Does Portfolio Rebalancing Help Investors Avoid Common Mistakes?

Does Portfolio Rebalancing Help Investors Avoid Common Mistakes? Steven L. Beach Assistant Professor of Finance Department of Accounting, Finance, and Business Law College of Business and Economics Radford University Radford, VA 24142-6951 Email: slbeach@radford.edu Clarence C. Rose Professor of Finance Department of Accounting, Finance, and Business Law College of Business and Economics Radford University Radford, VA 24142-6951 Email: crose@radford.edu 1

Does Portfolio Re-balancing Help Investors Avoid Common Mistakes? Introduction Investing decisions driven by normal human behavior can have a devastating impact upon long term wealth accumulation. Individual investors, and sometimes even professional fund managers, allow their emotions to get in the way of rational investment decision making. As investors, our emotions often encourage us to buy and sell investments at the wrong time. Investors have a costly tendency to buy high and sell low, pouring more money into the market when it is up and selling when things look dire. (Futrelle, 2004) From a long term wealth accumulation standpoint this is exactly opposite of what investors should do in order to enhance returns and accumulate wealth. This article presents an overview of some behavioral aspects of investor decision making and examines the impact of portfolio rebalancing on reducing common investment mistakes and achieving investment goals. Returns from annually rebalanced portfolios with different asset allocation mixes are compared to the returns from portfolios that chase the past year s investment winners. The analysis uses geometric returns from the different portfolio styles to compare long term investment portfolio performance. Investment Behavior Issues The area of research that examines the issues related to investor behavior is known as behavioral finance. Behavioral finance is a rapidly growing area of study which examines a wide variety of human actions which affect investment performance. Many basic investment errors caused by human behavior have been cited to justify common strategies recommended by financial advisors. These investment strategies are portfolio rebalancing (Buetow, et.al., 2002), dollar-cost averaging (Statman, 1995), and the let it ride strategy that is generally based upon the expectation of time diversification (Fisher and Statman, 1999). In addition, research indicates that overconfident investors trade too much, negatively impacting their performance (Barber and Odean, 2000) and that internet trading leads to costly overconfidence (Odean and Barber, 2002). 2

Often cited in the investment research literature are several behavioral issues which impact investment performance. Issues discussed in this paper are herd mentality, regret aversion and mental accounting. Herd Mentality The herd mentality reflects the natural tendency for individuals to do what is currently popular. The herd mentality feeds the penchant for investors to buy securities after the market has risen and sell securities when the market is down. Individuals tend to place more money into the stock market as fashion dictates that stock market investing is the in thing to do. Herding is defined as a group of investors following each other into (or out of) the same securities over a period of time. (Sias, 2004) The result is that investors who follow the crowd can miss opportunities to realize major gains. Individual investors are not alone in following the crowd. The herd mentality of institutional investors is clearly documented (Nofsinger and Sias, 1999). Regret Aversion People wish to avoid the pain of regret associated with bad decisions. This reaction is especially true in investment decision making. We have a natural desire to avoid admitting an error and realizing a loss (Kahneman and Tversky, 1982). Regret aversion can cause investors to hold onto losing positions too long. Regret aversion also keeps investors out of a market that has recently generated losses, when investment bargains may be most readily available. Having experienced stock market losses, our instincts tell us that to continue investing is not a prudent decision. However, these periods of depressed prices often present the greatest buying opportunities. Regret aversion can persuade us to stay out of the stock market, just when the time is right for investing more. Mental Accounting According to behavioral portfolio theory, mental accounting is used by investors to build portfolios as separate accounts. Experimental research indicates that investors do not consider the correlations among assets (Kroll, Levy, and Rapoport, 1988). Tversky and Kahneman (1986) 3

