worth results if total debt is more than total assets. For instance, if the sum of an individual's credit card bills, utility bills, outstanding mortgage payments, auto loan bills, and student loans is higher than the total value of their cash and investments, net worth will be negative.

Negative net worth is a sign that an individual or family needs to focus its energy on debt reduction. A tough budget, the use of debt reduction strategies such as the debt snowball or debt avalanche, and perhaps negotiation of some debts with creditors can sometimes help people climb out of a negative net worth hole and start building up their resources.

Early in life, a negative net worth is not uncommon—student loans mean even the most careful-with-money young people can start out owing more than they own. Family responsibilities or an unexpected illness can also push people into the red.

When nothing else has worked, filing for bankruptcy protection to eliminate some of the debt and prevent creditors from trying to collect on it might be the most appropriate solution; however, some liabilities—such as child support, alimony, taxes, and often student loans—cannot be discharged. It’s also worth bearing in mind that a bankruptcy will stay on an individual's credit report for many years.

What Is a Good Net Worth?

Determining what a "good" net worth is will vary for every individual, according to their life's circumstances, financial needs, and lifestyle. The average net worth of an individual in the U.S. was $121,700, in 2019, according to the latest data from the Federal Reserve.1

How Do I Calculate My Net Worth?

To calculate your net worth, you subtract your total liabilities from your total assets. Total assets will include your investments, savings, cash deposits, and any equity that you have in a home, car, or other similar assets. Total liabilities would include any debt, such as student loans and credit card debt.

How Much Should I Have Saved?

How much you should have saved will depend on your age, your career, your lifestyle, and your life's circumstances. Fidelity, for example, recommends having saved three times your annual salary by the time you are 40 across all of your retirement accounts.

Pre-market trading is the period of trading activity that occurs before the regular market session. The pre-market trading session typically occurs between 8 a.m. and 9:30 a.m. EST each trading day. Many investors and traders watch the pre-market trading activity to judge the strength and direction of the market in anticipation of the regular trading session.

Pre-market trading can only be executed with limited orders through an "electronic market" like an alternative trading system (ATS) or electronic communication network (ECN). Market makers are not permitted to execute orders until the 9:30 a.m. EST opening bell.1

Understanding Pre-Market Trading

Pre-market trading activity generally has limited volume and liquidity; therefore, large bid-ask spreads are common.1 Many retail brokers offer pre-market trading but may limit the types of orders that can be made during the pre-market period. Several direct-access brokers allow access to pre-market trading to commence as early as 4 a.m. EST from Monday through Friday.

It is important to remember there is very little activity for most stocks so early in the morning unless there is news. The liquidity is also extremely thin, with most stocks only showing stub quotes. Index-based exchange-traded funds (ETFs), such as the SPDR S&P 500 ETF (SPY), have moving quotes due to the trading in the S&P 500 futures contracts. Many of the most widely held top holdings in benchmark indices may also get movement in the event of a significant gap up or down in the S&P 500 futures. Large-cap, widely held stocks such as Apple Inc. (AAPL) tend to get trades as early as 4:15 a.m. EST.2

After-hours trading was introduced before pre-market trading. The New York Stock Exchange (NYSE) introduced after-hours trading in June 1991 by extending trading hours by an hour. The move was a response to increased competition from international exchanges in London and Tokyo and private exchanges, which offered more hours of trading, and 2.24 million shares changed hands in two sessions of trading.3 Over the years, as exchanges became increasingly computerized and the Internet's reach spread across borders, NYSE began extending the number of hours of trading available for trading, eventually allowing pre-market trading between the hours of 4 a.m. and 9:30 a.m.4

KEY TAKEAWAYS

• Pre-market trading is trading that occurs between 4 a.m. and 9:30 a.m. EST.

• Pre-market trading is characterized by thin liquidity, low trading volumes, and large bid-ask spreads.

