Enhancing Option Pricing & Portfolio Strategies: The Pioneering Work of Lisa Borland and the Kelly Criterion

This article is my narrative series on my prior experience as MD of Evnine & Associates for 13+ years and is not endorsed by any organization or to be perceived as a representation of any organization.

During my 13+ year career at Evnine & Associates, a quantitative market neutral strategy RIA, I was fortunate to work with extremely bright scientists who've made stellar contributions to quantitative finance. The firm itself had its origin in collaboration with the Nobel laureate Myron Scholes. It began its history as Scholes Consulting but later renamed itself after Jeremy Evnine Ph.D., a renowned academician of his own credited for designing the highly effective portfolio insurance system for Barclays Global Investment Advisors, jettisoned his proprietary trading group from his Financial Engineering consulting business. With such a pedigree and tutelage, it must have been destined that a refreshed and better derivative pricing method would later be invented at his firm.

This brief memoir attempts to focus on this refresh by Lisa Borland, Ph.D., and another well-known financial modeling formula that had a significant impact on how Evnine & Associates managed to generate its stellar 15-year track record with an Information Ratio of 1.1, net to investors.?

Lisa Borland, Ph.D., joined Jeremy’s firm back in 2000 and since then has made significant contributions to the field of financial modeling, particularly in enhancing traditional models such as the Black-Scholes Option Pricing Model. Her research focuses on refining the assumptions and methodologies underlying these models to produce more accurate and robust financial predictions. By improving volatility modeling and incorporating more realistic market behaviors, her work provides valuable insights for both investors and risk managers.

In the realm of portfolio management, the Kelly Criterion is a well-established mathematical formula used to determine the optimal size of investments to maximize long-term growth. It provides a systematic approach to capital allocation, helping investors manage risk while seeking to grow their portfolios efficiently. When applied correctly, the Kelly Criterion can prevent over-leveraging while allowing for the strategic deployment of capital.

At Evnine & Associates, Inc., these two methodologies were brought together in a successful collaboration. Leveraging Lisa Borland’s enhanced financial models alongside the Kelly Criterion for strategic capital allocation, the firm managed to further enhance its revered performance of its proprietary market-neutral signal. This impressive track record highlighted the effectiveness of combining sophisticated quantitative models with sound risk management principles, demonstrating a unique approach to sustained success in the investment world.

Who is Lisa Borland?

Lisa Borland, Ph.D., is a physicist and quantitative researcher known for her innovative work in financial modeling. With a background in physics, she applied her expertise to finance, particularly in understanding market dynamics and pricing models.

Lisa’s academic roots lie in complex systems and statistical mechanics. She transitioned from academia to finance, applying her knowledge to financial markets, particularly in option pricing and risk management. Her career includes significant contributions to quantitative finance, working alongside experts at firms like Evnine & Associates, Inc.

Overview of Her Research in Extending the Black-Scholes Model

The Black-Scholes model, a groundbreaking formula for pricing options, assumes a log-normal distribution of asset returns and constant volatility. Borland’s research recognized the limitations of these assumptions, especially in capturing real-world market behaviors, such as fat tails and volatility clustering. Her work focused on creating a more robust and adaptable framework that could better reflect market realities.

Enhancements Over Black-Scholes

1. Explanation of Traditional Black-Scholes Limitations

The Black-Scholes model has been a fundamental tool in finance for decades, but it has notable limitations. Its assumptions of constant volatility and log-normal distribution of returns often fail to account for market anomalies. Real markets exhibit features like skewness, kurtosis (fat tails), and volatility that change over time, which the traditional model struggles to handle.

2. How Borland’s Model Addressed These Issues

? Integration of Non-Gaussian Distributions: Borland introduced non-Gaussian distributions to account for skewness and heavy tails in asset returns. This provided a more accurate depiction of real market conditions, where extreme events (tail risks) are more common than the normal distribution would suggest.

? Use of Dynamic Volatility Models: Her work implemented models that allowed volatility to vary over time, making it a dynamic factor rather than a fixed one. This is crucial for better reflecting market movements and risk.

? Inclusion of Stochastic Processes: Borland’s approach included stochastic processes to account for phenomena such as volatility clustering and leverage effects. This enabled the model to adapt to real-world events, offering a more comprehensive risk assessment and pricing mechanism.

Impact and Applications

Borland’s enhancements have had significant implications in the field of quantitative finance. By offering a more realistic and adaptable approach to option pricing, her models provide better risk assessment tools for traders and portfolio managers. These models can be applied across various financial instruments, leading to more accurate pricing, improved hedging strategies, and enhanced risk management in turbulent market conditions. Her model has been battle-tested and is being used today traders and portfolio managers worldwide.

Who is Jack Kelly?

Jack Kelly, more formally John Larry Kelly Jr., was a researcher and scientist at Bell Labs, a private laboratory known to incubate the smartest of our kind, including former fellows such as Jeremy Evnine. Kelly is best known for developing the Kelly Criterion in 1956, a formula that has had profound implications in both telecommunications and finance. Kelly’s background was in physics and electrical engineering, and his work laid the groundwork for this groundbreaking approach to optimizing bet sizing.

