Mutual Fund Unlocked: Ulcer Index, another way of measuring investment risk
A lot of bytes and reams of paper have been used to explain the risk in mutual fund investment and various ways of assessing and evaluating them. The most popular being the standard deviation. Although, it is widely used, there are certain drawbacks of this measure of risk that may not entirely capture the pain of an investor. For example, as an investor, you are not worried much if your investment is continuously moving up. Standard deviation does not differentiate between upside and downside movement and treats both in a similar fashion. Moreover, it fails to capture series of losses that result in substantial fall in the investment value.
Ulcer Index developed by Peter G. Martin correctly captures the investor’s pain, which contains more information compared to standard deviation. Ulcer Index addresses the real concerns of investors and measures both the percentage of downfall and for what time such fall sustained from earlier highs.
Ulcer index is calculated as follows for ‘xx’ period.
o Percentage Drawdown = [(Close – ‘xx’ period High Close)/’xx’- period High Close] x 100
o Squared Average = (‘xx’-period Sum of Percentage Drawdown Squared)/’xx’
o Ulcer Index = Square Root of Squared Average
The following graph and explanation picked from his book correctly explain why standard deviation might not be the right metric to calculate risk and investor’s pain.
![](data:image/png;base64,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)
- The three hypothetical investments in the chart above have the same annualized return (-0.52%/year) and the same SD (4.66%/month), but no rational investor would consider them as having the same risk.
The longer the period, the better you can judge the performance of the investment. Daily and weekly NAVs will give you a better picture of investor’s stress.
The way to interpret ulcer index is lower the better and hence if a fund has Ulcer index of zero, the investment would have never lost money. This index should be used to evaluate the performance of different funds in terms of protecting the downside risk. Therefore, if you are a risk aversive investor you should check this index for different funds that you are contemplating to invest in.