Pre-Market Trading: Benefits

Pre-market trading and after-hours trading—collectively known as extended-hours trading—share similar benefits and risks. Let's look at the benefits first:

• Provides an opportunity to react early to overnight news: Pre-market trading provides the retail investor with an opportunity to react to overnight news before the regular trading session commences. Such news could be corporate earnings (although most companies report earnings after markets close, rather than before the open) or a major company announcement, overnight breaking news such as a geopolitical development, or news emanating from overseas markets. The caveat here is that the pre-market reaction to such news may reverse in the regular trading session. The limited trading volume in the pre-market may provide a signal of weakness or strength that may not be borne out when the market opens and regular trading volumes are reached. For example, a stock that reports an earnings miss may be down significantly in pre-market trading but could reverse course and end the day higher in the regular session.

• Convenience: This is a major benefit for the do-it-yourself investor because not everyone has a schedule that permits trading during regular market hours. The ability to start the day early and place trades in the pre-market is a big advantage for most people due to the frenzied pace of everyday life.

• Get a jump on the competition: Astute traders and investors who are familiar with trading patterns and experienced in extended-hours trading may use the pre-market to buy or sell stocks at more favorable prices, compared to prices obtained by other traders in the regular session. This is only possible if the pre-market reaction to news about a stock is accurate, and the stock does not fully discount the news in pre-market trading. In such instances, a stock that trades higher in the pre-market will continue to trend significantly higher in the regular trading session, while a stock that trades lower in the pre-market will trend lower during regular trading.

Pre-Market Trading: Risks

We now turn to the risks of pre-market trading, which include:

• Limited liquidity and wide bid-ask spreads: The number of buyers and sellers of stocks is far fewer in the pre-market, compared with the multitudes of traders and investors during regular trading. As a result, pre-market trading volumes are generally a fraction of volumes in the regular session. Low trading volumes result in limited liquidity, greater volatility, and wide bid-ask spreads.

• Price uncertainty: Prices of stocks traded in the pre-market may diverge significantly from the prices of those stocks during regular hours. Apart from the impact on stock prices from vastly differing trading volumes in pre-market and regular sessions, pre-market stock prices may only reflect prices from a single or handful of electronic communication networks (ECNs). During regular trading hours, multiple exchanges, ECNs, and market makers provide stock prices, leading to better price discovery; the stock quotes shown are consolidated and represent the best bid and offer across all trading venues.

• Limit orders may result in non-execution: Many brokerages only accept limit orders in extended-hours trading, so as to protect investors from unexpectedly adverse prices. Limit orders can only be executed at the limit price or better. The benefit of this feature of limit orders means that the investor knows the highest price at which a stock will be bought or the lowest price at which it will be sold. But this also means that if the market moves away from the limit price, the order will not be executed.

• Competition from institutional traders: Retail traders face an uneven playing field in pre-market trading because many of the participants are institutional and professional traders who have a trading edge on account of much deeper pockets and access to better, more timely information.1

These risks mean that only experienced traders should consider trading in the pre-market because the odds are stacked against retail traders. Seasoned traders have the knowledge and experience to gauge the many nuances that make trading a challenge—such as assessing whether the pre-market reaction to the news is an under-reaction or over-reaction—and taking decisive action on trading matters like opening a new stock position or closing an existing one, setting limit prices at certain levels for buys and sells, etc.

When Does Pre-Market Trading Begin?

Pre-market trading can start as early as 4 a.m. EST, although most of it takes place from 8 a.m. EST and before regular trading commences at 9:30 a.m. EST.54

What Securities Can Be Traded in the Pre-Market Session? Options?

Generally, only listed stocks can be traded in the pre-market session. Not all stocks, though. Stocks such as those that have a limited float or are not widely held, or small-cap stocks, may not have sufficient volumes to make pre-market trading a viable proposition. Options cannot be traded in the pre-market session.

Do Online Brokers Offer Pre-Market Trading?

