You might have noticed that the asset classes with the highest total returns also tend to have the highest standard deviations. That is no coincidence. Most investors are risk averse, which means in order to take on more risk, they must be compensated with greater expected returns. That also makes it difficult to compare the absolute returns of asset classes to one another, since riskier assets should have a higher return. You can’t say emerging market stocks are a better investment than REITs, just because emerging markets have had a higher return. You also have to take risk into account.

The way to do this is through the Sharpe Ratio, which is a risk adjusted performance measure. The higher the ratio, the better the risk adjusted rate of return. The ratio is calculated by subtracting the risk free rate of return (normally the return from treasury bills) from the actual return, and dividing that by the standard deviation of the risky asset. For example, U.S. small stocks had a total return of 10.5% per year from 1991-2015. The comparable rate of return for cash, which I use as a proxy for the risk free rate of return, was 3.2%. (10.5% - 3.2%)/19.3% = a Sharpe Ratio of 0.38.

Based on the Sharpe ratio, bonds easily had the highest risk adjusted return between 1991-2015, followed by REITs and U.S. stocks. So everyone should just invest in the asset classes with the highest risk adjusted asset classes, right? Again, not so fast. We also have to consider five very important things: 1.) specific return goals, 2.) how asset returns are correlated, 3.) time horizon, 4.) the impact of taxes and inflation, and 5.) changes in market conditions that could affect future returns.


Specific Return Goals

The Comparative Returns chart shows that U.S. bonds had the greatest risk adjusted returns between 1991-2015, with a Sharpe ratio of 0.60. But absolute returns still matter. For example, say you’ve calculated that you will need to earn a nominal annual return of 9% to meet your financial goal. Investing 100% of your funds in bonds likely isn’t going to get you there, since based simply on historical returns, bonds would have an expected return of only 6.2% per year. Remember, the expected return of a portfolio is the weighted average of the expected returns of the assets within it. To get to an overall expected return of 9%, you would need to add a proportional amount of riskier investments.


Asset Correlation

Continuing with the previous example, an investor could increase returns of a bond only portfolio by adding higher expected return assets with a high Sharpe ratio to help bring the expected portfolio return closer to 9%. Next on the list are Real Estate Investment Trusts, with a Sharpe ratio of 0.48. Based on history, those have an expected return of 12.1%. So if we had say a portfolio of 50% bonds and 50% REITs, we get an overall expected portfolio return of (.5)(.062) + (.5)(.121) = 9.2%. Bingo! That gets us to our goal.

Another cool thing in this case is that the returns of bonds and REITs are not highly correlated. In fact, between April 2009 and March 2016, they were negatively correlated. When bonds move higher, REITs tend to fall, and vice-versa. That means during this time, losses in one of these two asset classes were at least partially mitigated by gains in the other. This is a main benefit of diversification, which I discuss in more detail in the next installment of this series.


Time Horizon

One of the more controversial aspects of financial theory over the last two decades or so is the idea of time diversification, which is the notion that stocks are less risky over longer time periods than they are over shorter ones. The idea is rooted in statistics, in that the distribution of annualized returns converges as the investment horizon increases. For example, recall from the Comparative Returns chart that between 1991-2015, U.S. large-cap stocks had an annualized return of 10.1%, and a standard deviation of 18.3%. That yields a 1-year expected return band (95% confidence interval) of -26.6% to 46.7%. In other words, there is a 95% probability that the total return of U.S. large-cap stocks in the next year will fall somewhere between a loss of 27% or a gain of 47%, based on that standard deviation of 18.3%.

Now look what happens to the standard deviation if we look farther into the future, say thirty years. That standard deviation becomes 18.3%/the square root of 30, = 18.3%/5.477 = 3.3%. The 95% confidence interval for the expected annual return for large U.S. stocks is now 10.1% +/- (2*3.3%), or 3.5% to 16.7%. That's a much tighter range than the one year 95% confidence interval of -27% to 47%, and lower variability means less risk, or so goes the theory.

Those who oppose the notion of time diversification note that as time increases, the risk to the dollar value of your portfolio actually rises over time. To see this, we need to consider the idea of terminal wealth dispersion. Let’s plot out the 95% confidence interval I calculated above over a hypothetical 30-year period to see how $1,000 today would grow at the low, high, and expected return of that range. You can see if large U.S. stocks grow at 16.7% per year, which is the very top of the range, then $1,000 today becomes almost $103,000 in thirty years. We would all love that, but the probability of this happening is low. It is much more likely that we will experience a return closer to the historical average, which in this case is 10.1% per year. The bottom blue line represents the low case. Notice that the difference between the orange line (expected case) and blue line (low case) increases as time goes on. That is the reason time diversification does not work on an absolute basis, because the risk that your actual realized portfolio value does not meet its expected value grows over time.