Statistical Arbitrage in the Crude Oil Markets

Statistical arbitrage is a classic trading strategy, invented in the 1980s. We mostly see it being applied in the equity markets, but statistical arbitrage is not limited to equities. It can be applied to other asset classes as well. Reference [1] examined the statistical arbitrage strategy in the commodity markets, specifically crude oil. The author pointed out,

In this paper, we introduce the concept of statistical arbitrage through the definition of a trading strategy, called mispricing portfolio. We focus on mean-reverting strategies in order to capture persistent anomalies in the markets. Furthermore, we show how we identify statistical arbitrages and apply trading rules adopted from equity markets.

We show the empirical evidence of statistical arbitrage in crude oil markets. We have built the mispricing portfolio by using a cointegration regression in order to identify long-term pricing relationships between the WTI crude oil futures and the price of a replication portfolio composed of other two crude oils, Brent and Dubai. Finally, we apply trading rules commonly used in equity markets to profit.

Basically, the author utilized cointegration to construct a statistical arbitrage portfolio. Various methods were then used to test for stationarity and mean reversion: the Quandt likelihood ratio (QLR), augmented Dickey-Fuller (ADF) test, autocorrelations, and the variance ratio. The constructed strategy performed well both in- and out-of-sample.

This is another interesting aspect of statistical arbitrage, applied in a different market. We note, however, that the period tested was up to 2017, i.e., pre-COVID.

It would be interesting to see the results during COVID, to observe how the strategy withstood the period when the front-month oil futures price went negative.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Viviana Fanelli, Mean-Reverting Statistical Arbitrage Strategies in Crude Oil Markets, Risks 2024, 12, 106.

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Sum of the Years’ Digits Depreciation: Definition, Formula, Method, Example, Calculation

Companies use various depreciation methods to determine the depreciation expense for an asset. One of these methods is the sum of the years’ digits depreciation.

What is the Sum of the Years' Digits Depreciation?

Sum of the Years' Digits Depreciation (SYD) is an accelerated method used to depreciate an asset, which allocates a higher depreciation in the earlier years of the asset's useful life and a lower expense in the later years. This method is suitable for assets that rapidly lose value initially. SYD aims to match the depreciation expense with the asset's usage and productivity, which diminishes over time.

The SYD method calculates depreciation based on the sum of the years' digits of the asset's useful life. This sum helps create fractions that determine the annual depreciation expense. The result is a more significant depreciation expense in the first years, decreasing yearly. This approach is useful for tax and financial reporting, where reflecting higher early expenses can be advantageous.

How to calculate the Sum of the Years' Digits Depreciation?

As mentioned above, companies can calculate the sum of the years' digit depreciation by determining the useful life of an asset (n). Then, companies must add all digits from 1 to n to get the sum of the years' digits. The formula for it is below.

Sum of the years’ digits=n(n+1)​ / 2

As with other depreciation methods, companies must still determine the depreciation base for the asset, calculated as below.

Depreciable base=Initial cost - Residual value

Next, companies must calculate the depreciation fraction for the year. This fraction will determine the proportion of the asset's cost to be depreciated during a year (x). The calculation is as follows.

Depreciation fraction for year x = (n - x + 1)​ / Sum of the years’ digits

Finally, companies can calculate the depreciation expense for year x by multiplying the depreciable base with the depreciation fraction for the year, as follows.

Depreciation expense for year x = Depreciable base × Depreciation fraction for year x

Example

Red Co. owns an asset with an initial value of $10,000 and a residual value of $2,000. When the company acquired the asset, it determined its useful life to be five years. Red Co. wants to calculate the sum of the years' digits depreciation for the third year. Based on this information, the company will use the following steps.

1. Calculate the sum of the years' digits as follows.

Sum of the years’ digits = n (n+1) / 2

Sum of the years’ digits = 5 (5 + 1) / 2

Sum of the years’ digits = 15

2. Determine the depreciable base as follows.

Depreciable base = $10,000 - $2,000

Depreciable base = $8,000

3. Calculate the depreciation fraction for year 3, as below.

Depreciation fraction = (n - x + 1) / Sum of the years’ digits

Depreciation fraction = (5 - 3 + 1) / 15

Depreciation fraction = 3 / 15 or 20%

4. Calculate the depreciation expense.

Depreciation expense for year 3 = $8,000 × 20%

Depreciation expense = $1,600

Conclusion

The sum of the years' digit depreciation is a depreciation method that depreciates assets more in the earlier years of their useful life. The calculation for this method involves various steps. However, it can be more accurate when a company uses an asset more during its initial years. It can also have other benefits, such as tax savings.