Almost all online brokers offer pre-market trading, although the hours differ from one broker to the other. Here's a sample of pre-market trading hours at select online brokers as of Dec. 21, 2021 (note that these hours may be subject to change):

• TD Ameritrade offers pre-market trading from 7 a.m. EST to 9:28 a.m. EST.6

• At Charles Schwab, pre-market orders can be placed between 8:05 p.m. (on the previous trading day) and 9:25 a.m. EST, and are eligible for execution between 7 a.m. and 9:25 a.m. EST.7

• E*TRADE offers pre-market trading from 7 a.m. EST to 9:30 a.m. EST.8

• Interactive Brokers has pre-trading for its "IBKR Pro" accounts from 4 a.m. EST to 9:30 a.m. EST, and for its "IBKR Lite" accounts from 7 a.m. EST to 9:30 a.m. EST.9

• At Robinhood, the pre-market trading session is from 9 a.m. EST to 9:30 a.m. EST; trades may still be executed as early as 8:58 a.m. EST.10

• Webull allows pre-market trading from 4 a.m. EST to 9:30 a.m. EST.11

Can a Limit Order From Pre-Market Trading Carry Over into the Regular Session?

In most cases, limit orders from pre-market trading are only valid for that particular session and if not executed, do not carry over into the regular session. However, Interactive Brokers permits limit- or stop-limit-type orders that can be active in all trading sessions including pre-market, regular trading hours (RTH), and after-market; for such orders, the attribute "Allow Outside RTH" needs to be added.9

Why Are Extended Trading Hours Necessary?

Extended trading hours enable investors to react to news and events when the markets are closed. It is also a convenient way to trade for people who cannot buy and sell securities during the regular trading session.

What Is the Nasdaq-100 Pre-Market Indicator?

The Nasdaq-100 Pre-Market Indicator is calculated based on the last sale of Nasdaq-100 securities during the pre-market trading period of 8:15 a.m. to 9:30 a.m. EST. For Nasdaq-100 securities that do not trade in the pre-market, the calculation uses the last sale from the previous day's 4 p.m. closing price. The Nasdaq-100 Pre-Market Indicator and After Hours Indicator are useful gauges of market sentiment during extended trading hours.12

Is 24-Hour Trading for Stocks Going to Be a Reality Soon?

The 24-hour trading that is a feature of the foreign exchange and cryptocurrency markets may come to equity markets within the next few years. 24 Exchange, a Bermuda-based crypto and foreign exchange trading platform, aims to bring the round-the-clock trading of the digital currency realm to the stock market. In October 2021, 24 Exchange filed forms with the Securities and Exchange Commission in hopes of receiving a license to commence operating a 24-hour exchange in 2022.

The term work-in-progress (WIP) is a production and supply-chain management term describing partially finished goods awaiting completion. WIP refers to the raw materials, labor, and overhead costs incurred for products that are at various stages of the production process. WIP is a component of the inventory asset account on the balance sheet. These costs are subsequently transferred to the finished goods account and eventually to the cost of sales.

WIPs are one of the components of a company's balance sheet. The WIP figure reflects only the value of those products in some intermediate production stages. This excludes the value of raw materials not yet incorporated into an item for sale. The WIP figure also excludes the value of finished products being held as inventory in anticipation of future sales.

KEY TAKEAWAYS

• A work-in-progress (WIP) is the cost of unfinished goods in the manufacturing process including labor, raw materials, and overhead.

• WIPs are considered to be a current asset on the balance sheet.

• Minimizing WIP inventory before reporting it is both standard and necessary since it is difficult to estimate the percentage of completion for an inventory asset.

• A WIP is different from a finished good which refers to a product that is ready to be sold to the consumer.

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Work In Progress (WIP)

Understanding Works-in-Progress (WIP)

WIP is a concept used to describe the flow of manufacturing costs from one area of production to the next, and the balance in WIP represents all production costs incurred for partially completed goods. Production costs include raw materials, labor used in making goods, and allocated overhead.

When combs are manufactured, plastic is moved into production as a raw material. Then, labor costs are incurred to operate molding equipment. Since the combs are only partially completed, all costs are posted to WIP. When the combs are completed, the costs are moved from WIP to finished goods, with both accounts being part of the inventory account. Costs are moved from inventory to cost of goods sold (COGS) when the combs are eventually sold.