Brief Background on the Origin of the Kelly Criterion

The Kelly Criterion was originally introduced in Kelly’s paper, “A New Interpretation of Information Rate.” The idea stemmed from Claude Shannon’s information theory, where Kelly sought to apply mathematical principles to determine optimal bet sizing in gambling. By considering probabilities and outcomes, the Kelly Criterion maximized the logarithmic growth of capital over time, leading to consistent, long-term gains rather than short-term wins.

Theoretical Basis and How It Determines Optimal Bet Sizing

The Kelly Criterion formula helps to determine the optimal amount to wager on a particular bet by considering the probabilities of winning and losing, as well as the payout ratios. The fundamental idea is to maximize the expected logarithm of wealth, ensuring long-term capital growth.

The formula can be expressed as:

?The formula helps determine the proportion of the capital that should be allocated to a specific bet or investment to maximize long-term growth.

?If the expected probability ( p ) and the odds ( b ) are both favorable, the formula suggests a higher allocation. Conversely, if the probability of success or the potential return is lower, it recommends reducing exposure to manage risk effectively.

By calculating this optimal fraction, the Kelly Criterion prevents over-betting (which could lead to ruin) and under-betting (which leads to missed opportunities for growth).

Application in Finance

While initially developed for gambling, the Kelly Criterion found a natural application in the finance world. In portfolio management, it is used to determine how much capital to allocate to different investments by considering expected returns and risks. Its main appeal lies in balancing the trade-off between risk and reward, aiming to maximize long-term growth.

Benefits: Maximizing Long-Term Growth While Controlling for Risk

The Kelly Criterion is favored because it helps in controlling risks by setting limits on how much should be invested in a particular opportunity. Unlike more conservative approaches, it does not advocate for risk aversion but rather for risk optimization. The main benefits include:

? Maximizing Long-Term Growth: Focusing on the growth rate of wealth ensures the portfolio can compound more effectively over time.

? Risk Management: Prevents excessive risk-taking by capping the amount invested based on probabilities and outcomes, thus lowering the chances of significant losses.

The Kelly Criterion has been widely accepted by traders and investors who look for systematic approaches to optimize asset allocation, blending it with strategies like Borland’s financial models to form robust investment frameworks.

Integrating Borland’s Work with the Kelly Criterion

Synergies Between Advanced Option Pricing and Kelly Criterion

The integration of Lisa Borland’s enhanced models with the Kelly Criterion creates a powerful synergy in portfolio management. Traditional financial models, like Black-Scholes, may fail to capture the full spectrum of market behavior, leading to misestimations in risk and return calculations. Borland’s models, which incorporate more realistic distributions and dynamic volatility, provide a refined input for the Kelly formula, ensuring more precise probability assessments when determining optimal asset allocation.

How Borland’s Models Offer Better Probability Distributions Enhancing the Kelly Formula

Borland’s research focuses on addressing the limitations of models that assume constant volatility and a normal distribution of returns. By integrating non-Gaussian distributions, her models capture the skewness and fat tails observed in actual markets. This improves the accuracy of the input probabilities in the Kelly formula, leading to more reliable decisions on how much capital to invest in a given position reducing the likelihood of over or under-investing.

Practical Benefits: Improved Precision in Risk Assessment and Decision-Making

The integration leads to practical benefits by enhancing the precision of risk assessment. With a better understanding of asset behavior, portfolio managers can use the Kelly Criterion to determine the optimal bet sizes, factoring in the enhanced volatility predictions and tail risk considerations. This combination reduces the chances of catastrophic losses and helps in maintaining consistent, long-term growth.

Better Risk-Adjusted Returns

One of the key advantages of combining these methodologies is achieving better risk-adjusted returns. Borland’s models allow for more accurate estimations of future volatility and potential price movements. This refined input helps the Kelly Criterion in calculating the optimal proportion of capital to allocate, maximizing returns while controlling risk.

How Incorporating Accurate Volatility Predictions Determines the Optimal Bet Size

For instance, a more accurate prediction of a stock’s volatility over a period enables the Kelly formula to adjust the bet size based on realistic risk levels. If traditional models underestimated the probability of extreme price movements, the Kelly Criterion might suggest overexposure. However, with Borland’s model providing more accurate forecasts, the calculated bet size would better reflect true market conditions, preventing excessive risk-taking.

