Reducing Path Dependency in Options PnL

The profit and loss of an options trading strategy can be path-dependent, meaning that interim price movements, not just the final outcome, significantly influence profits and losses due to factors like dynamic hedging, early exercise risk, and volatility shifts.

A well-known example is the PnL of a delta-hedged option position, where the outcome depends on the path. Even if we estimate the realized volatility correctly, we still cannot determine the exact profit or loss, because the PnL is path-dependent.

How can we reduce this path dependency?

Reference [1] proposed the use of a laddering technique. The authors pointed out,

Laddering is a practical and effective solution to mitigate the risks of path dependency in option income strategies. Unlike single-path strategies that rely on fixed expirations and trade dates, laddering involves staggering option expirations and strike levels across different time frames. This approach reduces reliance on specific market outcomes, creating a smoother income stream and a more resilient portfolio structure.

Exhibit 28.2 highlights the significant benefits of laddering by combining one-month period for each trading day of the month. The results demonstrate that laddered strategies reduce return variability compared to single-path strategies, which depend heavily on specific market conditions at expiration. By diversifying expirations and strikes, laddering ensures a steady flow of income while minimizing the impact of adverse market events. The laddering approach may also improve liquidity, enabling portfolio managers to incrementally adjust their portfolios more effectively in response to market changes. This makes laddering an indispensable tool for managing path dependency and achieving consistent portfolio performance.

In short, the author advocates the commonly used approach of diversification, specifically, diversifying entry times and strike selections.

This approach is reasonable and widely accepted. However, we note that what the author refers to here is more accurately a mitigation of the negative outcomes resulting from “unlucky” paths. In a covered call strategy, since no dynamic hedging is performed, the final PnL depends on the terminal distribution of the underlying only. Nevertheless, the same technique applies equally to strategies that involve dynamic hedging.

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

References

[1] John Burrello, Managing Path Dependency and Balancing Yield in Option Income Strategies, In: Fabozzi, F.J., de Jong, M. (eds) Derivatives Applications in Asset Management. Palgrave Macmillan, Cham.

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Harvesting the Equity Risk Premia Through Options

The equity risk premium refers to the excess return that investing in the stock market provides over a risk-free rate, typically represented by government bonds. It compensates investors for taking on the higher risk associated with equities. Estimating the equity risk premium is essential for asset allocation, valuation models, and long-term return expectations in portfolio management.

Reference [1] investigates the use of stock options to capitalize on the equity risk premium. It studied all the U.S. optionable stocks. The study first utilized a machine learning method to estimate expected stock returns (ESR). Then, each month, it sorted at-the-money call options by the ESR of the underlying stock and constructed a long-short portfolio: buying calls on high-ESR stocks and selling calls on low-ESR stocks, holding these positions to maturity. The authors pointed out,

We study via a simple test whether options are a useful tool to harvest the risk premia of the underlying stocks. We introduce a trading strategy that buys calls on stocks with high expected stock returns, and sells calls on stocks with low expected stock returns, and vice versa for puts. We find that these two trading strategies deliver surprisingly low returns, which do not even outperform a naive investment that simply buys all available call or put options, i.e., the “market”…

This finding has two important implications. First, it shows that options are not a useful tool to extract stock risk premia. Second, it implies that option prices are not independent of the underlying’s expected return—violating a central insight of option pricing theory. To corroborate our findings, we apply machine learning techniques to predict expected option returns and option prices. We find that variables predicting stock returns well, do barely predict option returns, but explain option prices well. Moreover, if we use our direct estimate of the expected stock return as a predictor variable, we again find that it predicts price levels well, but not returns.

Finally, we find violations of put-call-parity consistent with our result. In particular, the level of expected stock return is a strong predictor of the implied volatility spread between a pair of calls and puts. This suggest that options are priced such that they largely offset the effects of the underlying’s expected return on the expected option returns.

In short, the article concluded that,

• Options are not effective instruments for capturing stock risk premia,
• Option prices are influenced by the expected returns of the underlying stocks, which challenges a core assumption of traditional option pricing theory.