A piece of inventory is classified as a WIP whenever it has been mixed with human labor but has not reached final goods status. Only some, but not all, necessary labor has been performed with it. WIP, along with other inventory accounts, can be determined by various accounting methods across different companies.

Thus, it is important for investors to discern how a company is measuring its WIP and other inventory accounts. One company's WIP may not be comparable to another's. Allocations of overhead can be based on labor hours or machine hours, for example. WIP is also an asset on the balance sheet. It is standard practice to minimize the amount of WIP inventory before reporting is necessary since it is difficult and time-consuming to estimate the percentage of completion for an inventory asset.

Works in progress may also be called in-process inventory.

Special Considerations

Accountants use several methods to determine the number of partially completed units in WIP. In most cases, accountants consider the percentage of total raw material, labor, and overhead costs that have been incurred to determine the number of partially completed units in WIP. The cost of raw materials is the first cost incurred in this process because materials are required before any labor costs can be incurred.

For accounting purposes, process costing differs from job costing, which is a method used when each customer's job is different. Job costing tracks the costs (e.g., cost of materials, labor, and overhead) and profits for a specific job, and it allows accountants to trace expenses for each job for tax purposes and for analysis (scrutinizing costs to see how they can be reduced). 

For example, suppose XYZ Roofing Company provides its residential clients' bids for roof repair or replacement. Each roof is a different size and will require specific roofing equipment and a varying number of labor hours. Each bid lists the labor, material, and overhead costs for the work.

On the other hand, a process costing system tracks accumulates and assigns costs associated with the manufacturing of homogeneous products. Consider a company that manufactures plastic combs. The plastic is put into a mold in the molding department and is then painted before being packaged. As the combs move from one department (molding to painting to packaging) to another, more costs are added to production.

Raw material costs appear on the balance sheet as a current asset, though sometimes a single line item is used that also includes WIP and finished goods inventory.

Work-in-Progress vs. Work-in-Process

Work-in-process represents partially completed goods. These goods are also referred to as goods-in-process. For some, work-in-process refers to products that move from raw materials to finished products in a short period. An example of a work-in-process may include manufactured goods.

Work-in-progress, as mentioned above, is sometimes used to refer to assets that require a considerable amount of time to complete, such as consulting or construction projects. This differentiation may not necessarily be the norm, so either term can be used to refer to unfinished products in most situations. This inventory is found on a manufacturing company's balance sheet. This account of inventory, like the work-in-progress, may include direct labor, material, and manufacturing overhead.

Works-in-Progress vs. Finished Goods

The difference between WIP and finished goods is based on the inventory's stage of relative completion, which, in this instance, means saleability. WIP refers to the intermediary stage of inventory in which inventory has started its progress from the beginning as raw materials and is currently undergoing development or assembly into the final product. Finished goods refer to the final stage of inventory, in which the product has reached a level of completion where the subsequent stage is the sale to a customer.

The terms work-in-progress and finished goods are relative terms made in reference to the specific company accounting for its inventory. They are not absolute definitions of actual materials or products. It's incorrect to assume that finished goods for one company would also be classified as finished goods for another company. For example, sheet plywood may be a finished good for a lumber mill because it's ready for sale, but that same plywood is considered raw material for an industrial cabinet manufacturer.

As such, the difference between WIP and finished goods is based on an inventory's stage of completion relative to its total inventory. WIP and finished goods refer to the intermediary and final stages of an inventory life cycle, respectively.

What Does Work-in-Progress Mean in Accounting?

In supply-chain management, work-in-progress (WIP) refers to goods that are partially completed. They may also be referred to as in-process inventory. This covers everything from the overhead costs to the raw materials that come together to form the end product at a given stage in the production cycle. In accounting, WIP is considered a current asset and is categorized as a type of inventory.

Is Work-in-Progress a Form of Inventory?

A piece of inventory becomes labeled as work-in-progress when raw material combines with human labor. When the product is finalized, it switches from WIP to being categorized as a finished product. Finally, when the product is sold, it moves from a form of inventor to cost of goods sold (COGS) on the balance sheet.

