Mental Accounting and Diversification

The previous chapter detailed how we use mental accounting to track the costs and benefits associated with every decision we make. Mental accounting also affects how we view our investment portfolios.

Fifty years ago, Harry Markowitz, the Nobel prize win­ner for economics, showed people how to consider all their investments as one whole portfolio. His idea was to own the investments that combine to form a portfolio that offers the highest expected return for the desired level of risk. Combining investments into a portfolio causes you to think in terms of diversification. Investors like the idea of diversi­fication. However, the way in which people implement diversification differs from what Markowitz's portfolio the­ory suggests.

To implement portfolio theory, you must consider three important characteristics of each potential investment. The first two parameters are the expected return and the level of risk (as measured by standard deviation of returns). Examining the risk and return makes sense to investors. The third important characteristic is the correla­tion between the returns of each investment. Correlation is how each investment interacts with the others. Mental accounting makes it difficult to implement this important characteristic.

MENTAL ACCOUNTING AND PORTFOLIOS

Stocks often experience large price gains and losses each day—just think about the wild ride of the recent stock market. Modern portfolio theory demonstrates that you can combine different investments to reduce this volatility. By comparing how the prices of different investments change over time, you can construct a portfolio that has a lower risk.

Consider two stocks whose prices move in different price pat­terns over time. The stocks of Techfirm and Bankfirm in Figure 9.1 have approximately the same return and variation in stock price over time. Both stocks experience large price changes. However, notice that, when Techfirm is advancing, Bankfirm is often declining. Because Techfirm and Bankfirm frequently move in opposite direc­tions, buying both stocks creates a portfolio with reduced risk; that is, the value of your portfolio experiences lower variation over time when you own both stocks than if you own just one.

However, creating a portfolio that reduces risk (in the modern portfolio theory sense) means considering the interaction between different investments. Unfortunately, people treat each investment as a separate mental account and tend to ignore the interaction between mental accounts. Instead, investors build portfolios by making buy decisions on each investment individually. Investors tend to pick investments as if they were picking food at a buffet like the one in Figure 9.2: "This looks interesting ... I think I will have some of that... maybe a little of this one ... I heard about that one ..." The decision to purchase a new security—and open a new mental account—does not include the investment's price move­ment with other investments because the mental accounts simply do not interact with each other.

The most useful tool in constructing portfolios and reducing risk the correlation between investments—is difficult for investors to utilize because of mental accounting.1

RISK PERCEPTIONS

Viewing each investment as a separate mental account causes you to misperceive risk. You evaluate each potential investment as if it were the only investment you will own. However, you probably already have a portfolio and are considering an investment to add to it. Therefore, the most important considerations for the evaluation are how both the expected risk and the return of the portfolio will change when a new investment is added. In other words, it is how the new investment interacts with the existing portfolio that matters. Unfortunately, you have trouble evaluating the interactions between mental accounts. Consider this problem:

You have a diversified portfolio of large domestic and interna­tional stocks with some fixed income securities. You are exam­ining the following investments:

____ Commodities

____ Corporate bonds (high grade)

____ Emerging markets stocks

____ Europe and East Asian stocks

____ High-yield bonds

____ Real estate

____ Russell 2000 Growth Index

____ Small-cap stocks

____ Treasury bills

How does the addition of each investment change the risk of the existing portfolio?

I asked 45 undergraduate and 27 graduate students taking my investments courses and 16 investment club participants to sort these nine investments by their level of risk contribution to the portfolio. You should take a minute to rank order these investments on their risk contribution to the portfolio. Give the investment that causes the smallest increase (or largest decrease) in risk to the portfolio a 1. Rank the other investments 2 through 9, where 9 is the one causing the largest increase in risk.

Treasury bills (T-bills) and corporate bonds as investments that would add the least risk, while they think real estate, commodities, and high-yield bonds would add higher risk. Small-capitalization stocks and foreign stocks cause the highest contribution of risk to the portfolio. Notice that all three groups of participants provide a similar ranking of how each investment contributes risk to the exist­ing portfolio. The last ranking in the figure was calculated using the investments' standard deviation of monthly returns from 1980 to 1997.2 Standard deviation is a good measure of an investment's risk. The contributions of the three different groups regarding rank order and magnitude of risk are very similar to the risk ranking using stan­dard deviation as the measure. These groups did a good job of understanding the risk of each investment.

However, standard deviation measures the riskiness of each individual investment, not how the risk of the portfolio would

change if the investment

were added! Doesnt that

sound    just    like    what

investors   do   because  of mental accounting limita­tions? Remember the earlier example where Techfirm and Bankfirm had the same risk but combined to reduce risk in a portfolio?