These findings are interesting and somewhat surprising. However, we note that they apply only to cross-sectional returns. As observed by the authors, if one has a directional bias, then simply buying calls can deliver respectable risk-adjusted returns. Hence, in the time-series momentum space, having a directional edge could be augmented by using options.

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

References

[1] d'Avernas, Adrien and Schlag, Christian and Sichert, Tobias and Sichert, Tobias and Waibel, Martin and Wang, Chunjie, Betting on Stocks with Options?, Swedish House of Finance Research Paper No. 2025-03 https://ift.tt/Ap1GTJQ

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Seasonality in Return Skewness: the Day-of-Week Effect

Seasonality is a well-studied phenomenon in financial markets. It manifests in returns, volatility, and the volatility risk premium. Despite being well documented, little (if any) research has been carried out on the seasonality of skew.

Reference [1] fills this gap by studying the day-of-week effect in return skewness. It analyzes the five leading stock indices in the US markets from 1928 to 2023. The authors pointed out,

The main contribution of our paper is introducing the day-of-the-week effect into time-varying skewness specifications for stock market return models. In the current study, we find that skewness on Mondays is negative and lower than on Fridays. This suggests that an investor might anticipate frequent small gains and occasional significant losses on Mondays compared to on Fridays. In line with the existing literature, we also report that daily returns are typically negative on Mondays, and expected Monday returns fall below Friday returns across the five leading US stock market indices, indicating the pervasive and persistent nature of the weekend effect. Moreover, Monday returns exhibit higher volatility than Friday returns do. These results are robust across various specifications and subsamples.

Thus, the strategies adopted for investment on days with negative skewness may need to be tailored to manage the inherent risk of substantial losses despite the allure of frequent small gains. Hedging strategies, particularly through options, are vital for downside protection. Emphasising low or no-leverage positions is crucial in such scenarios to mitigate the potential for amplified losses…

In short, Mondays exhibit the lowest and most negative skewness. This research also confirms other research findings, notably,

• Daily returns are typically negative on Mondays, and
• Monday returns show higher volatility than other days.

An interesting follow-up would be to examine the seasonality of the skew risk premium.

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

References

[1] N. Hande Sevgi, Mehmet Baha Karan &M. Hakan Berument, Day-of-the-week effect on stock market returns, volatility, and skewness,  1-24, 2025

Originally Published Here: Seasonality in Return Skewness: the Day-of-Week Effect

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Investor Behavior in Crypto During Geopolitical Shocks

Herd behavior refers to the tendency of investors to follow the actions of a larger group, often ignoring their own analysis or information. This collective movement can lead to asset bubbles during bull markets and sharp sell-offs during downturns. Understanding herd behavior is essential for identifying potential mispricings and avoiding emotionally driven decisions.

Herding behavior has been well studied in the equity markets but less so in the cryptocurrency market. One might expect stronger herding in crypto due to the prevalence of young, inexperienced traders and the fact that crypto markets are under-regulated, less transparent, and highly volatile. However, existing studies have produced inconclusive results.

Reference [1] extends the research on herding in the crypto space by examining behavior during major geopolitical events, such as the COVID-19 pandemic and the Russia–Ukraine war. The authors pointed out,

The main findings of this study are summarized as follows. First, severe herd behavior is documented over the entire sample period when considering abnormal impacts of the GPR and the GPR Threat. Second, herd behavior in cryptocurrency markets is not symmetric, presenting stronger results during bearish markets. Again, we find severe asymmetric herding with the GPR and the GPR Threat. We argue that a role of the GPR Act disappears because cryptocurrency traders subsume, digest, and analyze information related to geopolitical uncertainty since the news is released. Thus, cryptocurrency’s prices and its dispersions are already reflected. Actual realization does not play a role. Third, severe herd behavior during two recent extreme situations that are the COVID-19 pandemic and the Russia invasion to Ukraine are strongly observed in nearly all cases. Specifically, statistical significance of the GPR Act represents that an actual realization of adverse geopolitical events goes beyond investors’ expectations, creating a high uncertainty and subsequently reinforcing herding. Overall, we relate our findings to the “fear of missing out” (FOMO) phenomenon and the pump and dump schemes suggested by Baur and Dimpfl (2018).

