As purveyors of risk models, we spend much of our time immersed in the arcana of causes and implications of volatility. But we are often asked why investors should care about volatility (aka risk) and, in particular, if higher volatility drives higher returns, why is low volatility viewed as a positive market characteristic? Below, we illustrate the connection between volatility and investors’ perceptions of potential capital losses, which may color their decision to invest.
Risk is often defined as the probability of losing some (or all) of your money. Hence, in addition to return expectations, investors also want to know how much of their original investment they are risking to achieve those returns. For this reason, the investment industry has created two metrics (among others) to help investors compare the relative riskiness of investment choices, namely Value at Risk (VaR), and Conditional-Value-at-Risk (CVaR). Since neither of these can be known with certainty, they are estimated for a given confidence level, usually a 95%/5% confidence level, and reported for a given period, usually one day.
For example, a VaR of 2% at the 5% confidence level means that an investment can be expected to lose more than 2% in only one out of 20 days. VaR speaks to the probability (5% or 1/20) of losing more than 2% of an investment, but it does not quantify how much more than 2% one could lose. This is where CVaR comes in. CVaR estimates the average size of the loss when this 2% VaR is breached. VaR and CVaR complement the use of traditional risk models by stating the odds and magnitude of an unusually big loss (the worst case), while traditional risk models assess expected gains or losses across the full spectrum of outcomes.
Both VaR and CVaR are related to market volatility. In times of higher volatility, losses are bigger. In periods of extreme volatility, VaR is often exceeded both more times than predicted and by more than CVaR predicted, highlighting the fat-tailed nature of the distribution. For example, at the pre-COVID-19 market peak on February 19, 2020, a VaR estimate at the 5% confidence level, based on the previous 60 days of realized returns, predicted that one would only lose more than 0.91% of an investment in one out of the next 20 days. In fact, during the COVID-19 crash, the market lost more than that amount in 12 of the next 20 days. On February 19, 2020, the 5% CVaR predicted an average loss of -1.4% if this VaR level was breached, but the average loss over those 12 days was just over 4%. To be fair, as the realized losses started to enter the history used in the prediction of CVaR, this estimate of average loss increased, but, still, by the end of the 12 days, the then-current CVaR estimate had been exceeded six times.
We computed a short-term estimate of both VaR and CVaR for the broad US market using the US-LMS Axioma Market Portfolio . Our back-of-the-envelope calculation used the daily return of the benchmark portfolio for the previous 60 trading days to estimate the 5% VaR and CVaR each day for the full history of the portfolio going back to early 1982. We then compared the results (which emphasize the very recent past) to the short-horizon fundamental factor model (AXUS4-SH), which is designed to be more stable.
The chart below shows the full history of the VaR estimate (green line), the CVaR estimate (blue line), and the short horizon predicted risk for that portfolio (red line). Note that the volatility estimate is plotted on an inverted scale on the right axis, and that the three measures are highly correlated. I highlighted three dates on the chart when volatility was extreme and labeled the corresponding CVaR for those dates. It is interesting to note that COVID-19 caused a worse CVaR estimate than the GFC, and one exceeded only by the extreme volatility around Black Monday.
How can investors incorporate these admittedly backward-looking estimates into their investment decision-making process? One way to think about these risk metrics is that when these estimates of the frequency and size of potential losses drop below investors’ acceptable risk levels, they become more risk-tolerant in response. Conversely, when these estimates point to a higher frequency and size of potential losses, investors tend to become more risk averse. For example, an investor may view a loss of 5% in a day as the most they are willing to accept, so if the likelihood of that magnitude loss decreases, they may be willing to invest more. Conversely, they may decide not to add to their investment, or even reduce it, if the probably of loss and the potential magnitude of the loss becomes too high.
During the initial slowdown of the COVID-19 pandemic (April to June of 2020), when the stock market was rising while the data pointed to a worsening of the economy, many wondered if the rebound would last. To illustrate the progression of these calculations as market performance improved, the chart below shows the Var and CVaR estimates from the start of 2020. At the height of the pandemic crash, when volatility was extremely high, CVaR predicted that investors had a 5% probability of losing almost 10% of their investments in a single day. This estimate of the size of potential losses then fell continuously as market volatility declined, dropping initially to 4% by July 2020, then to 3.3% before the vaccine news in November 2020, to 2.4% after reassurances by the Fed that interest rates would be held steady in the near term, to just 1.6% by Friday July 9, 2021. Note that this level was still higher than in January 2020, but volatility was likewise still higher and could fall further, bringing down estimates of potential losses and boosting investors’ risk tolerance in the process.
As market volatility, and the probability and magnitude of potential losses declined, investors were more likely to commit new cash to the markets and/or to seek out riskier investments. As stock prices ratchet up slowly, volatility drops. And as risk falls, investors are more comfortable investing. This can create a virtuous cycle until, of course, it doesn’t anymore…
 Expected Shortfall is a term used to refer to Conditional Value at Risk (CVaR).
 We can either be 95% confident that an investment will have a return greater than X%, or 5% confident that an investment will not lose more than X% in the next period.
 Representative of the broad US market.