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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Crypto Treasury Models: Balance Sheet Risk and Bitcoin Price Dependency

As crypto currencies gain broader acceptance, some corporations have begun including crypto in their balance sheets, forming new "crypto treasury" models. However, these models entail significant financial risks. Digital asset price volatility can translate into earnings variability and elevated refinancing risk—effects that are amplified when acquisitions are debt-financed.

Reference [1] investigates the relationship between Bitcoin (BTC) and equity markets, focusing on firms that have adopted BTC as part of their corporate treasury strategy. The study uses a dataset of 39 publicly listed BTC-holding companies from 2017 to 2025. The author applies correlation analysis, single-factor return models, and transfer entropy methods to quantify both linear and nonlinear dependencies.

Of particular interest is the use of Transfer Entropy, an extension of Wiener-Granger causality, which can identify the causal direction of dependency. The authors pointed out,

This study offers a detailed empirical assessment of the evolving link between Bitcoin (BTC) and equity markets in the context of corporate treasury strategies centered on digital assets. Focusing on Strategy (MSTR), the largest public holder of BTC, we combine correlation analysis, single factor models, and transfer entropy (TE) techniques to quantify the direction and dynamics of informational dependence between BTC and MSTR equity returns

Our findings consistently indicate that BTC serves as the dominant source in the information flow. On average, TE_BTC→MST R is higher than in the reverse direction, and statistically significant directional dependence from BTC to MSTR is more frequent and persistent. These asymmetries become particularly pronounced during market-wide events. In contrast, TEMST R→BT C peaks are rare, localized, and confined mainly to firm-specific actions such as convertible bond issuances or balance sheet disclosures.

…Rolling TE reveals a richer structure, characterized by intermittent bursts of significant influence and prolonged periods of near-random noise. This calls into question the reliability of static hedge ratios and highlights the need for adaptive quantitative strategies and risk management approaches that respond to changing market conditions.

In short, there is a strong relationship between BTC prices and the stock prices of firms that adopted crypto treasury models. However, this relationship is mostly unidirectional, flowing from BTC to equity prices.

The article also points out that the relationship is not stable and can appear random for prolonged periods. This characteristic must be considered when designing hedging strategies.

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

References

[1] Sabrina Aufiero, Antonio Briola, Tesfaye Salarin, Fabio Caccioli, Silvia Bartolucci, Tomaso Aste, Cryptocurrencies in the Balance Sheet: Insights from (Micro)Strategy -- Bitcoin Interactions, arXiv:2505.14655

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Risk, Timing, and Strategy: Key Differences in 0DTE Options Trading Styles

We have discussed the impact of 0DTE options on the market, drawing from both practitioner insights and academic literature. Both sources point to the conclusion that 0DTE options have little or almost no impact on the market; they do not increase market volatility, contrary to what many investors have argued.

The CBOE recently updated its report with new data, which briefly reconfirmed that 0DTE options have little or no impact,

High volume doesn’t equal high risk. What matters for determining the potential impact of market maker gamma hedging activity is the balance of the volume between buys vs. sells, not the notional size. And what’s remarkable about SPX 0DTE flow is how balanced it is between buyers and sellers, puts and calls. As we outlined above, both institutional and retail investors use these options for a range of purposes – from tactical bets to systematic yield harvesting. This is why the put/call ratio for SPX 0DTE options have consistently hovered around one, in sharp contrast to non-0DTE options (where the primary use case is hedging). This is also why the net gamma exposure (or market maker positioning) of 0DTE options have been so minimal.

The report also compares retail and institutional traders, offering several useful insights.

• Both groups use similar strategies, with just over half of opening customer trades in outright puts and calls, and the remainder in multi-leg strategies. Institutional investors show a slightly higher preference for vertical spreads, while retail traders are more active in complex strategies like iron condors and butterflies.
• Institutional investors tend to initiate positions early in the trading day and leave them open longer—likely due to higher risk tolerance or the availability of alternative hedging methods. In contrast, retail traders are active both at the open and close of the trading session.
• Retail traders frequently initiate and unwind positions throughout the day, suggesting more hands-on risk management and a lower tolerance for risk.

The report highlights that while the strategies are broadly similar, the approach to timing and risk management differs meaningfully between the two groups.