Figure 9.4 plots the standard deviation of monthly stock returns for each investment versus the investment's contribution of risk to the existing portfolio, as measured by beta. A beta > 1 indicates that the investment would increase the risk of the portfolio. A beta < 1 indicates that adding the security would reduce the risk of the portfolio.

Notice that the last risk ranking (the standard deviation of returns) in Figure 9.3 is simply the y-axis of Figure 9.4. Because of mental accounting, investors misinterpret the risk of adding investments to their portfolios as the individual risk (standard deviation) of each investment. However, the investment's real contribution to portfolio risk is measured on the x-axis. Figure 9.5 shows just the x-axis from Figure 9.4—the interaction between the investment and the existing portfolio.

Figure 9.5 shows that, if you want to reduce the risk of your portfolio, you should add real estate and commodities. Does this come as a surprise? Figure 9.5 also shows that small-cap stocks and stocks like those in the Russell 2000 Growth Index increase the risk of the portfolio. Viewed by themselves, emerging markets stocks are the most risky investments in the example. However, according to Figure 9.5, they interact with the existing portfolio such that they would actually reduce the risk of the portfolio, if added!

Now let's consider the conservative investor who owns only bonds. This investor owns only bonds because she wants low risk. During the 30-year period 1970-99, her portfolio earned an average annual return of 9.56%. You may not appreciate standard deviation as a measure of risk, so consider these two alternatives: maximum annual loss and number of years with a negative return. The worst annual return during the 1970-99 period was -8.96%, while the portfolio lost money in 9 of the 30 years.3

If this conservative investor would add some stocks to her port­folio, she would see the miracle of diversification. A portfolio of 90% bonds and 10% large stocks would have averaged 10.09% per year. It's interesting that the worst return would have been -6.86% and that the portfolio would have lost money in only 7 of the 30 years. Again, this is hard for investors to understand because of mental accounting. The reduction in risk occurs because the prices of stocks and bonds often move in opposite directions. Mental accounting blocks an investor's ability to visualize the various movements of multiple investment categories, all of which can act together for the greater good of the portfolio.

Let's look at another example—the stock and bond markets in 1999 and 2000. If you owned long-term Treasury bonds, your returns were -8.7% in 1999 and 15.0% in 2000. If you think of risk as the chance to lose money, you might think there is a great deal of risk in this type of investment.

Instead, you probably owned stocks. The S&P 500 index earned 19.5% and -10.2% in 1999 and 2000, respectively. Again, there is a lot of risk here. However, if your portfolio consisted of 50% stocks and 50% bonds, your return would have been 5.4% and 2.4%. Owning both stocks and bonds is less risky than owning just stocks or just bonds. Here is the amazing part: If you owned bonds, your total return for the two years was 5.0%. The two-year return for stocks was 7.3%. If you had 50% stocks and 50% bonds (and rebal­anced to this allocation each year), your two-year return would have been 7.9%—higher than owning either just stocks or just bonds!

Modern portfolio theory is clearly an advanced investment topic. Unfortunately, mental accounting makes it a hard topic as well. However, there are several things to remember that will help you implement a diversified portfolio:

■    Diversification reduces risk and contributes to higher returns over time.

■    Diversification can be  implemented by owning many different asset classes.

■    Within each asset class, owning a variety of different securities further reduces risk.

Risk Perception in the Real World

Public pension systems demonstrate how the misperception of risk caused by mental accounting affects portfolios. Public pension sys­tems are the retirement plans of public employees such as teachers, police, and state and city employees. The state or local government sets aside money each year to be invested, which is ultimately used as the employees' retirement income. Professional money managers are hired to invest the money, but the government has the power to restrict the managers from investing in specific securities in an attempt to limit the risk of the portfolio. Because of mental account­ing, the government officials tend to use each security's individual risk (as shown in Figure 9.4) instead of the interaction risk effect (as shown in Figure 9.5) to make these decisions.

The Government Finance Officers Association surveyed public pension plans in 1999 about the investment restrictions under which they operate. A total of 211 retirement plans responded.4 Remember that Figure 9.5 showed that real estate, corporate bonds, and even foreign stocks can reduce the risk of a typical portfolio. However, 14 plans responded that they cannot invest in real estate. A total of 8 plans could not invest in corporate bonds, and 19 plans cannot invest in foreign securities. Many more plans have other limitations, such as a maximum investment of no more than 5% of the portfolio in real estate, corporate bonds, and foreign securities. It's interesting that three plans cannot invest in U.S. stocks at all! Those government policy makers need to read this book!