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

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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

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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

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