Reducing Overexposure to Risky Assets by Accounting for Tail Risks and Market Skews

By incorporating tail risks and accounting for skewed distributions, Borland’s models help reduce overexposure to high-risk assets. Traditional methods might miss out on extreme market movements, leading to unanticipated losses. The enhanced models capture these risks, and when used with the Kelly Criterion, they guide more conservative and balanced allocations. This ensures that portfolio managers maintain exposure levels that align with realistic risk scenarios, avoiding the pitfalls of over-leveraging during volatile periods. Advantages of Using Borland’s Model and Kelly Criterion Together

More Accurate Risk and Reward Assessment

Combining Borland’s advanced option pricing models with the Kelly Criterion allows for a more precise understanding of risk and reward. Traditional models often underestimate true market volatility by assuming a normal distribution, but Borland’s models incorporate non-Gaussian distributions that reflect actual market conditions, such as skewness and fat tails. This leads to a better assessment of true volatility, enabling the Kelly Criterion to optimize position sizes more accurately, ensuring each bet aligns with realistic risk projections and expected returns.

Optimization of Returns by Calibrating Position Sizes Accurately

The Kelly Criterion is designed to maximize long-term capital growth by determining the optimal bet size based on the probability of success and potential payout. With Borland’s enhanced volatility predictions and more accurate risk assessments, the application of the Kelly formula becomes even more precise. This synergy ensures that capital is allocated in a way that maximizes returns while controlling for risk, preventing over-exposure during periods of high volatility and allowing for more aggressive positioning when conditions are favorable.

Superior Portfolio Diversification

The combination of Borland’s models and the Kelly Criterion also offers significant advantages in managing portfolio diversification. Enhanced models help in understanding the risk associated with derivative positions more comprehensively. This leads to improved decision-making about asset allocation, allowing investors to diversify their portfolios more effectively. By blending insights from advanced option pricing and the probabilistic advantage of the Kelly Criterion, portfolio managers can balance their risk exposure across multiple assets, thus reducing the potential for heavy losses from any single position.

Using Enhanced Models to Manage Derivative Exposure

Borland’s improvements to traditional pricing models mean a better grasp of the true behavior of options and other derivatives. This can prevent mispricing and subsequent misallocation of funds. The integration with the Kelly Criterion allows for sizing positions based on more realistic data, leading to more stable and predictable returns. This approach is particularly valuable in managing derivatives, where accurate assessments of potential risks and rewards are crucial for maintaining healthy portfolios.

Combining Insights from Advanced Option Pricing with the Probabilistic Advantage

At the core of this integration lies a deeper understanding of probabilistic outcomes. Borland’s models enhance the ability to predict market moves, while the Kelly Criterion provides a systematic method to capitalize on these predictions. Together, they create a framework that not only enhances potential returns but also limits exposure to unpredictable, high-risk scenarios. This alignment makes the overall portfolio strategy more robust, adaptable, and effective in both calm and volatile markets.

The synergy between Borland’s advanced models and the Kelly Criterion is the deeper probabilistic insight it offers. Borland’s non-Gaussian distributions allow for more realistic modeling of market events, which, when paired with the Kelly Criterion’s focus on maximizing long-term growth, provides a strategic framework. Together, they help investors capture profitable opportunities while managing risks prudently, making the overall portfolio strategy more robust and adaptable to various market conditions.

Conclusion

The integration of Lisa Borland’s enhanced financial models with the Kelly Criterion represents a significant advancement in the field of portfolio management. By addressing the limitations of traditional models, Borland’s work provides more accurate risk assessments, dynamic volatility predictions, and real-world adaptability. Combined with the probabilistic insights of the Kelly Criterion, this approach optimizes position sizing and capital allocation, leading to better risk-adjusted returns and superior diversification strategies. These improvements not only enhance current financial modeling but also pave the way for future innovations in trading and investment strategies.

The synergy of these methods serves as a testament to the power of blending advanced mathematical research with practical financial tools. This combination offers a sophisticated framework that adapts to changing market conditions, ensuring more reliable and resilient investment strategies. For those looking to stay ahead in the rapidly evolving world of finance, understanding and applying these concepts can provide a distinct competitive edge.

For professionals and enthusiasts interested in cutting-edge financial strategies, exploring Borland’s work is a must. Her contributions have laid the groundwork for more accurate and adaptable financial models, and there’s still much to learn and discover from her research.

Feel free to reach out or connect if you’d like to discuss these strategies further. For those keen on diving deeper, check out Borland’s publications and related research to gain more insights into how these advanced models can be applied to optimize financial portfolios and strategies.

Sources

For an entertaining read on Jack Kelly, Claude Shannon, and Edward O Thorpe, whose alpha model was the basis of Evnine & Associates' statistical arbitrage strategy (that's for another topic), I refer you to:

Poundstone, William, Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street, Published by Hill & Wang, September 2006.

Referenced Published Research

Borland, Lisa, Option Pricing Formulas Based on a Non-Gaussian Stock Price Model, Iris Financial Engineering & Systems, October 2002.

Kelly, Jack L. Jr., A New Interpretation of Information Rate, AT&T Bell Laboratories, March 1956.

Scholes, Myron and Black, Fischer, The Pricing of Options and Corporate Liabilities, The Journal of Political Economy Vol. 18 No. 3, The University of Chicago Press, June 1973.

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