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January 2002 The Best Asset Allocation
Although many things have changed over the past several months, some haven’t including the following:
 their strategy, we thought this would be a good time to investigate which asset allocations historically performed the best. Our ultimate goal was to see if this information could be useful in helping investors build portfolios for the future.
We based our study on the 75-year period extending from January 1, 1926 through December 29, 2000. To test different asset allocations, we created 21 different portfolios mixing bonds and stocks in 5% increments. In other words, the first was 0% bonds, 100% stocks, the second was 5% bonds, 95% stocks, etc, all the way to last portfolio of 100% bonds, 0% stocks. To simplify matters and make the results as close to what a real investor could expect, we made the following assumptions:
Risk and ReturnNot surprisingly, the best returns over the 75-year period came from the portfolio of 100% stocks. Over the long-term -- especially this long a term -- stocks should be expected to outperform fixed income.But this is only looking at one part of the equation. Portfolios with higher stock percentages should outperform as they incorporate more risk. Investors typically expect greater returns to compensate them for assuming more risk. Chart 1 clearly illustrates this. The green bars represent the various portfolios’ annualized inflation-adjusted returns while the purple bars show their standard deviations. Standard deviation measures the variability of returns around their average. Returns should fall within one standard deviation -- either above or below the average -- two thirds of the time. The greater the standard deviation, the wider the range of expected returns. Since "risk" is often described as the likelihood of not achieving the expected return, portfolios with higher standard deviations are riskier. As you’d expect, the all-stock portfolio not only had the greatest return, it also had the greatest risk. Risk and return are rarely evenly distributed. While aggressive portfolios may have higher returns, they may also have disproportionate risk. In a general sense, risk-averse investors demand equal or greater amounts of additional return for each increase in risk. Rather than focusing on absolute return, investors should consider risk-adjusted return. The Sharpe Measure is an easy and intuitive way to measure risk-adjusted return. Essentially it compares excess return over a risk-free rate to the risk assumed. Higher values are preferred since they imply 1)greater return, 2)lower risk, or 3)both.
Chart 2 compares the Sharpe Measures for each of our portfolios. There are several things to notice. First, although the all-stock portfolio had the highest return over the period, it didn’t have the highest risk-adjusted return. That award goes to the 60% bond/40% stock mix. The 100% stock investor was not fully rewarded for the risk she assumed. Secondly, the most efficient risk-adjusted portfolios fall in the middle of the spectrum. This is an argument for diversification. It’s understandable that all-stock or even mostly-stock portfolios (those appearing on the left side of the chart) would be more volatile, so it makes sense that they are less efficient. But the same also holds for the most conservative portfolios -- those appearing on the right side of the chart. That too, is understandable since they are heavily concentrated in one asset class. While bonds -- especially intermediate term government bonds -- aren’t nearly as volatile as stocks, they do only represent one asset class. Anything negatively affecting it will have a much greater impact on these portfolios than those that are diversified across classes. So there you have it: For the period 1926 to 2000, the most efficient asset allocation was 60% bonds, 40% stocks. This mix produced the highest risk-adjusted return. Time HorizonBut do you really plan to hold your investments for 75 years? Probably not. Even if you’re investing for your retirement you probably have a 40-year time horizon at most. If you’re saving for your child’s education it’s more like 10 years and it could be even less if you’re building a down payment for a home. Would that same 60/40 mix be the best alternative for these shorter time periods?
To test this, we looked at different 10-year periods from 1926 to 2000. We chose 10 years because that’s a fairly average investment horizon and one that most would consider "long-term". First, consider how this mix would have fared in the decade of the ‘90s. Chart 3 shows the annual arithmetic returns for all 21 of our portfolios. The 60/40 mix is highlighted in red and the portfolio with the highest Sharpe Measure is marked in yellow. Not surprisingly, the all-stock portfolio had the highest average return -- after all, that was the decade of the stock market euphoria. What is surprising is the most efficient mix. While stocks were lighting up the returns, the most conservative, lowest returning portfolio had the highest risk-adjusted return. How can that be? The key lies in the concept of risk. Recall that standard deviation is a measure of the average dispersion of returns both above and below the mean. Throughout the ‘90s, stocks yielded returns well above their historical norms. As a result, they had high standard deviations and were therefore "risky".