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Mean-Reverting Trading Strategies Across Developed Markets

A mean reversion trading strategy is based on the concept that asset prices will revert to their historical average or mean over time. This strategy identifies securities that have deviated significantly from their historical averages, with the expectation that they will eventually return to those levels. The goal is to buy low (when prices are below the mean) and sell high (when prices are above the mean), capitalizing on price corrections. This approach relies on the assumption that deviations from the norm are temporary, thus offering profitable opportunities for traders who can accurately identify and time these reversals.

Reference [1] studies the mean reversion strategy across developed markets. It shows that the mean-reversion strategy is not profitable in all markets. However, when we apply filters for stock characteristics, the strategy becomes profitable. The authors pointed out,

This study documents in detail the reversal strategy and its link with firms’ characteristics and market volatility for the five developed markets of Canada, France, Germany, Japan, and the United Kingdom. We conducted the analysis using portfolio analysis and FM cross-sectional regression. Using portfolio analysis, we found that the reversal effect was mostly present for smaller, higher book-to-market ratio, and higher volatility stocks. Nevertheless, we found the strongest effect for stocks with higher book-to-market ratios across all developed markets. We also discovered that reversal returns were mostly positive when market volatility was higher. Further, the reversal returns, once present, cannot be explained by the usual asset pricing models such as the CAPM, FF-3 and CF-4…

One reason for the higher reversal in smaller, high book-to-market, high volatility stocks is the lack of liquidity in these stocks, which gives rise to the reversal phenomenon. Lehmann (1990) and Nagel (2012) expounded that reversal returns proxy for the cost of liquidity provision. Therefore, we expect that when funding constraints are higher, reversal returns are also higher.

This article demonstrates that when applying filters, the mean-reversion strategy is profitable within a certain category of stocks across developed capital markets.

We used to think that choosing the stocks that work best for a certain trading strategy would suffer from survivorship bias. But as discussed in this article, if we use filter rules that have fundamental justification, is there still survivorship risk?

Let us know what you think in the comments below or in the discussion forum.

References

[1] Hilal Anwar Butt and Mohsin Sadaqat, When Is Reversal Strong? Evidence From Developed Markets, The Journal of Portfolio Management, June 2024

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Divestiture: Definition, Examples, Accounting, Framework, Meaning in Business

Divestiture plays a crucial role in the business world. It helps companies focus on their core strengths and can lead to better financial health.

By selling off non-essential parts, businesses can become more efficient and effective. It's a common strategy that big companies use to stay competitive.

Understanding divestiture is key to seeing how companies grow and change over time.

What is a Divestiture?

A divestiture (or divestment) happens when a company or government decides to get rid of some or all of its assets - this can be done by selling, exchanging, shutting them down, or through bankruptcy.

As companies expand, they often juggle too many business activities.

Divesting helps them stay focused and profitable. By doing this, companies can reduce costs, pay off debt, concentrate on their main businesses, and boost shareholder value.

This means that the divestiture also affects shareholders, as they may receive cash from the sale of assets or see an increase in stock value.

How Divestiture Works

Divestiture works when a company or government decides to sell off or close certain parts of their business. This can involve selling assets, divisions, or even subsidiaries to other companies.

Sometimes, they exchange these assets for something else of value, or they simply shut them down.

The goal is to streamline operations and focus on the main areas of the business - this process helps to cut costs, reduce debt, and increase overall efficiency.

By getting rid of non-core assets, the company can put more energy and resources into what they do best. This often leads to better performance and higher shareholder value.

The entire process requires planning and careful decision-making to ensure it benefits the company in the long run.

Reasons Why Companies Divest

There are many reasons why companies may choose to divest - here are some of the most common ones

1. Strategic focus: As companies grow, they may diversify into different industries or business activities. Over time, they may realize that some of these areas are not as profitable or aligned with their core goals. Divesting allows them to refocus and concentrate on their primary strengths.
2. Financial stability: Companies may divest to raise capital and reduce debt. By selling assets or subsidiaries, they can generate cash flow and use it to pay off loans or invest in other areas of the business.
3. Regulatory requirements: In some cases, governments may require companies to divest certain assets in order to comply with antitrust laws and prevent monopolies.
4. To increase resale value: Divesting can also be a strategic move to increase the value of the company. By shedding non-core assets, they may become more attractive to potential buyers or investors.
5. To sell off redundant business parts: If some operations of a business are no longer necessary or profitable, divesting them can improve overall efficiency and cut costs. This means the company can focus on growth opportunities and streamline its operations.
6. To reduce risk: By divesting certain assets or business units, companies can mitigate potential risks associated with those areas. For example, if a subsidiary is facing legal issues or financial troubles, divesting can protect the parent company from any negative impact.