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

References

[1] 0DTEs Decoded: Positioning, Trends, and Market Impact, CBOE, May 2025

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Market Regimes and Strike Selection: A Case Study on the Call Condor

Parameter optimization is a technique used in trading strategy design. It is used to identify the best set of parameters for maximizing performance and to study the strategy dynamics in order to gain insights. However, while this technique is frequently applied to linear instruments, it is used less often on non-linear instruments, such as options. This is likely due to the complexities involved in modeling non-linear instruments.

Reference [1] attempts to optimize the parameters of a popular options strategy, the call condor. The authors studied strike selection within the context of a specific market regime. They pointed out,

Next, the study examines how market scenarios impact the results mentioned above. As shown in Pane A of Figure 4, widening outside ranges is more feasible for the neutral market than for the bullish and bearish markets. Three curves represent the dynamics of fair value for the LCC strategy over the widths of the outside ranges given three market scenarios. The fair values gradually increase over the widths of the outside ranges for all market scenarios. However, a wider range of outside strikes can boost profits more in the neutral market scenario because the future market price is more likely to fall in the range. Our findings suggest that a wider range of outside strikes is more appropriate for the neutral market.

Although a wider inside range (K3 – K2) of strike prices can yield a lower fair value for the LCC strategy, the trader obtains relatively lower profits in both bearish and bullish markets and higher profits in the neutral market. The economic implication is that strategy traders can achieve greater profits by choosing an exact portfolio of options with a narrower range of strikes to capture specific market scenarios. Suppose the strategy traders remain in a bullish or bearish market. In that case, they should adjust their choice of inside ranges to align closer with the prevailing bullish or bearish market conditions, respectively.

In short, by analyzing the optimal parameters, the authors identified the most favorable market environment for each strike selection.

Note that the study was conducted using theoretical option prices rather than traded prices, but it still offers valuable insights. Portfolio and risk managers can benefit from this type of simulated study to enhance their understanding of strategy and decision-making.

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

References

[1] Jin-Ray Lu, Motsa Zandile Tema, Evaluating the Choices of Strike Ranges for the Long Call Condor Strategy, International Review of Accounting, Banking and Finance, Vol 17, No. 1, Spring, 2025, Pages 42-56

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Trend vs. Mean Reversion: A Statistical Physics Approach to Financial Markets

Trend and mean reversion are two prevalent forces in financial markets. Studying their interplay is important, as it provides clues for developing accurate timing models. Reference [1] formally examines the relationship between trend and mean reversion in financial markets, across timeframes ranging from intraday to monthly, and spanning over 300 years.

The authors propose a lattice gas model of financial markets, where the lattice represents the social network of investors, and the gas molecules represent shares of an asset. Mathematically, for a given market and time horizon, they define the strength ϕ of a trend using its t-statistic. They find that tomorrow’s return, 𝑅(𝑡+1) (normalized to have variance 1), is well modeled by a cubic polynomial of today’s trend strength,

R(t + 1) = a + b · ϕ(t) + c · ϕ(t)^3 + ϵ(t)

• …trends tend to revert before they become statistically strongly significant. In other words, by the time a trend has become so obvious that everybody can see it in a price chart, it is already over. This is consistent with the hypothesis that any obvious market inefficiency is quickly eliminated by investors.
• The parameters b, c are universal in the sense that they seem to be the same for all assets within the limits of statistical significance. This is in line with the fact that many successful trend-followers use the same systematic trading strategy for all assets.
• c is negative and does not seem to depend much on the trend’s time horizon T. However, b depends on the horizon: it peaks at T ∼ 3-12 months, which is in line with the time scales on which trend followers typically operate. b decays for longer or shorter horizons and appears to become negative for T < 1 day or T > several years.
• While c has been fairly stable over time, b appears to have vanished over the decades. This is in line with the fact that trendfollowing no longer works as well today as it did in the 1990’s. Markets seem to have become quite efficient with respect to trends.

In short, the authors develop an interesting model of the financial market and conclude that markets tend to be in a trending regime over time scales from a few hours to a few years while exhibiting mean reversion over shorter and longer horizons. In the trending regime, weak trends tend to persist, whereas in the reversion regime, weak trends tend to reverse.

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

References

[1] Sara A. Safari, Christof Schmidhuber, Trends and Reversion in Financial Markets on Time Scales from Minutes to Decades, https://ift.tt/mjHlSqe

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Forecasting Volatility in Digital Assets: A Comparative Study

Modeling the volatility of cryptocurrencies is important for understanding and managing risk in these markets. Reference [1] provides a literature review of various volatility prediction approaches and evaluates three models: GARCH, EGARCH, and EWMA.