In short, the authors found that herding intensifies during such events and is clearly present throughout these periods.

This research is an important contribution to behavioral finance in the crypto market, as it enhances understanding, supports regulators in designing more informed policies, and contributes to greater market stability.

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

References

[1] Phasin Wanidwaranan, Jutamas Wongkantarakorn, Chaiyuth Padungsaksawasdi, Geopolitical risk, herd behavior, and cryptocurrency market, The North American Journal of Economics and Finance Volume 80, September 2025, 102487

Article Source Here: Investor Behavior in Crypto During Geopolitical Shocks

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Hedging with Puts: Do Volatility and Skew Signals Work?

Portfolio hedging remains a complex and challenging task. A straightforward method to hedge an equity portfolio is to buy put options. However, this approach comes at a cost—the option premiums—leading to performance drag. As a result, many research studies are focused on designing effective hedging strategies that offer protection while minimizing costs.

Reference [1] presents the latest research in this area. It examines hedging schemes for equity portfolios using several signals, including MOM (momentum), TREND, HVOL (historical volatility), IVOL (implied volatility), and SKEW. The study also introduces a more refined rehedging strategy for put options:

• If, during the investment period, a put option’s delta falls to −0.9 or lower, the option is sold to lock in profits and avoid losing them in case of a sudden price reversal.
• Put options are bought when implied volatility is below 10%, as they are considered cheap. No position is taken if implied volatility is above 30%, to avoid overpaying for expensive options.

The authors pointed out,

The results from the backtests of the long-put strategy, presented in Table 5, also indicate that the TREND signal is the most effective among those tested for selecting the underlyings on which to take option positions. Specifically, the TREND signal substantially reduces the portfolio’s risk without sacrificing annual return when compared with the BASE signal, the equity-only portfolio, with no option positions. This suggests that the TREND signal offers a compelling balance between downside protection and performance preservation. The SKEW signal contributes positively to the GMV allocation, although it fails to show the same effectiveness under the EW allocation scheme. Consistent with the findings from the covered call strategy, the introduction of additional trading rules, TR1 and TR2, does not consistently improve the performance of the portfolios. Their impact appears to be in the best-case marginal and in most cases negative …

The bootstrapped results from Table 6 diverge from the ones of the backtests. The TREND signal no longer outperforms the BASE portfolio. Instead, the HVOL and IVOL signals emerge as the most effective, outperforming the BASE portfolio in risk-adjusted terms, with and without trading rules. The different findings from bootstraps vs. historical backtests indicate that the added value of these signals is dependent on the market regime.

In short, buying put options using the TREND signal appears to improve portfolio risk-adjusted returns. While SKEW and IVOL add little in backtests, they perform better in bootstrapped results, suggesting that the effectiveness of put protection strategies is regime-dependent.

This study offers a comprehensive evaluation of various hedging rules. There is no conclusive answer yet, implying that designing an efficient hedging strategy is complex and requires ongoing effort. Still, the article is a strong step in the right direction.

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

References

[1] Sylvestre Blanc, Emmanuel Fragnière, Francesc Naya, and Nils S. Tuchschmid, Option Strategies and Market Signals: Do They Add Value to Equity Portfolios?, FinTech 2025, 4(2), 25

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Applying Volatility Management Across Industries

Volatility management is a risk and portfolio management technique proposed by Moreira and Muir in 2017 [1]. It has since been widely adopted by industry practitioners. The technique relies on the idea that volatility is autocorrelated but only weakly correlated with future returns. Practically, this means increasing exposure to the underlying asset when volatility is low and decreasing exposure when volatility is high. This approach allows investors to improve risk-adjusted returns.

