Michael Hee
Managing Director, Investment Research
CMG
In my previous post we discussed “What is Risk.” As a follow-up, we will begin to explore how to measure risk. When considering investment options, analyzing performance statistics without consideration of risk does not provide a view of the complete picture.
One of the most common measurements of risk is standard deviation, which statistically measures how observations are dispersed around a central tendency. From an investment perspective, standard deviation measures how performance may be dispersed about an expected return.
For example, from January 1, 2007 through December 31, 2013, the annualized return of the S&P 500 TR Index was +6.13%. As a comparison, the return of the Barclays Aggregate Bond TR Index (Agg Bond) was +4.91%. However, the standard deviation of the S&P 500 Index was 16.91% compared to 3.44% for the Agg Bond. From an average return perspective, not much difference, however the potential dispersion is significant.
Statistically speaking, assuming returns are normally distributed, we can expect returns to fall within two standard deviations of the mean 95% of the time. In other words, we can expect S&P 500 TR returns to be 6.13% +/- 33.82%, 95% of the time. That is quite a range, one that your clients may likely not be comfortable with. In comparison, we can expect the Agg Bond returns to be 4.91% +/-6.88%, 95% of the time.
Another common measurement of risk is Value at Risk (VAR). The idea behind VAR is to quantify how bad a loss on an investment could be with a given level of confidence over a defined period of time. For example, the following statement would be an example of VAR: “On an investment of $100,000, with a 95% level of confidence, the most you stand to lose on this investment over a specific time horizon is $X.” Or, in other words, 5% of the time you can expect to lose more than $X.
The confidence level is a probability statement based on the statistical characteristics of the investment and the shape of its distribution curve. As a continuation of our example above, the VAR, with a 95% confidence level over the period of January 1, 2007 through December 31, 2013, of the S&P 500 Index is 8.34% compared to 1.29% for the Agg Bond. Again, there is quite a significant difference in risk between these two investment options.
While these concepts can be complex, it is important to consider the relative risk levels of one investment over another. When developing diversified portfolios for clients, we always consider the risk associated with each investment, and the risk associated with the whole portfolio. We find that clients appreciate the thoughtful application of risk-adjusted portfolio construction before we invest their capital.
In our next post we’ll consider the how to measure risk and return in one statistic such as the Sharpe Ratio and the Sortino Ratio. – Michael Hee
