Theoretically, investing has a “risk/reward” relationship. In essence, the more risk the investor assumes as defined by standard deviation, the greater the reward as defined by the geometric return. Looking back over the last 15 years, this has not always been the case. Using Morningstar Category average mutual fund performance for Aggressive Allocation Funds (80% stocks, 20% bonds), Moderate Allocation Funds (55% stocks, 45% bonds), and Conservative Allocation Funds (30% stocks, 70% bonds) and a starting account balance of $100,000 with no ongoing contributions, we will examine the levels of reward and risk over different back-tested periods.
The risk component holds true for all periods: the Aggressive portfolio has the highest standard deviation number, followed by Moderate, and lastly, Conservative. Standard deviation is the positive square root of the variance; a measure of dispersion in the same units as the original data. In other words, how much do the actual returns vary from the average returns over that period? In a normal distribution, approximately 68% of returns will fall within plus or minus 1 standard deviation, 95% of data plus or minus 2 standard deviations and 99% of the data plus or minus 3 standard deviations. Using the Aggressive Allocation 3-year numbers as an example, 68% of the returns would fall between -5.85% and 21.45% (7.80-13.65; 7.80+13.65), 95% of the returns would fall between -19.50% and 35.10, 99% of the returns would fall between -33.15% and 48.75%.
The reward component tells a different story. Over the last 3-year period ending December 31, 2012, the results are to be expected that the highest-risk portfolio gave the highest reward as depicted in the ending balance of $125,272.66, followed by Moderate and Conservative. The same can be said for the last 10 years. Where we find inconsistencies is in the 5-year return, where the results are inverted (with the Conservative finishing on top with an ending balance of $119,516.00 and the Aggressive finishing worst with an ending balance of $104,945.01) and the 15-year return, where Moderate was the best-performing followed by Conservative and then Aggressive.
The main point to consider when investing for long-time horizons is to invest in a well-diversified portfolio consistent with your personal risk tolerance, because, as demonstrated, you are not always rewarded according to the level of risk.
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