On the other hand, bonds -- especially short and intermediate term governments -- were relatively staid. Their annual returns were much closer to their averages giving them a much lower standard deviation and significantly less "risk". So it’s no wonder "risky" stocks were much less efficient in terms of risk-adjusted return. Still, in the ‘90s most investors would have preferred the risky portfolio to the efficient one. They would have preferred it to the 75-year efficient portfolio as well. Does this call into question the Sharpe Measure as a means of finding the best asset allocation? Before coming to that conclusion, we should consider other 10-year periods. After all, the decade of the ‘90s was a period of phenomenal stock performance, perhaps one that will never be repeated again. It would be helpful to look at other periods, perhaps those where stocks actually underperformed. In this vein, we considered the 10-year periods covering the equity bear market of the ‘70s (1/70 - 12/79), the two recessions following World War II (1/45 - 12/54), and the Great Depression (1/29 - 12/38). Results were surprising. In no instance did the 75-year portfolio have either the highest return or the greatest efficiency. Even more notable is each period’s most efficient mix.
In the bear market of the ‘70s (Chart 4) and the post World War II recessions, the stock-heavy portfolios were still able to produce the highest arithmetic returns. This was in spite of adverse economic and market conditions, and is a testament to the recovery ability of stocks. The bond portfolios actually had negative risk-adjusted returns once their gross returns were adjusted for the above average levels of inflation. In the depression years (Chart 5), the stock-heavy mixes still had the highest arithmetic returns. The best was a combination of 20% bonds and 80% stocks. The most efficient risk-adjusted portfolio was at the other end of the spectrum, 90% bonds and 10% stocks. From a return standpoint, investors would have been better off weathering the storm in equity laden portfolios while the best risk-adjusted approach would have been to stick to bonds. In fact, this is the problem throughout the measurement period: Equity-heavy mixes tend to have higher arithmetic returns while more conservative portfolios may be more efficient. Even in periods like the ‘70s and post-World War II recessions when equities prove to be most efficient, they may be the hardest to hold for risk-averse investors. Good Risk and Bad RiskThis apparent dilemma can be resolved by reconciling investors’ risk aversion with the appropriate quantitative measure of risk. We would suggest that standard deviation -- the traditional measure of risk -- does not capture most investors’ concept of risk.
To see why, consider Chart 6. From 1926 - 2000, equities as measured by the S&P 500 had an average inflation-adjusted arithmetic return of 7.73%. The blue line on Chart 6 represents this. Over the same period, stocks had a standard deviation of 20.32%. This means that two thirds of the time, annual returns for an all equity portfolio fell within the range of 28.05% (7.73% + 20.32%) and -12.59% (7.73% - 20.32%). That’s a wide range (40.64%) and in traditional terms would indicate that stocks are quite risky. But think about the ‘90s: Investors were still risk-averse, yet they couldn’t get enough stocks. They sought them out. Were they actually risk-seeking? Indeed they were and it’s not hard to see why. Look back at Chart 3. The average inflation-adjusted annual return for the all-equity portfolio was 15.7%, well above the 7.73% mean. In fact several years produced returns in excess of 20%. Equity returns in the ‘90s were in the upper end of their standard deviation. In such an environment, why wouldn’t rational investors embrace this "risk"? Recently the tables have turned as stocks have corrected and annual returns have been negative. These results are well below the mean and are at the lower end of one standard deviation. In contrast to the "good" risk of the ‘90s, investors shun this "bad" risk. In general investors don’t mind and even pursue "good" risk -- the chance that their return will be above the mean. No one objects to making more than he or she originally anticipated. The green bracket in Chart 6 designates this "good" risk. On the other hand, the red bracket shows the "bad" risk -- the chance their return will be below the mean. But investors don’t necessarily shun "bad" risk. While no one enjoys earning less than anticipated, as long as the return is positive there’s less concern than if there’s an loss. In a sense, it’s like playing with house money -- you haven’t really lost anything and there’s still the chance for future gain. It’s only when actual losses are incurred that investors become risk-averse. Chart 6 illustrates this distinction by dividing "bad" risk into "house money" (yellow part of the bar) and "loss" (red part of the bar). We would submit that investors’ risk-aversion is focused on the risk of loss rather than overall risk. Investors aren’t risk-averse they’re loss-averse. Standard deviation fails to distinguish between "good" risk, "bad" risk, and risk of loss. While it’s true that investors do view alternatives with higher standard deviations as riskier, it’s only because these options have more "bad" risk and greater risk of loss. For most investors, standard deviation is not the appropriate measure of risk when assessing potential asset allocations. Loss Aversion and Holding PeriodIf this is correct, investors should still focus on return, risk, and time horizon when selecting the most appropriate investment mix. But instead of relying upon standard deviation to measure risk, they should consider risk of loss.To incorporate this, we once again turned to the 75 years of data from 1926 - 2000. This time, however, we looked at the greatest losses incurred for each of the 21 portfolios over rolling 5, 10, 15, and 20 year periods. The results are shown in Chart 7. This is perhaps the most eye opening of all the charts we’ve considered. Look first at the 5-year holding periods (blue bars). It comes as no surprise that the equity-heavy mixes to the left of the chart suffered the greatest losses over this time frame. Five years is, after all, a relatively short time horizon and bear markets for stocks can last several years.