contend that the difficulty individuals have in addressing the interaction of different investments leads investors to construct portfolios in a layered pyramid format. Each layer of the portfolio addresses a particular investment goal, independent of the other investment goals. Investors target low-risk investments like cash and money market funds to preserve wealth, they target bonds and dividend-paying stocks to provide income, and they target risky investments like emerging market stocks and IPOs to have a chance to get rich. Opportunities to reduce risk by combining assets with low correlations may be neglected and inefficient investing may result from offsetting positions in the various layers (Shefrin and Statman, 2000). Investors quite often do not evaluate investments based on the contribution to the overall portfolio return and total risk, but only upon the recent performance of the asset layer. Investors may feel overwhelmed by the complexity of the investment environment. While wealth maximization is the generally accepted paradigm guiding investment decisions, a landmark study of the decision-making process shows that individual decision makers are more likely to satisfice than maximize (Cyert and March, 1963). In order to maximize, an investor must select the best alternative from among all available options. This process is very complex and time consuming and beyond the ability of most decision makers. Decision makers satisfice by looking for a course of action that is satisfactory or good enough within the overwhelming complexity of the real world (Simon, 1955). Comparing Investment Returns: The Chase versus Rebalanced Portfolios In order to examine the impact of human behavior on investment returns and the potential benefit of portfolio rebalancing as a structured investment strategy, we investigate the return performance of two styles of investing. One is the chase portfolio, which is the approach of chasing the returns of the previous year s best investment return segment. The other style is one of rebalancing the portfolio annually to some predetermined weights among stocks, bonds, and cash (t-bills). It is generally asserted that investors can establish their proper allocation to the three asset classes according to their level of risk aversion and investment time horizon. 4

In evaluating the investment returns, all calculations use geometric returns (as opposed to arithmetic returns). When applied to a portfolio, the use of geometric returns helps to document the ending value of portfolios over their holding period. Transaction costs are not considered, however, it is likely that they would be relatively similar across the various investment portfolios. Data Analysis The annual returns from 1926 to 2002 on three asset classes: large company stocks, longterm corporate bonds, and treasury bills, all from the Ibbotson data (Ibbotson, 2003) are used in our analysis. In the chase portfolio, 100% of the available investment funds are moved each year to the asset class with the highest previous year s return. The rebalancing portfolios contain weights varying from 100% in stocks to 100% in long-term bonds. The portfolios between the 100% extremes are constructed with a 5% allocation to t-bills. While approximately 90 percent of investors own some type of cash vehicle, such as t- bills and/or money market mutual funds, the preferred allocation for cash depends on a number of factors, including the investor s risk tolerance and investment time horizon (Davis, 2004). In our analysis, we assume a long-term investment time horizon and a minimum need for liquidity. As a result, the allocation to cash remains constant at 5% and the stock and long-term bond allocations are adjusted at 10% increments. Performance Results Over the period of analysis, as expected, stocks provided the highest average annual return and the highest standard deviation of the three asset classes. T-bills provided the lowest average annual return and the lowest standard deviation of the three asset classes. The bonds annual average returns and standard deviation fell in between. Bond returns had about the same correlation with the stock and t-bill returns (19.3% and 20.5%), while the stock and t-bill returns are slightly negatively correlated (-1.6%). Summary statistics are provided in TABLE 1. The Sharpe ratio (average excess return / standard deviation of return) was highest for the large stock portfolio. Assuming investors make their decisions based on the risk and return tradeoffs, this 5