Reference [2] continues this line of research by applying volatility-managed techniques to U.S. industry portfolios. It uses four measures of volatility: one-month realized variance, one-month realized volatility, six-month exponentially weighted moving average (EWMA) of realized volatility, and GARCH-forecasted one-month volatility.

The author pointed out,

From my analysis, volatility management significantly improves the performance of nearly all sector allocations, providing evidence that volatility management can be a useful tool for investors intending to increase exposure to specific industries. Consistent with my prior belief, certain industries respond better to volatility management, including technology and defensive sectors. Although marginally similar in generating enhanced Sharpe ratios, volatility management using a six-month exponentially weighted moving average volatility is the most consistent in delivering strong results in the face of leverage constraints and transaction costs. The strategy boosts the Sharpe ratios for the technology, telecom, and utilities sectors by 27.6%, 30.5%, and 25.5%, respectively. This suggests that volatility management is not just theoretically appealing but practical for a mean-variance investor. However, the statistical significance of volatility-management strategies wanes when testing performance over selected subperiods and recessionary periods. Therefore, I provide evidence that the investors can confidently implement volatility-management strategies for the technology portfolio, over other industries, due to its economically and statistically significant improvements regardless of sample period and transaction costs.

In short, the article concluded that,

• Volatility management using a six-month EWMA volatility measure is the most consistent,
• The strategy improves Sharpe ratios in the technology, telecom, and utilities sectors, though not all sectors benefit equally. Technology performs best due to the persistence of its volatility,
• The statistical significance of volatility-managed strategies weakens when tested over selected subperiods and recessionary periods.

Have you applied volatility management techniques to your portfolio?

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

References

[1] Moreira, A., & Muir, T. (2017), Volatility-managed portfolios. Journal of Finance, 72(4), 1611–1644.

[2] Ryan Enney, Sector-Specific Volatility Management: Evidence from U.S. Equity Industry Portfolios, Claremont McKenna College, 2025

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Product Confusion: Why Retail Investors Lose Money in VIX ETPs

Behavioral finance has studied why retail investors lose money. We discussed one such study in a previous post. Retail investor losses can be attributed to, among other factors, overconfidence, overtrading, sensation seeking, issuers’ overpricing, etc.

Reference [1] observed that in the VIX ETP space, retail investors experienced an annualized return of -11.09%. The study investigates why investors lose money and proposes a new behavioral factor contributing to these losses: product confusion.

Specifically, retail investors mistakenly believe that VIX ETPs allow them to trade the VIX index directly. However, the VIX index is non-tradable, and VIX ETPs are actually linked to a VIX futures index, not the VIX index itself.

The authors pointed out,

As evidenced by the negative aggregate dollar profits from retail trading, I show that retail investors, in aggregate, incur losses in the VIX ETP market. With negative risk-adjusted returns on retail investors’ VIX ETP portfolio in normal and leveraged products, my results also suggest that the use of VIX ETPs as a means to acquire protection against surges in market volatility or stock market downturns appears to be insufficient in explaining losses. Instead, I show that retail trading would not be characterized by losses and poor selection and market timing if the VIX ETPs do in fact track the leverage-scaled VIX index. If retail investors trade VIX ETPs attempting to exploit the mean-reverting behavior or other predictable patterns of VIX, these trades would generally not be profitable since such predictable future movements of VIX are already priced in the VIX futures market and thereby in the VIX ETP market. Hence, these results are consistent with product confusion where retail investors believe that they buy and sell the VIX index when trading VIX ETPs. Although there may exist theoretical justifications in terms of diversification and hedging benefits to provide retail investors with access to the VIX ETP market, my findings indicate that, in aggregate, their ability to extract value from the products is limited and that retail investor sophistication is a potential cause of this.

This represents an interesting contribution to the literature on retail investor behavior.