Conclusion

In conclusion, divestiture is a helpful strategy for companies looking to stay focused and profitable. By selling or closing less important parts of their business, they can reduce costs and debt while concentrating on core activities. This not only streamlines their operations but also enhances overall performance and increases shareholder value. Understanding how divestiture works can help in making smart financial decisions and maintaining a strong, efficient business.

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Further on the Profitability of Pairs Trading

Pairs trading is a market-neutral trading strategy that involves taking simultaneous long and short positions in two correlated stocks to profit from their relative price movements. There are recent research papers that argue that pairs trading is no longer profitable, especially when using traditional pairs selection methods. Reference [1], however, contradicts these results and demonstrates that pairs trading is still profitable. The author pointed out,

In this paper, we replicate the results of pairs trading strategy initially proposed by Gatev et al. (2006) using stock price data from the past twenty years. We find that pairs trading results are still robust under transaction cost despite the changing market environment, with our top performing strategy producing a compounded annual excess return of 6.2%. Compared to most papers in the literature, our best performing strategy uses a larger pool of stocks to average out the influence of outliers whose price jumped “overnight” in response to delisting or stock split news. We then analyze two determinants of pairs trading profit: the medium-term momentum factor and the default spread, which closely tracks the investor risk premium holding other macroeconomic variables constant. This supports Gatev et al. (2006)’s hypothesis that arbitrageurs are compensated for restoring the “Law of One Price”. Our empirical results are then confirmed in simulation, using equilibrium prices predicted by a psychology-based model.

In short, the paper shows that the benchmark pairs trading strategy specified in Gatev et al. [2] has delivered robust returns over the past twenty years. However, the risk nature of the strategy has changed over the past 20 years. Additionally, regressing pairs trading profitability on macroeconomic variables identifies aggregate risk premium as a determinant of pairs trading returns, suggesting that arbitrageurs are compensated for providing liquidity and enforcing the Law of One Price

Let us know what you think in the comments below or in the discussion forum.

References

[1] Xuanchi Zhu, Examining Pairs Trading Profitability, 2024, Yale University

[2] Gatev, E., Rouwenhorst, K. G., and Goetzmann, W. (2006). Pairs trading: Performance of a relative value arbitrage rule, 2006, Yale ICF Working Paper No. 08-03

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Audit Data Analytics (ADA): Definition, Examples, Procedures, Advantages, Limitations

Auditors come across a significant volume of information and data during audit and assurance engagements. They must analyze and examine this data as a part of their services. However, it requires a substantial time commitment, which may not always be possible. Therefore, auditors use audit data analytics to simplify the process while increasing audit quality.

What is Audit Data Analytics?

Audit data analytics (ADA) revolutionizes the audit process by leveraging advanced data analysis techniques to scrutinize extensive datasets, detect anomalies, identify patterns, and extract meaningful insights. Auditors utilize ADA tools to extract and prepare data from diverse sources, ensuring its accuracy and relevance for analysis.

ADA facilitates data visualization through charts, graphs, dashboards, and heat maps, enabling auditors to present audit findings visually. It aids in conveying complex data patterns and relationships to stakeholders, enhancing their understanding and decision-making capabilities. Additionally, ADA supports continuous monitoring and auditing, empowering auditors to detect anomalies or irregularities in real time and proactively manage risks.

How does Audit Data Analytics work?

Audit data analytics streamlines the audit process through advanced data analysis techniques. Initially, auditors extract and refine relevant data from diverse sources like accounting systems and electronic records, ensuring data accuracy and consistency. Next, employing statistical methods, regression analysis, anomaly detection, and predictive modeling, auditors scrutinize the data to uncover patterns, anomalies, and trends.

Data visualization tools are utilized to present these insights visually, enhancing comprehension and facilitating decision-making for auditors and stakeholders. Furthermore, ADA enables continuous monitoring and auditing, allowing auditors to detect irregularities in real time and proactively manage risks. By leveraging ADA, auditors enhance audit accuracy and efficiency and derive actionable insights that support strategic decision-making and assurance processes within organizations.

What are the advantages of Audit Data Analytics?

Audit data analytics offers several advantages that enhance the audit process and contribute to improved audit quality and efficiency. Firstly, ADA enables auditors to analyze entire datasets comprehensively, moving beyond traditional sampling methods. This approach increases audit coverage and accuracy, as auditors can detect patterns, anomalies, and potential risks more effectively.

