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# Measures of Risk

Discussion in 'Strategy Development' started by nonlinear5, Jan 16, 2007.

1. ### nonlinear5

I am looking for a good measure of risk to use for evaluation of my trading strategies. I looked at various existing standard trading stats measures, and they looked unsatisfactory to me. Here is a summary (by no means complete):

1. Largest drawdown. Suppose you compare two systems, A and B. The largest drawdown for A is 20%, but the rest of the drawdowns did not exceed 5%. The largest drawdown for B is 18%, but the system suffered through 10 of them in the same test period. Now, if you use the largest drawdown measure, system B will be deemed less risky, while I think it's obvious that the opposite is true.

2. Sharpe's Ratio. The denominator uses the standard deviation of returns. What this means is that the risk of strategy A which made {-5%, +5%, -5%, +5%} in four months is the same as the risk of strategy B which made {+5%, +15%, +5%, +15%} in the same four months, since the standard deviation of returns for both strategies is the same , 5.77.

3. Sortino's Ratio. This tries to address the above problem with the Sharpe's ratio by using the standard deviation of negative returns only. But this leads to even greater bias. Suppose strategy A performance is this: {+5%, -15%, +5%, -15%, +5%, -15%}. Guess what the risk is according to Sortino's ratio? Zero. That's because all negative returns are the same.

While thinking about all the problems associated with these standard measures of risk in trading systems, I recalled the "efficiency" measure that Perry Kaufman proposed (for completely different purposes). It occured to me that it could the a perfect measure of risk in a strategy. Adapted for the strategy risk evaluation, it would look like this:

Risk (of a strategy) = TP

where TP is a total path of the equity measures the legth of the total path. Example: compare the equity curves of two strategies (both made the same return by starting with \$100 and ending up up with \$140)

A: {\$100, \$90, \$120, \$110, \$140}
B: {\$100, \$70, \$150, \$100, \$140}

The risk of A is: abs(100-90) + abs(120-90) + abs(110-120) + abs(140-110) = 80
The risk of B is: abs(100-70) + abs(150-70) + abs(100-150) + abs(140-100) = 200

What do you think?

Are they really relevant?

3. ### MGJ

First figure out what you want.

Do you really WANT to measure "risk"?

Or do you want to measure "pain" so you can compute a gain-to-pain ratio?

Some of the more common measurements of "pain" include standard deviation of returns, downside deviation of returns, maximum drawdown, Ulcer Index, and R-squared*.

There's really only one agreed upon way to measure "risk": how much would you lose if each and every one of your positions went against you today and ran all the way to your exit point (your stoploss). Even that is just an estimate, since the market price could gap well beyond your stop loss order(s) and give you a much worse fill than you expect.

*R-squared is the goodness-of-fit statistic when you perform linear regression on the equity curve (on semilog axes). The ideal equity curve is a perfectly straight line with no wiggles (i.e. perfectly constant returns and no drawdowns) so the ideal value of R-squared is 1.00. Real life equity curves do however exhibit drawdowns so real life R-squared values are less than 1.00.

You might want to lay hands on a book or two from the library, that go over these topics in great detail.

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