Hedging Tail Risk & Why VaR Does Not Manage Risk

THE KNOWN UNKNOWN

Markets have become reacquainted with volatility over the last 7 months and with a host of omnipresent macroeconomic factors still unresolved, this seems like a good time to discuss tail risk.

Throughout my career, I've found that a lot of institutional asset managers rely on Value-at-Risk (VaR) as a risk management tool.  Unfortunately, this practice is completely inadequate as VaR cannot protect against against outsized, downside losses - also known as tail risk -... probably because it was never intended to.

VaR is merely an interval threshold measurement given an assumed degree of confidence.  So if we assume a 95% confidence interval for daily, monthly or annual returns, VaR will tell us the single point at which we would expect 5% of our returns to fall below.  Conversely, VaR represents the point where you expect returns to be greater than 95% of the time.

VaR does not, however, give the user any information about the shape of a given return distribution or the size of the area beyond its confidence interval... again, this is considered tail risk.  This is significant because tail risk can be devastating to a portfolio; even fatal in the case of leveraged strategies.  This is the 'known unknown.'


VaR, UGH... WHAT IS IT GOOD FOR? ABSOLUTELY NOTHING

In spite of the subtitle, VaR can be a useful risk management tool if used correctly.  I wanted to test how VaR could be used as a hedging tool for a high vol portfolio.

To do this, I took monthly returns for a group of 4 assets over the last 150 months and used Modern Portfolio Theory to build an optimal portfolio with an annualized volatility of 12%.  Somewhat to my dismay, the model returned a portfolio with only two allocations, 66% to QQQ and 34% to the Tremont Hedge Fund Index.

I used the same methodology in a previous blog that discussed dynamic programming...
http://tancockstradingblog.blogspot.com/2015/09/creating-vix-signal-to-manage-asset.html

Parametrically, my model portfolio had an annualized expected return of 9.71% with a 12% volatility.  This translates into an expected monthly return of 0.773% with a 3.46% standard deviation.  Using these metrics, I created a parametric monthly return simulation and located my 95% confidence interval VaR at -4.75% as marked by the red line in the chart below.

As you can see, the distribution follows a normal pattern and the expected value of the area to the left of the confidence interval is -5.7%.  This is also referred to as the expected shortfall.

Not entirely satisfied with the parametric distribution, I then ran a Monte Carlo simulation of my model portfolio which produced the return distribution seen below.

Interestingly enough, the 95% confidence interval VaR was the same as the parametric distribution at -4.75% but the expected shortfall was significantly higher at -8.5%.  Looking at the chart, this distribution has a negative skew and a very fat left tail... it is plain to see that there are a host of simulated monthly returns that fall below -10%.

This is a prime example of how VaR fails to capture tail risk.

Lastly, I compared both of these charts to a historical distribution as seen below:

The historical distribution only has 150 observations to the 500 simulations run on the parametric and Monte Carlo charts... but it bears a striking resemblance to the Monte Carlo chart with its negative skew and fat left tail.  Again, the 95% confidence interval is measured at -4.75% but the expected shortfall was -7.5%... still more severe than the parametric measurement of -5.7%.


HOW & WHEN TO HEDGE TAIL RISK

Now that we've spotted our tail risk, we should immediately hedge it, right?... WRONG!

Tail risk in a well diversified portfolio is almost entirely a function of systemic risk.  Outside of an unexpected random event, systemic risk will typically forecast itself.  As I wrote in a previous blog titled, Analysis of Variance - An Empirical Study on Relative Means and Their Implications on Price Action, systemic corrections are almost always preceded by a gradual breakdown of technical indicators.

http://tancockstradingblog.blogspot.com/2016/03/analysis-of-variance-empirical-study-of.html

We can also use dynamic programming in our asset allocation process to protect against systemic corrections.

Due to the expensive nature of hedging, it doesn't really make sense to hedge against a dramatic market correction when indicators suggest that the likelihood of such an event is very low.  If we look at the SPY chart right now, we can deduce that there is not a high likelihood of an immediate market selloff...

However, if there was a threat of a market correction, we can use VaR to place the strike on put protection.  Going back to the model portfolio I put together for this piece, we remember that it has a 66% allocation to QQQ.  However, the portfolio beta is actually higher to the S&P than the QQQ, therefore, I would buy put protection on the SPY at the 1 month option associated with a -4.75% move.  If I were to do this today, the SPY is trading at 205.5, I would buy the 1 month April 29th $196 put for $0.70 which has a leverage factor of 41.9x and a payoff function that looks like this...

http://tancockstradingblog.blogspot.com/2016/03/understanding-option-leverage.html