Secondly, ADA enhances audit efficiency by automating routine tasks such as data extraction, cleansing, and analysis. This automation reduces manual effort and allows auditors to focus on high-value tasks such as data interpretation and strategic analysis, leading to more efficient audit processes. Additionally, ADA supports continuous monitoring and auditing, enabling auditors to detect anomalies or irregularities in real time or at regular intervals.

What are the limitations of Audit Data Analytics?

Audit data analytics brings substantial benefits to the audit process but is not without limitations. One challenge is the need for specialized skills in data analysis techniques and tools among auditors. Adequate training and proficiency in statistical methods, data mining software, and data visualization tools are essential to leverage ADA effectively.

Furthermore, the ADA's reliance on data quality poses another limitation. Inaccurate, incomplete, or inconsistent data can lead to incorrect conclusions or misinterpretation of audit findings, emphasizing the importance of thorough data validation and cleansing processes. While ADA excels in structured data analysis from accounting systems, handling unstructured data may require additional expertise and tools.

Conclusion

Audit data analytics help auditors use advanced techniques to examine data. These tools allow auditors to assess significant data efficiently and effectively. It can offer several advantages, such as improved audit quality and accuracy. However, it also comes with its limitations, for example, training costs and data quality.

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Skewness Risk Premium in the Options Market

Skewness of return is a statistical measure that captures the asymmetry of the distribution of an asset's returns over a specified period. It is particularly important in risk management and option pricing, where the skewness of returns can affect the valuation of derivatives and the construction of portfolios.

Reference [1] studies the skewness risk premium in the options market. It decomposes the skewness risk premium into two components: jump skewness and leverage skewness risk premium. The authors pointed out,

We introduce novel distinguishing notions of realized skewness that can be replicated with model-free trading strategies. They admit a decomposition into a tradable jump skewness component and a tradable leverage effect component. Our replicating strategies dynamically rebalance option and forward positions with a common expiration date to produce settlement payoffs matching high-frequency realized jump skewness and realized leverage over horizons that may not coincide with the underlying forward and option maturities. When markets are open, this feature allows us to identify daytime jump and leverage components of the skewness risk premium. Furthermore, it allows us to separate them from the skewness risk premium earned overnight.

We analyze the properties of the excess returns of our skewness strategies in the market for short maturity S&P500 options, both intraday and overnight, to learn more about the size of the market skewness risk premium, its seasonal variation when markets are open or closed, and its cyclicality. We find that the skewness risk premium is large, greater when markets are closed than when they are open, countercyclical, and distinct from the variance risk premium. During market open hours, when the jump and leverage skewness components can be traded separately with our approach, we also find that the skewness risk premium is dominated by priced jump skewness risk.

In short, the authors constructed a tradable basket of options to measure the skewness risk premium. This means that this study is model-free.

They reconfirmed that

• The skewness risk premium is different from the variance risk premium.
• The variance risk premium is compensation for bearing overnight risks.

Additionally, they pointed out,

• Like the variance risk premium, the overnight skewness risk premium is higher than the daytime skewness risk premium
• The daytime skewness risk premium consists mostly of the jump skewness risk premium.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Piotr Orłowski , Paul Schneider , Fabio Trojani, On the Nature of (Jump) Skewness Risk Premia, Management Science, Vol 70, No 2

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Voluntary Lien: Definition, Types, Examples, Meaning, vs. Involuntary Lien

Voluntary liens are crucial in finance and property ownership. They play a big role in making sure that loans are secure and that lenders feel confident giving out money.

Understanding voluntary liens can help anyone looking to buy property or secure a loan. It plays a crucial role in real estate transactions and can affect the buying process.

What is a Voluntary Lien?

A voluntary lien happens when a property owner willingly gives someone else a legal claim to their property as a guarantee for a loan.

The property owner agrees to this arrangement with the lender, using the property as a kind of backup if they can't pay back the loan.

If the borrower fails to make the required payments, the lender can take the property to recover the money.

This setup helps lenders feel secure about lending money because they know they have the property as collateral.

Voluntary liens are common in situations like mortgages, where the house itself secures the loan. Understanding this concept is key for anyone dealing with property and loans.

How Voluntary Lien Works

A voluntary lien works by allowing a property owner to use their property as a guarantee for a loan. The property owner agrees to give the lender a legal claim to the property, which means the lender can take the property if the loan isn’t repaid.