How Is Work-in-Progress Calculated?

In accounting, inventory that is work-in-progress is calculated in a number of different ways. Typically, to calculate the amount of partially completed products in WIP, they are calculated as the percentage of the total overhead, labor, and material costs incurred by the company. A construction company, for example, may bill a company based on various stages of the project, where it may bill when it is 25% or 50% completed, and so forth.

Zero-one integer programming (which can also be written as '0-1' integer programming) is a mathematical method of using a series of binary functions; in particular, yes ('1') and no ('0') answers to arrive at a solution when there are two mutually exclusive options.

In the world of finance, zero-one integer programming is often used to provide answers to capital rationing problems, as well as to optimize investment returns and assist in planning, production, transportation, and other issues.

KEY TAKEAWAYS

• Zero-one integer programming relies on mutually exclusive yes (1) and no (0) decisions to find solutions to logic problems.

• In zero-one integer problems, each variable is represented only by 0 ('no') or 1 ('yes'), and could represent selecting or rejecting an option, turning on or off electronic switches, or a straight-forward yes or no answer used in various other applications.

• This type of programming can be useful for companies making decisions on issues like what to invest in or which of two proposed products are easiest to manufacture.

Understanding Zero-One Integer Programming

Integer programming is a branch of mathematical programming or optimization, which involves creating equations in order to solve problems. The term "mathematical programming" is connected with the fact that the goal of solving various problems is choosing programs of action. Assigning a simple yes/no value can be a powerful way to establish a linear problem-solving framework to identify inefficiencies.

Fundamentally, the most basic instructions executed by a computer are binary codes, consisting only of ones and zeros. Those codes are directly translated into the “on” and “off” states of the electricity moving through the computer’s physical circuits. In essence, these simple codes form the basis of “machine language”, the most fundamental variety of programming languages. These on and off positions can also be construed as assigning a "yes" or "no" to a logical function.

Of course, no human would be able to construct modern software programs by explicitly programming ones and zeros. Instead, human programmers must rely on various layers of abstraction that can allow them to articulate their commands in a format that is more intuitive to humans. Specifically, modern programmers issue commands in so-called “high-level languages”, which utilize intuitive syntax such as whole English words and sentences, as well as logical operators such as “And”, “Or”, and “Else” that are familiar to everyday usage.

Ultimately, however, these high-level commands need to be translated into machine language. Rather than doing so manually, programmers rely on assembly languages whose purpose is to automatically translate between these high-level and low-level languages.

Real-World Example of Zero-One Integer Programming

A simple example of how zero-one integer programming might be used in capital rationing would be in determining the number of product development projects that can be completed by a company by a certain date or within a certain budget. For example, a number of variables for each project can be given values that ultimately result in a 1 (yes) or 0 (no) binary decision about whether or not to include the project in a budget. This can be helpful to companies that are unsure about a specific business decision and are looking for a straightforward way to assess the possibilities.

An onerous contract is an accounting term that refers to a contract that will cost a company more to fulfill than what the company will receive in return.

The term is used in many countries worldwide, where international regulators have determined that such contracts must be accounted for on balance sheets. The United States has a different system, based on generally accepted accounting principles, or GAAP, as set forth by the U.S.-based Financial Accounting Standards Board.

KEY TAKEAWAYS

• An onerous contract is an accounting term defined under the International Financial Reporting Standards (IFRS), used in many countries around the world.

• Companies that follow those standards are required to report any onerous contracts they're committed to on their balance sheets.

• In the United States, companies typically follow a different set of accounting standards and generally don't have to account for their onerous contracts.

Understanding Onerous Contracts

The International Accounting Standards (IAS) defines an onerous contract as "a contract in which the unavoidable costs of meeting the obligations under the contract exceed the economic benefits expected to be received under it."1

The term "unavoidable costs" also has a specific meaning for accounting purposes. The IAS defines it as "the lower of the cost of fulfilling the contract and any compensation or penalties arising from failure to fulfill it."1

Onerous Contract Example

An example of an onerous contract might be an agreement to rent a property that is no longer needed or that can no longer be made use of profitably. For instance, suppose a company signs a multiyear agreement to rent office space, then moves or downsizes while the agreement is still in effect, leaving the office space, which it now has no use for, vacant. Or consider a mining company that has signed a lease to mine for coal or some other commodity on a piece of land, but at some point during the term of the contract, the price of that commodity falls to a level that makes extracting it and bringing it to market unprofitable.