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

References

[1] Christine Bangsgaard, Retail investors and product confusion: The case of VIX investments, Behavioural Finance Working Group 18th International Conference, 2025

Post Source Here: Product Confusion: Why Retail Investors Lose Money in VIX ETPs

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Using Random-Maturity Arbitrage to Price Perpetual Futures

Traditional futures contracts have maturity dates, upon which the futures price converges to the spot price. In the cryptocurrency market, the most popular contracts do not have a maturity date. They're called perpetual contracts. Unlike fixed-maturity futures, perpetuals do not expire. This feature enhances the liquidity of the contract. Because they have no set expiration date, perpetuals are not guaranteed to converge to the spot price of their underlying asset at any given time, and the usual no-arbitrage pricing formulas do not apply.

To minimize the gap between perpetual futures and spot prices, long position holders periodically pay short position holders a funding rate proportional to this gap, incentivizing trades that help narrow it. Typically, the funding rate is paid every eight hours and approximately equals the average futures-spot spread over the preceding eight hours.

How do you price a perpetual contract, given that the usual no-arbitrage condition does not apply?

Reference [1] proposed the use of random-maturity arbitrage to price perpetual futures. Basically, random-maturity arbitrage generalizes traditional arbitrage by allowing for a positive payoff at an uncertain future time. The authors also developed bounds for the random-maturity arbitrage price and used these bounds to construct an arbitrage strategy that delivered a high Sharpe ratio. They pointed out,

In an ideal, frictionless world, we show that arbitrageurs would trade perpetual futures in such a way that a constant proportional relationship would hold between the futures price and the spot price. In the presence of trading costs, the deviation of the futures price from the spot would lie within a bound.

Motivated by our theory, we empirically examine the comovement of the futures- spot spread across different cryptocurrencies and implement a theory-motivated arbitrage strategy. We find that this simple strategy yields substantial Sharpe ratios across various trading cost scenarios. The evidence supports our theoretical argument that perpetual futures-spot spreads exceeding trading costs represent a random-maturity arbitrage opportunity.

Finally, we provide an explanation for the common comovement in futures-spot spreads across different crypto-currencies: arbitrageurs can only accommodate market demand if the price deviation exceeds trading costs. As a result, the overall sentiment in the futures market relative to the spot market is reflected in the spread. Our empirical findings suggest that past return momentum can account for a significant portion of the time-series variation in the futures-spot spread.

An interesting conclusion of the paper is that overall sentiment in the futures market relative to the spot market is reflected in the spread. Empirical findings suggest that past return momentum accounts for a significant portion of the time-series variation in the futures-spot spread.

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

References

[1]  He, Songrun and Manela, Asaf and Ross, Omri and von Wachter, Victor, Fundamentals of Perpetual Futures (2022). https://ift.tt/MTVNzDd

Article Source Here: Using Random-Maturity Arbitrage to Price Perpetual Futures

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Speeding Up Derivatives Pricing Using Machine Learning

A financial derivative is a financial contract whose value depends on the price of an underlying asset such as a stock, bond, commodity, or index. Accurate valuation of financial derivatives and their associated sensitivity factors is important for both investment and hedging purposes. However, many complex derivatives exhibit path-dependency and early-exercise features, which means that closed-form solutions rarely exist, and numerical methods must be used.

The issue with numerical methods is that they are often slow. As a result, efforts are being made to improve the efficiency of numerical techniques for valuing financial derivatives. Reference [1] proposed a fast valuation method based on machine learning. It developed a hybrid two-stage valuation framework that applies a machine learning algorithm to highly accurate derivative valuations incorporating full volatility surfaces. The volatility surface is parameterized, and a Gaussian Process Regressor (GPR) is trained to learn the nonlinear mapping from the complete set of pricing inputs directly to the valuation outputs. Once trained, the GPR delivers near-instantaneous valuation results.