This agreement is made willingly by both parties - for example, when someone takes out a mortgage, they give the bank a lien on their house. If the mortgage payments aren’t made, the bank can take the house to recover the money.

This system helps lenders feel safe about lending because they know they have the property as security. Understanding this process is important for anyone borrowing money with property involved.

Types of Property that Fall Under Voluntary Lien

Voluntary liens can be placed on various types of property. The most common type is real estate - houses, apartments, land, etc. However, they can also be placed on personal property such as vehicles or other valuable assets.

For instance, if someone takes out a car loan, the lender may put a voluntary lien on the vehicle until the loan is paid off - this means that if the borrower defaults on their payments, the lender can repossess the car to recoup their losses.

Real estate and personal property are not the only types of assets that can have voluntary liens. Businesses can also use their tangible and intangible assets as collateral for loans, such as inventory or intellectual property.

Difference Between Voluntary and Involuntary Liens

The key difference between voluntary and involuntary liens is the willingness of the property owner - as mentioned, a voluntary lien agreement is made willingly by both parties.

On the other hand, an involuntary lien is placed on a property without the owner's consent - involuntary liens are usually court-ordered and can occur for various reasons such as unpaid taxes, lawsuits, or debts owed to creditors.

It is important to note that involuntary liens take precedence over voluntary liens in terms of repayment.

Conclusion

Voluntary liens play an essential role in the lending industry by providing security for lenders and allowing borrowers to access credit. It is crucial for borrowers to fully understand the implications of placing a voluntary lien on their property and ensure they are able to fulfill their repayment obligations.

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Retail Options Traders’ Behaviour

Retail investors are individual, non-professional investors who buy and sell securities, such as stocks, options, and mutual funds, for their personal accounts rather than for an organization or institution. Unlike institutional investors, who manage large sums of money on behalf of clients or large entities, retail investors typically trade in smaller quantities and often use online brokerage accounts to facilitate their transactions.

A considerable amount of research has been devoted to studying retail investors' behaviour. A recent paper by the CBOE [1] utilizes its own data and refutes some academic research findings. The author pointed out,

Utilizing Cboe data focused on orders initiated by retail platform customers and executed on Cboe Options Exchange (C1), we observe a noteworthy presence of retail investors in the options market. Their participation has grown substantially from 18% to 31% between the fourth quarter of 2019 and the fourth quarter of 2023, underscoring their evolving role.

In contrast to recent academic research on retail options trading, which frequently overlooks complex orders initiated by retail investors, our analysis of open positions in terms of notional value reveals that retail investors' complex orders accounted for 58% to 76% of retail open positions during the same period.4 This challenges the prevailing assumption that retail investors exclusively maintain long positions. Our study unveils the versatility of retail investors' trading strategies.

…our analysis of market maker order imbalance in SPX options over a longer historical window shows a significant reduction since mid-2020. The monthly market maker order imbalance has decreased from -14% in December 2016 to -12% in May 2023. This finding challenges the notion that the recent growth of 0DTE SPX options has increased market maker order imbalance.

In our robustness analysis, we exclude SPX options from the sample. This analysis reveals that retail trades represent 32% to 40% of the non-SPX options traded on C1 from the fourth quarter of 2019 to the fourth quarter of 2023 in terms of notional value.

This research by the CBOE, using more complete data, sheds light on the behaviour of retail options traders. It provides more insight into the changing dynamics of the options markets.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Selina Han, Unveiling the Sophistication: Understanding Retail Investors' Trading Behavior in the U.S. Options Market, May 2024, CBOE

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Syndicate: Definition, Types, Importance, Meaning, Examples

Syndicates play a big role in today's business world - they are important because they bring together different corporations to achieve common goals.

This teamwork helps in sharing resources and reducing risks. By working together, companies can tackle bigger projects and reach wider markets.

Understanding syndicates can help people see how businesses can grow stronger through collaboration and shared efforts.

What is a Syndicate?

A syndicate is when businesses team up temporarily to handle big projects that are tough to manage alone.

By working together, they can share both resources and risks. This teamwork makes big tasks easier and spreads out the potential losses.

For example, a group of investment banks might join forces to launch a new set of stocks.

In simple words, a syndicate is a temporary partnership between two or more companies to achieve a common objective.

So when companies form a syndicate, they pool resources and expertise to tackle tasks that would be difficult to handle individually.

Different Types of Syndicates

There are mainly three types of syndicates: Business syndicates, Finance syndicates, and Insurance syndicates.

1. Business syndicates

A business syndicate brings together different companies to combine their resources and skills for a specific project.