Special Considerations

The rules for how onerous contracts should be treated in a company's financial statements are part of the International Financial Reporting Standards (IFRS), for which the IAS Board is the independent standard-setting body. The governing body, the IFRS Foundation, is a not-for-profit organization based in London.2

International Accounting Standard 37 (IAS 37), "Provisions, Contingent Liabilities, and Contingent Assets," classifies onerous contracts as "provisions," meaning liabilities or debts that will accrue at an uncertain time or in an unknown amount. Provisions are measured using the best estimate of the expenses required to satisfy the current obligation.3

Under IAS 37, any business or company that identifies a contract as onerous is required to recognize the current obligation as a liability and to list that liability on its balance sheet. This process is meant to be undertaken at the first indication that the company expects a loss from the contract.1

The IFRS and IASB standards are used by companies in many countries throughout the world, although not in the United States. The U.S. requires companies to follow another set of standards under GAAP. Under GAAP, losses, obligations, and debts on committed onerous contracts typically are not recognized or dealt with. However, the FASB has been working with the IASB to establish compatible standards worldwide.

XD is a symbol used to signify that a security is trading ex-dividend. It is an alphabetic qualifier that acts as shorthand to tell investors key information about a specific security in a stock quote. Sometimes X alone is used to indicate that the stock is trading ex-dividend.

Qualifiers can vary depending on where the stock is quoted, because the various news and market data services that provide stock quotes may use different qualifiers. These symbol letters may occur as part of a display on a broker's trading platform, on a charting program, or in a timely published report.

KEY TAKEAWAYS

• "XD" appears as a footnote, subscript, superscript, or suffix to a ticker symbol to signify the stock is ex-dividend.

• Stocks trading immediately past the dividend distribution may be lower in price, by the amount of the cash dividend payout.

• XD is one of many qualifiers or suffixes that can be attached to a ticker symbol to denote some status or event related to a stock.

Understanding XD

A dividend is a distribution of part of a company's earnings to the company's shareholders. When a stock is trading ex-dividend, the current stockholder has received a recent dividend payment and whoever purchases the stock will not receive the dividend. The stock's price is likely to be lower as a result.

There are quite a few qualifiers that relate to dividends. For example, -j as a suffix indicates that the stock paid a dividend earlier in the year but currently does not carry a dividend.

Comparing XD With the Record Date

You'll need to look at two important dates to determine who should get a dividend—the "ex-date" (or XD) and the record date.

An investor must be on the company's books as a shareholder to receive a dividend. Once the company sets the record date, the ex-dividend date is set. The ex-dividend date for stocks is usually set one business day before the record date. An investor who purchased shares before the ex-dividend date will get the upcoming dividend. If a purchase took place on or after the ex-dividend date, then the seller gets the dividend.

Companies also use the record date to determine to whom to send financial reports, proxy statements, and other required information.

Special Rules for Determining XD

If a dividend is 25% or more of the stock's value, then special rules will apply to determine the ex-dividend date. When this happens, the ex-dividend date is deferred until one business day after the dividend is paid.  

Sometimes a company pays a dividend in the form of stock rather than cash—either as additional shares in the company or in a subsidiary that is being spun off. Setting the ex-date for stock dividends may be different from cash dividends. It will be set the first business day after the stock dividend is paid (and is also after the record date).

Selling before the ex-dividend date includes an obligation to deliver any shares acquired as a result of the dividend to the buyer of your shares since the seller only receives an I.O.U. from their broker for the additional shares.

According to the Securities and Exchange Commission (SEC), the day you can sell your shares without being obligated to deliver the additional shares is "not the first business day after the record date, but usually is the first business day after the stock dividend is paid."