comparison suggests that stock investing performs better than bond investing. Over the 77 years analyzed, bonds produced higher returns than stocks in 30 years, T-bills produced higher returns than stocks in 29 years, and stocks produced the highest returns in 44 years. TABLE 1: AVERAGE ANNUAL RETURNS 1926 2002 Avg. Annualized Return Std. Deviation Correlation Stock Bonds T-Bills Sharpe Ratio Lg Stock 10.19% 20.63% 19.3% -1.6%.4001 LT Bond 5.88% 8.72% 19.3% 20.5%.2742 T-bill 3.79% 3.15% -1.6% 20.5% NA As shown in TABLE 2, the highest portfolio returns are for the 100% stock portfolio (10.19%), however, the stock-only portfolio also had the highest standard deviation (20.63%). The 45% stock portfolio has the highest Sharpe ratio, providing the highest return premium per unit of risk. The chase portfolio has a lower Sharpe ratio than almost all of the rebalanced portfolios. The chase portfolio did not generate additional returns sufficient to compensate investors for the higher risk. TABLE 2: ANNUAL RETURNS FOR THE CHASE PORTFOLIO VERSUS REBALANCED PORTFOLIOS 1927-2002 Annualized Std. Sharpe Return Deviation Ratio Min Max Chase 8.25% 14.36%.3626-35.63% 43.61% 100/0/0 10.19% 20.63%.4001-43.34% 53.99% 95/0/5 9.97% 19.59%.4001-41.12% 51.31% 85/10/5 9.71% 17.72%.4086-36.97% 46.94% 75/20/5 9.40% 15.90%.4178-32.82% 42.58% 65/30/5 9.06% 14.15%.4273-28.67% 38.22% 55/40/5 8.67% 12.51%.4362-24.52% 33.86% 45/50/5 8.23% 11.00%.4422-20.37% 31.44% 35/60/5 7.76% 9.72%.4410-16.23% 33.56% 25/70/5 7.25% 8.74%.4247-12.08% 35.67% 15/80/5 6.70% 8.19%.3841-7.93% 37.79% 5/90/5 6.10% 8.15%.3159-7.38% 39.90% 0/100/0 5.88% 8.72%.2742-8.09% 42.56% Chase portfolio: Annually move 100% to asset class with highest previous year return Other portfolios are 100% stock, rebalanced portfolios with Stock/Bond/T-bill investments, 100% Bond. To examine a more relevant set of results for many investors, we have continued the analysis with an assumed 20-year investment time horizon (see TABLE 3). Now, the results for each portfolio are for 57 observations of 20-year investments, with annual rebalancing. The first 6

observation for each portfolio is the 1927 to 1946 period and the last observation is the 1983 to 2002 period. The 100% stock portfolio provides the highest average annualized 20-year return (11.43%), combined with the highest average standard deviation of the returns (18.13%). Investors with the greatest risk aversion over a 20-year time horizon would have best invested 45% in stocks, which provided a minimum return performance of a relatively solid 4.62% over a 20-year period. The risk and return tradeoff suggests that even for conservative investors, it may be undesirable to allocate less than 45% to stocks. The chase portfolio generated an average return (7.62%) similar to the portfolios with 25% to 35% allocations to stocks, however its standard deviation (13.22%) was more aligned with the higher stock allocation portfolios. No portfolio suffered a loss for any 20-year investment period. TABLE 3: 20-YEAR HOLDING PERIOD SUMMARY Avg. Annualized 20-yr Return Avg. Annual Std.Deviation for 20-yr Returns Min Max HPs w/ return higher than Chase (of 57) Chase 7.62% 13.22% 2.84% 12.58% 100/0/0 11.43% 18.13% 3.11% 17.87% 53 95/0/5 11.13% 17.21% 3.16% 17.36% 53 85/10/5 10.64% 15.64% 3.59% 16.71% 53 75/20/5 10.11% 14.13% 3.95% 16.04% 54 65/30/5 9.56% 12.68% 4.24% 15.35% 51 55/40/5 8.98% 11.31% 4.46% 14.66% 47 45/50/5 8.63% 10.04% 4.62% 13.97% 42 35/60/5 7.72% 8.91% 4.42% 13.28% 31 25/70/5 7.05% 7.97% 3.91% 12.80% 26 15/80/5 6.34% 7.32% 3.37% 12.44% 23 5/90/5 5.61% 7.12% 2.10% 12.05% 18 0/100/0 5.28% 7.62% 1.34% 12.13% 14 Results of returns over 20-year periods in a chase portfolio and stock/bond/t-bill rebalanced portfolios Last column: the number of 20-year holding periods with higher returns than the chase portfolio For any allocation of 75% or more to stocks, the rebalanced portfolio produced a higher ending wealth than the chase portfolio in at least 53 of the 57 20-year investment holding periods. Since these average returns and standard deviations are from overlapping observations, which limits statistical inference, the remaining discussion will primarily focus on average, minimum, 7

