The measurement of risk is a lot of models in finance is inappropriate to some extent. And in my own arsenal of tools, I have continually tried to err away from using traditional assumptions. These assumptions were made popular from the titans of portfolio theory. (I am not going to give a bash on the MPT and how it’s a minority view that EMH is wrong, as it isn’t a minority view…)
In the convenient and accepted norm, risk = whether you can sleep at night or put another way the “volatility” of your portfolio. With such objective and quantitative measure came a whole sort of metrics, (Sharpe ratio, black Scholes formula, etc). Does it do a good job intuitively to model the real world? If you look at the equation for standard deviation, you will see that it doesn’t differentiate between upside and downside volatility. Further on, ask yourself if you care about upside volatility? Evidence from multiple bull market shows the euphoria that takes place when the stock market goes up as a whole. I am not afraid to deduce that people treat upside volatility with a welcome.
Then it must be I intuitive to accept that downside volatility is a better measure of risk. What metric can one use to measure such things? Below are a few of my favorites.
Where r is return, r(f) is risk free rate, and the denominator is the downside standard deviation
Ulcer Performance Index (UPI)
Where p(i) is price, p(max) is the max price during period
Where r is return, and r(f) is risk free rate
The above ratio are modified versions which I use a lot in strategy testing as a measure of goodness. I once only concentrated on the MAR but then found other measures to add value. I personally use the above and a few others.
*A note on the Sortino Ratio: There are variations to calculations to this ratio. Some calcualtions take into account the zeros which are days with upside return. There are disagreements with to whether this is correct. Readers should be aware and know which one you are using.