## The BCK Volatility Blog

### ULCER PERFORMANCE INDEX - EVEN BETTER THAN THE SHARPE RATIO

July 31, 2018

In our previous post, we discussed the Sharpe Ratio as a way to measure risk within one's portfolio. If you have not read our post, we highly recommend familiarizing yourself with the important (and perhaps over sensationalized) statistic that we, as well as many others throughout the investment community, use. Follow this link to read more on the Sharpe Ratio. We mentioned the main issue with the Sharpe Ratio; it penalizes a portfolio when there are upward swings. We like to make money, so why should we be penalized when we do well? In looking for a solution, investors will often turn to another risk-adjusted measure: the Ulcer Performance Index.

The Ulcer Performance Index (UPI)
Whereas the Sharpe Ratio is a metric derived strictly from ALL deviations from the mean return, the Ulcer Performance Index does not penalize for periods in which we have positive returns. The equation for UPI is as follows:

Ulcer Performance Index = (Portfolio Return - Risk Free Rate) / Ulcer Index

Notice how the key difference in the equation compared to the Sharpe Ratio is the denominator. With the Sharpe Ratio, we are dividing by the standard deviation (which also includes good periods in which we generate positive returns in our portfolio).

Ulcer Index
To further understand this equation, we need to continue unpacking what the Ulcer Index is. This Ulcer Index is calculated in three steps:

1. Percentage Drawdowns = ((Close - N Period Highest Close) / N Period Highest Close) * 100
2. Squared Average = (Sum of N Period Percentage Drawdowns2) / N Period
3. Ulcer Index = Squared Average1/2

To the layman investor, much of the math may be confusing. So, to put it simply, the Ulcer Index seeks to measure the longevity and severity of drawdowns relative to returns. Just like the Sharpe Ratio, the higher the UPI, the better.