Given the recent pick-up in volatility from recent global market highs, investors should now be even more interested in learning how to manage the risk of their portfolio in case of a significant market correction. Popular risk measures are lower order metrics that look at such calculations as variance or standardized covariance (e.g., beta). These measures ignore the higher order risks that are in your positions, such as skew or kurtosis. Kurtosis is a measure of fat tails in the return distribution.

In the green triangles of the chart below we show the 95% daily tail Value-at-Risk (i.e., TVaR) associated with the normal distribution of the S&P 500 and respective sector returns. For example, we take the worst 5% of daily returns, and then average it. Skipping the mathematical proof, the theoretical estimation for a normal return distribution is:

*average + standard deviation * density at risk level / (1 - risk level)*

So for the S&P 500, we see that it is 0.0%+1.3%*0.1/(1-95%)=-3%. You can see this in the green triangle below.

For reference, the S&P and sector ETFs for the above chart are as follows:

Category | ETF ticker |

S&P 500 | (SPY) |

Consumer Discretionary | (XLY) |

Consumer Staples | (XLP) |

Energy | (XLE) |

Financial | (XLF) |

Health Care | (XLV) |

Industrial | (XLI) |

Materials | (XLB) |

Technology | (XLK) |

Utilities | (XLU) |

Additionally in the chart, we use red circles to show the actual 95% daily TVaR. The traditional risk measures again would assume that these equity ETFs move in a theoretically normal distribution, though we see the actual results are fatter tailed with greater risk to your portfolio.

However, not all of the S&P sectors move in perfect (linear or nonlinear) correlation. And as a result, if instead of holding the S&P 500, you had held the component sector ETFs, those component sector ETFs would experience TVaR at different times. Put differently, the component sector ETFs would not always experience TVaR when the S&P 500 itself is. We show this result below, where we show a chart similar to above, except in lieu of the theoretical normal distribution we show in blue diamonds the sector ETFs expected daily value when the S&P 500 is in TVaR.

We see that consumer discretionary's XLY is the sector ETF that offers the closest proxy to the broader market. XLY's tail risk and levels are approximately the same as that of the SPY ETF. On the other extreme, utilities' XLU is the sector ETF that offers the least similar proxy to the broader market. XLU's tail risk and levels are the least similar to that of the SPY ETF. And lastly, financial's XLF is a notable sector ETF in that its tail risk isn't the most aligned to that of the broader market, though the ETF's risk level is nearly 60% greater than that of the S&P 500's.

Hedging would allow the ability to reduce your portfolio exposure to unwanted risk. For example, let's say that you only own $100 of XLY and you wanted to hedge this position. The typical hedge would use a ratio of the price levels and divide by the correlation between the two assets. An approximation with the chart above is 100% (for the risk ratio between XLY and SPY) / 90% (for the ratio between value and TVaR). So one would need to short about $110 of SPY to hedge the XLY risk.

Now let's instead say that you only own $100 of XLF and you wanted to instead hedge this position. An approximation with the chart above is 130% (for the risk ratio between XLF and SPY) / 80% (for the ratio between value and TVaR). So one would need to short about $160 of SPY to hedge the XLF risk.

So the latter chart above shows a perspective on the tail risk within the S&P 500. For sector ETFs such as XLF, we see it is more expensive and less precise to hedge this ETF. Conversely, if you are warily holding the S&P 500 and wanted to hedge with the XLF, then it would be the cheapest sector ETF to use, though it comes at a cost of being the least precise sector ETF to hedge the S&P 500 with.

Comments()