Posted by Dan Hung
October 3, 2007
It’s been a while, but we’ll finally finish up the portfolio performance metrics that I intended to introduce during the whole portfolio performance series that I’ve been writing on and off over the last few weeks. If you remember, the last post was on the Sharpe Ratio. The Sharpe
ratio is a slightly more exacting portfolio risk calculation in comparison to the beta and alpha combination, but, for all intents and purposes, delivers similar information in that it attempts to quantify how much a portfolio strategy made in excess of the volatility (risk) it assumes. The Sortino Ratio is an adjustment on the Sharpe Ratio in that it only penalizes downside
volatility. This is done by creating a value known as downside deviation which is based on
some minimum acceptable return (MAR) which is a rate of return that an investor can set.
This could be 0%, if you want to judge your portfolio on how well it operates with respect to never losing money. Or, .43% which is the approximate monthly rate of return you would receive on a 5% annual risk free asset (unrealistic given current interest rates). The equation for the Sortino Ratio is actually quite easy:
Sortino Ratio = (Compound Period Return – MAR)/Downside Deviation
Compound monthly return is calculated by taking the total return over a given number of periods then calculating the rate of return that would have to be compounded in each period to yield such return. An equation might look someting like this:
Compound Period Return = (1+Total Return)^(1/N) – 1
N is the number of periods. Total Return is simply the percent return over a number of periods. For example, 20% return over one year would yield a compound monthly return of 1.2^(1/12)-1 = 1.53%.
If you’re really lazy, you can usually just average the period returns for a relatively decent approximation provided that your portfolio returns are not overly volatile. Downside Deviation is the most difficult number to calculate. Here are the steps:
1. Subtract MAR from each period’s return.
2. If negative, record the value. If positive, set value to 0.
3. Square all the period returns and sum them.
4. Divide by the number of periods.
5. Take the square root of your result.
There you have it, all the tools to calculate Sortino Ratio. Give it a try. I’ll upload an excel
file in a final post which will do calculations of the metrics I mentioned in this post series so don’t worry if my instructions are hard to follow.