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10.46 Ulcer Index

The Ulcer Index by Peter Martin is a measure of downside volatility. For a given N-day period the closing prices are considered from oldest to newest and for each close a retracement percentage is calculated, relative to the highest close so far.

       price[i] - maxprice so far
R[i] = --------------------------
           maxprice so far

So for instance a price $5.00 falling back to $4.50 is a -10% retracement. These are averaged with a quadratic mean, which has the effect of emphasising large drawdowns, but incorporating all into the result.

              / R[1]^2 + R[2]^2 + ... + R[N]^2 \
Ulcer = sqrt |  ------------------------------  |
              \              N                 /

The index can be calculated over the kind of period one might hold an investment to calculate a measure of the ulcer-producing drawdowns suffered during that period.

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