VaR Example
VaR, or value at risk, is a portfolio management statistic that measures portfolio risk-- specifically, the potential downside. Var measures the minimum amount a portfolio can lose in a given period, and it can be measured in percentage terms or dollar terms. For example, If I have an investment portfolio worth $50 million, and the 5% monthly VaR is 2.6%, I can expect to lose at least 2.6% of value approximately every year and a half. Or that can be read in terms of likelihood,"There is a 5% chance I will lose 2.6% of my portfolio this month." In dollar terms, there is a 5% I can lose $1.3 million of portfolio value this month.
To better understand the internals, I have a detailed VaR example. Imagine I have an equally weighted portfolio of stocks, SPY, and bonds, LWC. I calculated monthly returns for SPY and LWC from November 2011 to November 2016 and then averaged each of them. I calculated each of their respective standard deviations and then a portfolio standard deviation with the formula for a two asset portfolio:
(w1^2 * STD1^2 + w2^2 * STD2^2 + 2 * w1 * w2 * corr * STD1 * STD2) ^ 0.5.
If you used covariance instead of "corr*STD1*STD2" in the formula above, same thing.
I calculated the correlation between SPY and LWC with five years of monthly returns. I calculated portfolio monthly returns by simply averaging SPY and LWC monthly returns under the assumption that the portfolio is rebalanced each month to 50/50 weightings. Then, I averaged the portfolio monthly returns to find the mean portfolio monthly return. Once all that was finished, I just plugged and chugged the formulas for portfolio VaR:
Parametric: (Mean Return - 1.65 * Portfolio STD) * -1
Historical: 5th percentile of monthly portfolio ranked returns
Parametric and historical VaR were nearly identical-- off by two basis points. I used "1.65" in the parametric method because the t score for a 90% confidence interval is 1.64 and some change, so I rounded it to 1.65.
The VaR in this example reads that my portfolio has a 5% chance of losing at least 2.6% per month.