and maximum returns. Acknowledging this statistical limitation, it is useful to examine the efficient frontier of the different asset allocations and the chase portfolio for the 20-year returns. As shown in EXHIBIT 1, it appears that the chase portfolio would not be a likely choice for any risk-averse investor, due its low return relative to its risk. EXHIBIT 1: EFFICIENT FRONTIER FOR 20-YEAR INVESTMENT HORIZON 12% 20-year Investment Horizon 10% 100% Stocks 8% Chase Portfolio Annualized Return 6% 4% 100% Bonds 2% 0% 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% Average Annual Standard Deviation) In TABLE 4, the portfolio results are presented in dollar amounts assuming a $1,000 investment with a 20-year time horizon. The 20-year investment time horizon results suggest that investors can maximize portfolio value by placing all investment in stocks, however, most of us need a greater level of security than that provides. The best minimum ending portfolio value of $2,469 was earned by the 45% stocks, 50% bonds and 5% t-bills portfolio. By chasing last year s investment winners, investors received at best an ending portfolio value of $10,702 over any 20- year investment period. This return is comparable only to rebalanced portfolios with less than 25% in stocks. For investors who recognize the risk of this active and aggressive approach, the long-term payoff from the chase portfolio would not be satisfactory. 8

TABLE 4: 20-YEAR ENDING PORTFOLIO VALUES Avg. ending Min Max 1983-2002 Chase $4,754 $1750 $10702 11.61% 100/0/0 $10363 $1844 $26816 12.71% 95/0/5 $9669 $1862 $24575 12.41% 85/10/5 $8656 $2024 $21973 12.36% 75/20/5 $7747 $2169 $19583 12.27% 65/30/5 $6933 $2293 $17396 12.16% 55/40/5 $6203 $2394 $15424 12.01% 45/50/5 $5550 $2469 $13683 11.84% 35/60/5 $4964 $2375 $12098 11.64% 25/70/5 $4438 $2154 $11128 11.42% 15/80/5 $3966 $1940 $10425 11.17% 5/90/5 $3542 $1515 $9730 10.89% 0/100/0 $3397 $1305 $9867 10.99% Results of ending portfolio values for $1000 invested for 20 years in a chase portfolio and stock/bond/t-bill rebalanced portfolios. Finally, when we consider the last 20-year period, running from 1983 to the end of 2002, all rebalanced portfolios with stock allocations of 35% or more outperformed the chase portfolio even though the last two years were particularly devastating for the stock returns. For 2001 and 2002, stock returns were -11.88% and -22.1%. With the chase portfolio in those 2 years, the returns would have been 10.65% and 16.33% with a 100% investment in the bond market. The chase portfolio also had returns of 23.07%, 33.36%, 28.58%, and 21.04% with 100% stock allocation in 1996-1999. It is quite impressive that the rebalanced portfolios provide slightly better returns over the 20-year period that ended on such a weak note for stocks. Summary and Conclusions In summary, for a 20-year investment time horizon and for the risk involved, the chase portfolio had relatively weak returns. When rebalanced annually, only the most conservative asset allocation portfolios provided lower returns than the chase portfolio. These historical results should be of great interest to investors who may be attracted to chase last year s investment winners and financial planners who may be requested by their clients to chase the market. Based on historical investment results, an allocation of 45% to stocks provided the best risk and return tradeoff, measured by the Sharpe ratio. It also produced the largest minimum return over a 20- year investment horizon. Allocating a greater proportion to stocks provided higher average 9

returns with higher risk. Thus, an allocation of 45% to stocks in rebalancing portfolios may be viewed as the minimum stock investment for achieving a long-term goal of maximizing wealth over a 20-year investment time horizon. It appears that the forced discipline of portfolio rebalancing, with a significant allocation to stocks, can help investors achieve long-term investment goals and help investors avoid behavioral investment mistakes. 10

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