For instance, real estate firms and construction companies might team up to work on a large development project.

By joining forces, they can share the workload and make the most of their combined expertise. This approach helps them tackle bigger challenges and complete projects that would be too difficult to handle alone.

2. Finance syndicates

A financial syndicate is when a group of banks or investors comes together to lend money to one business venture. This team-up is temporary and helps spread the risk among all the participants.

By pooling their funds, they can provide a larger loan than any single bank or investor could offer on their own. This collaboration makes it easier for big projects to get the funding they need to move forward.

3. Insurance syndicates

An insurance syndicate is a group of companies and underwriters that join forces to cover risks and pay claims, much like an insurance company.

These groups work together to secure industries or properties that are either high-risk or very valuable.

By spreading the risk among multiple parties, they can provide coverage for situations that would be too challenging for one company to handle alone.

Importance of Syndicate

Syndicates are important because they bring together different companies to tackle big challenges. By pooling resources and expertise, syndicates can handle projects that would be too tough for one company alone.

This teamwork helps spread the risk, making it safer for businesses to invest in large ventures. Syndicates also allow companies to share their strengths and knowledge, leading to better results.

Whether it's in finance, insurance, or real estate, syndicates enable businesses to take on bigger projects and reach new heights. This collaboration makes it easier to achieve goals and drive growth in various industries.

Conclusion

Syndicates are a big part of the business world - they not only bring together companies but also help reduce risks and drive growth. By collaborating, businesses can take on bigger projects, provide larger loans, and cover high-risk ventures that would be too challenging for one company alone. In simple terms, syndicates make it easier for big projects to get the funding they need and move forward successfully.

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Modeling Short-term Implied Volatilities in the Heston Stochastic Volatility Model

Stochastic volatility models, unlike constant volatility models, which assume a fixed level of volatility, allow volatility to change. These models, such as the Heston model, introduce an additional stochastic process to account for the variability in volatility, providing a more nuanced understanding of market dynamics. By incorporating factors like mean reversion and volatility of volatility, stochastic volatility models offer a robust framework for pricing derivatives, managing risks, and improving investment strategies.

Despite their advantages, stochastic volatility models have difficulty in accurately characterizing both the flatness of long-term implied volatility (IV) curves and the steep curvature of short-term ones. Reference [1] addresses this issue by introducing a term-structure-based correction to the volatility of volatility (vol-vol) term in the classical Heston stochastic volatility model. The authors pointed out,

In this paper, we propose a novel and simple approach to precisely capture the shapes of implied volatility of real options with all maturities simultaneously, by introducing a term-structure-based correction to the volatility of volatility term of the classical Heston stochastic volatility model. Numerical experiments and empirical results show that the introduction of the term-structure-based correction term surely overcomes the deficiency of the classical Heston model in capturing the short-term option IVs, thus improving notably the quoting performance of the Heston model for the whole options.

Although the classical Heston stochastic volatility model is used as the plant model in this paper, this work can be easily extended to other kinds of stochastic volatility models. In addition, for future research, one can consider embedding the strike of option into the correction function to reinforce the model’s ability to characterize the whole surface of the implied volatility of option accurately.

In brief, both short- and long-term IVs are accurately modeled in the new Heston variant.

This paper improves the existing Heston model. Thus, it helps portfolio managers and risk managers to better manage the risks of investment portfolios.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Youfa Sun, Yishan Gong, Xinyuan Wang & Caiyan Liu, A novel term-structure-based Heston model for implied volatility surface, International Journal of Computer Mathematics, 1–24.

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Real Account: Definition, Example, Meaning, vs Nominal Account,

Accounts in accounting are systematic records that categorize and track financial transactions related to a specific aspect of a business. They serve as the building blocks of financial statements, providing a structured way to organize and report financial information. They may have several types based on specific criteria. One of these types is real accounts.

What is a Real Account?

Real accounts in accounting are fundamental components that represent tangible assets, liabilities, and equity within a company's financial structure. These accounts are referred to as "real" because they pertain to physical or financial entities that exist in reality, such as cash, inventory, accounts payable, loans, property, and equipment.

Real accounts help maintain accurate financial records and provide a continuous snapshot of the company's financial position over time. Unlike nominal accounts, which are temporary and reset at the end of each accounting period, real accounts are permanent, and their balances are carried forward from one period to the next.

How does a Real Account work?

Real accounts operate within an organization's accounting system by systematically recording tangible assets, liabilities, and equity. These accounts are permanent and maintain ongoing balances carrying forward from one accounting period to the next. They encompass assets like cash, inventory, property, and equipment, liabilities such as accounts payable and loans payable, and equity components like owner's equity and retained earnings.