The EGARCH model is an extension of the GARCH model that accounts for the asymmetric impact of positive and negative shocks on volatility. It reflects the common belief that bad news tends to cause larger market reactions than equally sized good news. The authors pointed out,

The EGARCH (1,1) volatility estimation model demonstrated superior performance. This finding aligns with the outcomes of a study conducted by Alexander and Dakos (2023), Ngunyi et al. (2019), and Naimy and Hayek (2018) demonstrating that the asymmetric GARCH model exhibited superior performance across several cryptocurrencies. Further, Bergsli et al. (2022) found that the EGARCH and APARCH model exhibited superior performance compared to other GARCH models. According to the findings of the aforementioned study, the GARCH (1,1), EGARCH (1,1), and EWMA volatility estimation model exhibited limitations in capturing high volatility fluctuations and demonstrate improved accuracy when the observed daily volatility is at a lower level. However, it is crucial to acknowledge that the aforementioned discoveries are only relevant to Bitcoin and Ethereum. The maximum threshold of high volatility is expected to be linked to the degree of uncertainty. This finding might assist investors and prospective investors in evaluating the risks and rewards associated with the Bitcoin and Ethereum.

In short, the EGARCH(1,1) model performs the best for both Bitcoin and Ethereum.

This article is important because it highlights effective tools for forecasting crypto market volatility. It also discusses the weaknesses of these forecast models, notably their limitations in capturing periods of high volatility, while showing improved accuracy when daily volatility is relatively low.

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

References

[1] Irawan, Andree and Utam, Wiwik, Modelling cryptocurrency price volatility through the GARCH and EWMA model, Management & Accounting Review (MAR), 24 (1): 6. pp. 153-179.

Article Source Here: Forecasting Volatility in Digital Assets: A Comparative Study

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Joint Calibration of SPX and VIX Options Using the Willow Tree Method

The willow tree method is a powerful technique with many applications in derivative pricing. We have discussed how it can be used to determine the implied volatilities of American options. It can also be applied to price convertible bonds by simultaneously [glossary_exclude]accounting [/glossary_exclude]for equity and credit risks. In addition, it is useful for calculating the value of complex path‐dependent derivatives and associated risk measures, such as Asian options and American moving average barrier options. Reference [1] proposed using the willow tree method to build a model that describes the volatility dynamics of both SPX and VIX options concurrently.

Among the methods commonly used to jointly calibrate SPX and VIX options, the non-parametric approach typically reconstructs the risk‐neutral density (RND) using only SPX option prices. The authors employed the implied willow tree (IWT) method to extract the RND of both SPX and VIX options, thereby accommodating both sets of market-observed option prices effectively. They pointed out,

In this study, we propose a novel nonparametric discrete‐time model called the joint implied willow tree (JIWT) approach to tackle the joint calibration challenge. The JIWT method bypasses the need for model‐based simulation techniques by using discrete‐time nonparametric methods to derive the risk‐neutral probabilities from observable SPX and VIX option prices. Our method offers three primary contributions. First, we delve into the conditional probability distributions between two maturities using both SPX and VIX option prices. While solely SPX option prices provide insight into SPX unconditional RNDs, they offer limited information on conditional densities. Leveraging the VIX definition (1) grounded in the SPX, we can identify conditional densities that align with VIX and its options prices. It enables us to capture the volatility smile in both the SPX and VIX markets, especially for short‐term maturity. Second, our JIWT method is simpler, more straightforward to implement, and efficiently extends to multiple maturities of SPX and VIX options as compared with the nonparametric discrete‐time model proposed by Guyon (2023)… Third, our JIWT method operates without the need for any prespecified mathematical model for SPX. Instead, it extracts the entire RNP directly from market‐observable option prices, making it both model‐free and data‐driven.

In short, this paper proposed a nonparametric method for calibrating SPX and VIX option prices simultaneously. The method has proven successful in addressing the joint calibration challenge of the SPX and VIX markets. As a result, it will enable risk and portfolio managers to identify new opportunities and manage risks more effectively.

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

References

[1] Bing Dong, Wei Xu, Zhenyu Cui, Joint Implied Willow Tree: An Approach for Joint S&P 500/VIX Calibration, Journal of Futures Markets, 2025; 1–22

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