VALUE AT RISK SENSITIVITY
If we are looking for the most efficient way to alter the risk of a portfolio while minimizing the change in allocation, value at risk sensitivity can show us how much a change to each asset class will impact the total portfolio risk. Value at risk sensitivity is, in a sense, a form of “What If” analysis that allows us to see how a change in allocation to one asset class will impact the total portfolio value at risk. It can be used to measures the impact of a re-allocation across all asset exposures. While a specific asset’s exposure is increased by the increment, the remaining portfolio’s components are reduced proportionally to preserve the initial investment value of the portfolio throughout the process. The ranking of the portfolio’s value at risk sensitivities will not necessarily match the ranking of the portfolio’s percentage exposure or the ranking of the individual components’ value at risk. The WCA displays the VaR sensitivity of each asset class at the same time. It does not display the adjusted weight to each asset class in the portfolio.
Let’s investigate the Risk Budgets of a simple $1,000 portfolio, consisting of 50% US Stocks and 50% US Bonds. We set our Time Horizon at three years and our Probability Threshold at 5%. Looking at the individual value at risk assignment of these two asset classes we can see that at the 5% threshold, US Stocks could lose $60 or more at the end of three years. At the same threshold, US Bonds could lose $37 or more at the end of three years. Additionally, we can see that US Stocks account for approximately 208% of the portfolio capital at risk while the proportion attributable to Bonds is negative 109%.
If we are looking to decrease total portfolio risk, value at risk sensitivity shows us how a re-allocation to US Bonds will change total portfolio risk. We can see that an allocation increase of 5% to Stocks assuming a proportional decrease to the remaining asset classes (only bonds in this example) would increase total portfolio value at risk by $6.50. However, that same increase to Bonds (assuming the proportional decrease to Stocks) would actually decrease total portfolio value at risk by about $5.