The functionality of real accounts extends beyond transaction recording to facilitate continuous monitoring and assessment of a company's financial health and performance. By maintaining accurate and up-to-date balances, real accounts provide a reliable snapshot of the organization's assets, liabilities, and equity at any given time. This information is crucial for stakeholders, including investors, creditors, and management.

What are the differences between Nominal and Real Accounts?

The differences between nominal and real accounts come from different aspects, some of which are below.

Nature

Nominal accounts record transactions related to revenues, expenses, gains, and losses. They capture the flow of income and expenses over a specific period, such as sales revenue, salaries, rent, interest income, etc.

On the other hand, real accounts deal with tangible assets, liabilities, and equity. They record transactions related to physical or financial entities that exist in reality, such as cash, inventory, accounts payable, property, plant, and equipment.

Treatment

At the end of each accounting period, nominal accounts are closed by transferring their balances to the retained earnings or income summary account. This process resets their balances to zero to start fresh for the next accounting period.

Real Accounts are not closed at the end of accounting periods. Instead, their balances are carried forward to the next period. This continuous balance-carrying characteristic makes them permanent accounts.

Impact

Transactions recorded in nominal accounts directly impact the income statement. They determine the company's net income or net loss for the period, influencing profitability measures and performance evaluation.

Real accounts primarily affect the balance sheet. They contribute to the presentation of assets, liabilities, and equity in the company's financial position, reflecting the resources, obligations, and ownership interests.

Conclusion

A real account is a systematic record of financial transactions for an asset with a physical form. They relate to tangible assets and get the name "real". Although the classification does not impact accounting, the categorization is necessary to differentiate between real and nominal accounts. The differences between the two come from their nature, treatment, and impact on the financial statements.

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Realized Volatility, the Good and the Bad

Realized volatility (RV) refers to the actual movement of an asset's price over a specific period, typically measured using high-frequency data. Unlike implied volatility, which is derived from options prices and reflects market expectations, realized volatility is computed from historical price data and provides an empirical measure of how much an asset's price has fluctuated in the past.

Reference [1] further divides realized volatility into good and bad RV. It derives good and bad RV from the square sum of positive and negative intraday returns within a day, respectively. The authors then study the impact of the volatility risk premium on realized volatility, as well as on good and bad RV, under different market conditions. They pointed out,

Overall. whether it's a call option or a put option, the prediction model containing the implied information of options can predict the daily realized volatility significantly better than the weekly and monthly forecast horizons. If we further classify options according to moneyness, we can conclude that the implied information content of deep out-of-the-money options has the highest prediction accuracy for weekly good realized volatility. Thus, it is very meaningful for this paper to divide the realized volatility into good and bad volatilities and study the differential performance of volatility risk premium between them, which can provide a new perspective for investors to the changes of future stock market volatility. Especially,  investors need to grasp the good and bad volatilities relationship of the underlying securities, be alert to the impact of the implied information changes in options market on the stock market, and grasp the stock market sentiment from a global perspective and sector perspective so as to improve investment.

In brief, the paper shows that the volatility risk premium has a significant influence on both good and bad volatilities. In particular, the impact of the volatility risk premium on good volatility is significantly stronger than that on bad volatility. In addition, the results show that the implied information content of deep out-of-the-money options has the highest prediction accuracy for weekly good realized volatility.

We note that the study was conducted in the Chinese market. However, the framework can be easily applied to the US and any other developed market.

Let us know what you think in the comments below or in the discussion forum.

References

[1]  Z Li, J Shen, W Xiao, Volatility risk premium, good volatility and bad volatility: Evidence from SSE 50 ETF options,  The North American Journal of Economics and Finance, Volume 74, September 2024, 102206

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Input Cost: Definition, Types, Calculation, Examples, vs. Output Cost

Companies must know the total cost of producing a product or rendering services. This cost has various components, one of which is input cost.

What is Input Cost?

Input cost refers to the total expenditure incurred by a business in acquiring the necessary resources and materials for its production processes. It includes expenses such as raw materials, labour costs, equipment, utilities, and any other resources essential for manufacturing goods or delivering services. Effectively managing input costs is crucial for companies.

Businesses can control input costs by implementing strategies such as negotiating favourable terms with suppliers, adopting cost-effective production methods, optimizing resource utilization, and closely monitoring expenses. By managing input costs effectively, companies can enhance their financial performance, improve their bottom line, and achieve greater operational efficiency.

