A remedy for painful drawdowns: CVaR

Updated: 7 days ago

Written by Sabrina Herold and Steven Van Winkel at Tom Capital AG

The intensity of pain versus that of gain is at least twice as high, as the mathematical psychologists Amos Tversky and Daniel Kahneman have found and as today’s market sentiment might confirm for some long-only investors in traditional markets.

Not only are investors concerned with pains more than with gains, they are also much more concerned with extreme drawdowns than with overall volatility, such that Bollerslev and Todorov (2011, p. 2187) coined the fear for extreme crashes “crash-o-phobia”. Examples of extremely negative performance events are what Nassim Taleb coins black swan events. They include examples such as the terrorist attack of September 11, 2001, the subprime mortgage crisis of 2008, and COVID-19, in which asset correlations converge to a point where diversification alone is insufficient to absorb the shock.


How to avoid extreme drawdowns for normally and non-normally distributed returns, and how one of these methods (CVaR) can also be beneficial for enhancing returns is described in the following paragraphs.


Managing extreme drawdowns for normally distributed returns

When asset returns follow a standard bell-shaped distribution, managing volatility by applying a volatility target to the portfolio can be enough to avoid extreme losses, even in times of crisis (Szegö, 2002 and Strub, 2013). However, volatility includes both upside and downside deviations and hence reducing volatility can also sacrifice returns.

Most financial asset returns, including the S&P 500, deviate from a normal distribution. In the example below, we observe that the tails of the distribution of the S&P 500 are fatter than a theoretical normal distribution would suggest. Even if this deviation is sufficiently small, so that most financial theorems continue to assume a normal return distribution, it is big enough to change the likelihood of extreme events significantly.


S&P 500 distribution on monthly returns from 1950 - 2022 vs. normal distribution


Managing extreme drawdowns for non-normally distributed returns

With asset returns usually not normally distributed, Value at Risk (VaR) became very popular and useful to manage downside risk. VaR calculates the maximum loss expected for a specified time frame and a defined confidence level. For example, a one-month S&P VaR of -7% for a 95% confidence interval indicates a 5% chance to lose 7% or more of your portfolio value in a single month. Consequently, investment managers could calculate the rolling VaR based on historical returns and define a target VaR for which to optimize the overall portfolio risk. The drawback of Value at Risk is that it is a point measure and does not provide any indication of the size of the losses in the tail of the distribution. Applying VaR targeting to the above scenario would leave you blind to the probable and extreme -30% losses. By applying Value at Risk targeting to the S&P 500 index, the investment team would not cut enough losses when extreme negative returns occur. The graph below demonstrates this vividly:


S&P 500 distribution on monthly returns from 1950 -2022 including VaR and CVaR


A relative of the above introduced VaR is Conditional Value at Risk (CVaR or expected shortfall), which has seen increased popularity among regulators in the past decade. Analogous to VaR, CVaR can be derived using historical returns. CVaR informs us about the size of a probable loss within a specified time frame and a defined confidence interval. Therefore, CVaR informs about the average loss size if the situation is even worse than the VaR threshold assumes, as indicated in the graph above. CVaR provides information about the size of the tail, making it suitable for return distributions with 'fat tails'. A CVaR of -10% for a 95% confidence interval for instance states, that in the worst 5% of returns, the loss will be -10% on average.


CVaR targeting explained for drawdown management and enhanced returns

This simplified example illustrates how extreme drawdowns or tail risk can be managed using CVaR:

  1. Calculate the historical CVaR, using a lookback period of e.g. one year (or longer)

  2. Determining a target CVaR based on targeted risk/return, e.g. targeting an average loss of 2.5% for the worst 5 days of a portfolio with a 95% confidence interval

  3. Gearing portfolio exposure according to the Target CVaR, usually after portfolio allocation

In the third step, exposure gearing can be applied bi-directionally. That is, if the portfolio’s CVaR is below the Target CVaR, leverage can be used to increase exposure to enhance returns. Contrary, if the CVaR is above the target CVaR, the exposure should be reduced to avoid large losses (e.g. during black swan events). The chart below maps the moments when a portfolio would have increased or decreased exposure using the above steps to match the CVaR Target against the log-normal returns of the S&P 500.

Tail Risk Exposure & Gearing vs. log-normal S&P 500 returns


Conclusion

The utility of tail risk targeting to achieve an enhanced risk/return profile has been proven to be high in various studies. We at Tom Capital gear our portfolios for CVaR to manage drawdowns and achieve more constant returns over time.

As always, the condition for successfully applying this to a portfolio is that the analysis and forecast of all underlying factors is robust (Rickenberg, 2020, Wang et. all, 2012). In addition, CVaR and VaR , just as other financial theorems, assume homoscedastic volatility over time. In reality, volatility has been observed to behave conditional to the past and can exhibit clustering. Techniques such as Autoregressive Conditional Heteroskedacity (ARCH) or Generalized Autoregressive Conditional Heteroskedacity (GARCH) reflect this tendency and thus render more realistic results applicable to tail risk targeting.



Tom Capital AG is an investment boutique that applies machine learning to the entire investment process, from data selection to portfolio construction. Do not hesitate to contact us at info@tomcapital.ch for more information or inquiries.



Sources:


Bollerslev, T., & Todorov, V. 2011. Tails, Fears, and Risk Premia. The Journal of Finance, 66(6), 2165–2211. http://www.jstor.org/stable/41305187

Gormsen, N. J. and Jensen, C. S. 2017. Higher-moment risk. Available at SSRN 3069617.

Rickenberg, L. 2020. Tail Risk Targeting: Target VaR and CVaR Strategies. Available at SSRN: https://ssrn.com/abstract=3444999 or http://dx.doi.org/10.2139/ssrn.3444999

https://towardsdatascience.com/are-stock-returns-normally-distributed-e0388d71267e

Strub, I. S. 2013. Tail hedging strategies. Available at SSRN 2261831.

Szego, G. 2002. Measures of risk. Journal of Banking & Finance, 26(7), 1253–1272

Taleb, Nassim Nicholas.1960. The Black Swan : the Impact of the Highly Improbable. New York :Random House, 2007.

Wang, P., Sullivan, R. N., & Ge, Y. 2012. Risk-based dynamic asset allocation with extreme tails and correlations. Journal of Portfolio Management, 38, 26–42.

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