In our previous posts on risk we examined the definition of risk and how to measure risk. In this post we will examine how to measure risk and return through statistics by examining ways to compare the risk-adjusted performance of investments with differing risk and return profiles. Incorporating these ideas will help you determine the most appropriate investment choices for your clients.
The Sharpe ratio, developed by Nobel Laureate William F. Sharpe, is a statistic which measures risk-adjusted performance. The ratio expresses how much additional return is received from an investment portfolio for each additional unit of risk taken on. It is calculated by subtracting the risk free rate of return, such as the 3-month T-bill rate, from the rate of return for an investment and dividing by the standard deviation of the portfolio returns.
The greater a portfolio’s Sharpe ratio, the better its risk-adjusted performance has been.
A similar statistic to the Sharpe ratio, the Sortino Ratio removes the effects of upward price movements on standard deviation to measure return against downward price movements only (downside deviation). The Sortino ratio subtracts the risk-free rate of return from the rate of return for an investment and divides by the downside deviation.
As an example, let’s consider two diverse investment options, large cap equities (S&P 500 TR Index) and gold (SPDR Gold Shares ETF – GLD). From the table below we can see these two investment options are uncorrelated to one another (GLD’s correlation to the S&P is essentially zero, 0.06, over the 7 year period of July 2007 through June 2014). The S&P has had an annualized return of +6.16%, a standard deviation of 16.92%, Sharpe ratio of 0.40 and Sortino ratio of 0.56. As a comparison, GLD has an annualized return of +10.14%, standard deviation of 21.05%, Sharpe ratio of 0.54 and Sortino ratio of 0.82. The third row of the table below represents an investment of 50% S&P 500 TR Index and 50% GLD over the same time period. The annualized return of the 50/50 blend is +9.59%, standard deviation is 13.87%, Sharpe ratio of 0.69 and Sortino ratio of 1.04. Notice that by combining non-correlating investment risks you actually achieve a superior risk adjusted investment, as evidenced by the higher Sharpe and Sortino ratios, than by investing in either of the investment options themselves.
The following chart represents how a $100,000 investment would have grown over this time period. The yellow line represents an investment in GLD. The blue line represents an investment in the S&P 500 TR Index. The green line represents an investment in the 50/50 blend. Notice how much more smooth the ride for the 50/50 investor is over the other two options.
At CMG, our cornerstone belief is that risk must always be addressed along with potential reward when considering investment options. The Sharpe ratio and Sortino ratio are two statistics that can help you determine the most appropriate investment choices for your clients through simultaneously considering risk and returns. –Michael Hee