The authors provided examples, notably, the valuation of American put options using a Crank-Nicolson finite-difference solver. They pointed out,

In this work, we introduce a ML framework that takes all the relevant risk factors as input, including the parameters modeling the shape of the volatility surface, and generates the price and related Greeks as output directly almost instantly. To illustrate this methodology, we have used idealized volatility surfaces where the volatility surface for any given maturity is described by the 5-parameter SVI parameterization, and the term structure is specified by a single parameter. Within this idealized framework, we then apply this methodology to evaluate two kinds of derivatives products, namely the fair strike Kvar of a variance swap, and the price V and Greeks (∆, Γ, Θ) of an American put. For each of these products, we have prepared a training set and a testing set using valuations obtained by highly accurate numerical models commonly used by derivatives practitioners. The training data are then used to train a GPR to learn the mapping between the input risk factors and the output valuation variables directly, and the performance of the GPR is validated using the testing data where the high accuracy numerical model valuations are used as the ground truth. For the variance swap, a very high precision prediction with an overall 0.5% relative error is achieved. As for the American put, the price V and first order Greeks ∆ and Θ all have accurate predictions with relative error at 1.7%, 3.3% and 3.5% , respectively. However, partly due to the discontinuity of the Gamma Γ profile in the strike dimension, the GPR’s performance of this higher order derivative valuation is notably less accurate. Nonetheless, the key message from this study is that by training ML to directly map the relationships between pricing inputs and valuation outputs, this methodology has reduced the computation time by 3 to 4 orders of magnitude for the American put, offering significant improvement and potential in performing large scale real-time valuations of derivative products with early exercise features.

In summary, the authors developed an efficient method to price complex financial derivatives using a machine learning technique. However, it is noted that GPR’s performance in valuing higher-order greeks is noticeably less accurate. Additionally, the study was conducted using synthetic data, so it would be useful to see the method applied to real-world scenarios.

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

References

[1] Lijie Ding, Egang Lu, Kin Cheung,  Fast Derivative Valuation from Volatility Surfaces using Machine Learning, arXiv:2505.22957

Article Source Here: Speeding Up Derivatives Pricing Using Machine Learning

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Leveraged ETFs: Do They Really Decay?

Leveraged ETFs (LETFs) are financial instruments designed to amplify the daily returns of an underlying index, typically by a factor of two or three. They have received criticism for performance drag or value erosion over time. Despite these concerns, they continue to attract attention and capital from investors.

A recent trend in the literature has been to revisit the merits of LETFs. We have discussed some of these findings in previous editions. Reference [1] continues this line of research, examining the claim that LETFs deviate from and lose value over time relative to their non-reset counterparts. The authors pointed out,

We compare LETF returns over time to n times the underlying index return for the same holding period (after properly accounting for the necessary financing cost required to lever those index returns), which we call the “non-reset portfolio” in this paper. This is the natural comparison for us to evaluate the concerns raised by Cheng and Madhavan (2009) and the SEC (2009).

Simulations show that as long as volatility is not too high, LETFs generally have very high correlations to their non-reset portfolios, except for the 252-day holding period for the most volatile indices. When the underlying index volatility is very high (e.g., the EAFE, high volatility case, which has a daily volatility of 4.56% and annual volatility of 72.4%), our findings indicate LETFs continue to correlate with their non-reset portfolio closely if the holding period is not too long (i.e., 21 days) or the leverage ratio is not too high (i.e., 2x). However, as we emphasized, such high volatility has not been observed across all the considered indices in the past 20+ years. We also notice that when an LETF does not track its non-reset portfolio very closely, the LETF tends to outperform, and LETF and non-reset portfolio differences tend to be highly positively skewed: sizable LETF underperformance is less likely than same-sized outperformance in the samples and simulations we observed.

Overall, the value of LETFs does not erode in the long run. The concern that they do not correlate closely with the non-reset portfolio over time is not supported by the facts.

In short, the authors refute earlier studies suggesting that LETFs inherently suffer from value erosion. Their analysis shows that LETFs’ multi-day returns generally track closely with those of equivalent non-reset portfolios across most indices and holding periods (up to one year). While substantial deviations can occur under high volatility and extended holding periods, these deviations tend to be positively skewed and generally favorable.

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

References

[1] Wang, Baolian, Multi-day Return Properties of Leveraged Index ETFs (2025). https://ift.tt/1U3LPih

Originally Published Here: Leveraged ETFs: Do They Really Decay?

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