But what is surprising is the fact that the bond-heavy portfolios on the other side of the chart can also sustain significant losses over five year periods. In essence, they are subject to the same risk as stock laden portfolios since they too are exposed to the performance of one asset class. If bonds enter a bear market, portfolios heavily concentrated in them will suffer more than those holding a combination of stocks and bonds. This then, is a prime example of the benefits of diversification. Indeed, a well-diversified portfolio is the winning mix over the period. It’s our old friend the 75-year portfolio of 60% bonds and 40% stocks. It had the least loss over the rolling 5-year periods. If you’re a loss-averse investor with a 5-year time horizon, this has historically would been the best alternative for you. Moving to the 10-year periods, again all mixes suffered losses. Notice though, the losses weren’t as severe as for the 5-year periods. With a longer holding period each had a greater opportunity to recover from losses. Also notice the mixes with the least losses have become a little more aggressive, moving towards the left of the chart. In fact, the portfolio with the least loss is now tilted towards equities: 45% bonds, 55% stocks. Across the board, the 15-year periods have lesser losses than the comparable 5 and 10-year results. Once again the smallest loss is in a even more aggressive mix, 35% bonds, 65% stocks. Diversification still works for this time frame, but the more growth-oriented mixes have better recovery potential. In contrast, diversification adds no benefit to the 20-year rolling periods. Here mixes with at least 25% equities suffered no inflation-adjusted losses. The most aggressive portfolio, 100% stocks, came out the best, returning just under 1% in the worst 20-year period. While you often hear that stocks have the best returns over the long-term, did you ever expect they would also be preferable from a risk standpoint? Back to the Original QuestionSo given all this, what is the best asset allocation? There’s little question that the answer depends on the investor’s required return, acceptable risk level, and time horizon.Statistics clearly show that stocks offer the highest return over the long-term. Investors must determine the degree of stocks they are willing to hold given their time horizon and risk aversion. In addition we would suggest that the definition of risk is the most important factor. For the rational, risk-averse investors of Modern Portfolio Theory, the 75-year portfolio of 60% bonds, 40% stocks is probably the best for the long-term. The jury is out for shorter periods as the best risk-adjusted mix can be found at either end of the spectrum of alternatives. The specific time horizon and current market and economic conditions play critical roles in the determination. But for real investors -- those who aren’t always completely rational and who may be more loss-averse than risk-averse -- the choices are actually a little easier. We would suggest a relatively straightforward process in selecting the most appropriate asset allocation:
Markets are constantly changing. Investors’ views of "good" and "bad" risk can change right along with them, yet for most loss-aversion remains relatively constant. By focusing on the most appropriate concept of risk, investors have a better opportunity to select the best asset allocation and even more importantly, stick with it through changing market conditions. Search this site! Just enter you key word or words:
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OR MOST INVESTORS, THE PAST 18 MONTHS have been extremely difficult. Not only have they had to deal with the first bear market in a decade, they’ve also had to navigate the political and economic uncertainty stemming from the September 11th attacks. It’s no wonder many investors are questioning their asset allocation or whether they should be in the market at all.