What are the components of Input Cost?

Input costs have three primary components listed below.

Direct materials

Direct materials are the fundamental resources used directly in the production process to manufacture goods or deliver services. Examples include raw metals, chemicals, fabrics, and agricultural products.

Direct labor

Direct labour encompasses the expenses of hiring and compensating employees involved in production activities. It includes wages, salaries, benefits, training costs, and payroll taxes.

Manufacturing overheads

Manufacturing overheads are indirect costs incurred during the production process that are not directly attributable to specific output units. They include expenses such as rent for production facilities, utilities, depreciation of equipment, maintenance costs, insurance, and other operating expenses essential for manufacturing operations.

What are the differences between Input and Output Cost?

The differences between input and output costs come from two primary aspects: definition and timing.

Definition

Input cost refers to the expenses incurred by a business in acquiring or producing the raw materials, components, labour, and other resources needed to initiate and carry out the production process. Inversely, Output cost, also known as production cost or cost of goods sold (COGS), refers to the total cost incurred by a business in producing and delivering goods or services to customers.

Timing

Input costs occur before and during the production process. They are the costs associated with inputs to create goods or deliver services. On the other hand, output costs are incurred after the production process is complete, representing the costs associated with producing and delivering the final output to customers.

How to calculate Input Cost?

Calculating input cost involves identifying and totaling all expenses of acquiring or producing raw materials, labour, and other resources essential for the production process. It includes costs such as raw material purchases, labour wages, benefits, payroll taxes, and manufacturing overheads like utilities, rent, depreciation, and maintenance expenses.

The formula to calculate input cost is as below.

Input cost = Raw material cost + Labor cost + Manufacturing overheads

Example

Red Co. recently purchased 10,000 units of raw material X for $2 per unit. Additionally, the company employs 50 workers who work 8 hours a day at an average wage rate of $15 per hour for 20 days. Furthermore, Red Co. incurred manufacturing overhead expenses totaling $50,000.

Based on this information, the input cost for Red Co. will be as follows.

Input cost = Raw material cost + Labor cost + Manufacturing overheads

Input cost = (10,000 x $2) + (8 hours x 20 days x $15 x 50 workers) + $50,000

Input cost = $20,000 + $120,000 + $50,000

Input cost = $190,000

Conclusion

Input cost consists of all the expenses incurred in producing an item or rendering a service. It includes three components: direct material, direct labour, and manufacturing overheads. Together, the sum of these components constitutes the total input cost for a company. However, input cost differs from output cost based on definition and timing.

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Stock Returns After Extreme Loss Events

An extreme loss event in the stock market refers to a sudden and significant decline in stock prices, often resulting from unexpected and severe market conditions. These events, also known as market crashes or financial crises, can be triggered by a variety of factors including economic downturns, geopolitical tensions, natural disasters, or systemic failures within the financial system.

Reference [1] studies the returns of US stocks after they suffer an extreme loss event. It defines an extreme loss event as a negative return lower than 97.5% of a given asset's daily returns. The authors pointed out,

This study analyzes the daily returns of 2,651 equities in the Russell 3000 Index continuously traded between January 2, 1950, or the date of the IPO, and early 2019. We examine extreme loss events for assets in our sample, which we define as a negative return lower than 97.5% of this asset's daily returns.

This study finds that the average extreme loss is -8.2105%...However, on average, we observe that the equities realize a daily return of 0.8459% on the first day after an extreme loss event and a cumulative return of 1.8099% during five trading days after the event that counts for only 20.23%, i.e., 1.8099%/8.9445%, of the full recovery.

The gradual and partial recovery from the extreme loss suggests that overreaction and a panic sentiment explain approximately 20% of the loss and that extreme losses are mainly due to materialized reasons for the revaluation of the asset…

The results strongly support an extremely negative loss reversal strategy. Investors can profit if they buy an asset on the day of its extreme loss event, right before the market closes, then sell it within five trading days when the market closes. On average, this strategy can generate a daily return of 0.8459% during the first trading day, and 1.8099% in total during five trading days after entering the position.

In short, stocks usually recover after an extreme loss event, and a winning trading strategy can be designed to exploit this tendency. Furthermore, the instant loss on the event day is caused by investors’ overreaction (20%) and revaluation (80%) of the asset.

Let us know what you think in the comments below or in the discussion forum.

References

[1] X. Guo, H. Dong, and G. A. Patterson, Equity Returns Around Extreme Loss: A Stochastic Event Approach, American Business Review, May 2024, Vol.27(1) 207 - 220

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