Investments: Analysis and Behavior Chapter 4- Risk and Return

Learning Objectives Know the risk and return characteristics of different asset classes. Be able to compute risk and return of a two-asset portfolio. Recognize optimal portfolios. Learn how gains and losses affect investor perceptions of risk.

Components of Return Required Return Nominal risk-free rate The return required to compensate for the amount of risk expected. Nominal risk-free rate Risk-free rate Inflation Required risk premium Return that varies with the risk entailed

Computing Returns Arithmetic average return Geometric mean return Example 1: (0.10+0.08-0.04)/3 = 0.0467 or 4.67% Example 2: (0.50-0.50)/2 = 0 or 0% Geometric mean return Example 1: (1.1×1.08×0.96)1/3 – 1 = 0.0448 or 4.48% Example 2: (1.5×0.5)1/2 – 1 = -0.134 or -13.4%

Table 4.1 Risk and Return in the Stock Market

Risk Variation, or volatility of return Most investors probably are more interested in the chance of losing money Standard deviation Example 1: {[(0.10-0.0467)2 + (0.08-0.0467)2 + (-0.04-0.0467)2] / (3-1) }1/2 = 0.0757 or 7.57%

Risk and Return Risk/Return relationship The greater the risk, the more return should be demanded. Coefficient of Variation CoV = 7.57% / 4.67% = 1.62

Annual data, 1950 to 2007 Long-Term Short-term Common Treasury Inflation Stocks Bonds Bills Rate Arithmetic average 13.15% 6.37% 4.89% 3.87% Median 15.05% 3.65% 4.75% 3.19% Geometric mean 11.84% 5.92% 3.83% Standard deviation 16.99% 10.35% 2.67% 2.94% Coefficent of variation 1.29 1.62 0.55 0.76

More Returns Total Return Inflation Includes dividends, interest, income, and capital gains (losses) Inflation Reduces future buying power Nominal return Return with inflation included Real return Return with inflation removed Return as a buying power measurement

Forming a Portfolio Don’t put all your eggs in one basket! The purpose of owning different types of stocks and different asset classes is diversify. The goal of diversification is to reduce overall investment risk. Maximum return for a given risk. Minimum risk for a given rteturn.

Statistical Measures The risk of a portfolio is determined by how the individual securities co-move over time. Covariance is a measure of that co-movement: However, the standardized measure of correlation is more popular: Between -1 and 1

Example: The stock market earned the following returns; 10%, 8%, -4% Example: The stock market earned the following returns; 10%, 8%, -4%. During the same period, gold earned returns of 5%, -3%, 10%. What is the covariance and correlation between the stock market and gold? First compute the average and standard deviation for stocks and for gold. The statistics for stocks were computed earlier (average=4.67, standard deviation=7.57%). Gold’s average return = (5-3+10)/3 = 4%. Standard deviation=[(1/2)((5–4)2+(-3–4)2+(10–4)2)]1/2 = 6.6% Covariance = (1/N)∑{(Stock Returnt – Stock Average)  (Gold Returnt – Gold Average)} = (1/3){(10-4.67)(5-4)+(8-4.67)(-3-4)+(-4-4.67)(10-4)} = -23.33 Correlation = Covariance / (Standard Deviation Stock  Standard Deviation Gold) = -23.33 / (7.576.6) = -0.47 A negative correlation means that stocks and gold tend to move in opposite directions.

Table 4.3 Correlations in Total Returns for Stocks, Bonds, Bills, and Inflation, 1950-Present 1.00 0.11 -0.05 0.30 -0.23 -0.17 0.63

Portfolio Risk and Return Expected Portfolio Return Standard Deviation of Portfolio Returns

Figure 4.3 Expected Rate of Return and Risk Are Fundamental Economic Characteristics of Investment Opportunities Panel A Investment Opportunities Offer Different Combinations of Expected Return and Risk X Expected Return (E(R)) Y Risk (SD)

Combining Investments Allows for Risk Reduction The goal of the investor is to form a portfolio the moves to the upper-left corner of the risk/return graph. The very highest level of return for each level of risk desired is the efficient portfolio. All the efficient portfolios make up the efficient frontier. The optimal portfolio for you is the one that maximizes your utility (given your risk aversion)

Figure 4.3 Expected Rate of Return and Risk Are Fundamental Economic Characteristics of Investment Opportunities (cont)

Figure 4.3 Expected Rate of Return and Risk Are Fundamental Economic Characteristics of Investment Opportunities (cont)

Table 4.5 Portfolio Risk Increases with the Volatility of Individual Holdings and the Extent to Which Holdings Have High Covariance Combining similar assets don’t produce much risk reduction…but different assets do! Month Exxon Mobil Chevron 50/50 Portfolio A Procter & Gamble Walmart B June 1.5% 1.2% 1.4% 0.2% -4.5% -2.1% July 0.7% 2.9% 1.8% 1.0% -5.0% -2.0% August 8.0% 6.6% 7.3% 5.5% 0.0% 2.8% September -0.6% -2.2% -1.4% 4.6% 3.6% 4.1% October -3.1% -4.1% -3.6% 6.0% 3.5% November 5.1% 6.3% 5.7% -0.8% 2.5% December -8.5% -10.8% -9.7% -13.5% 6.8% -3.4% January 3.2% -2.3% 0.5% February -2.8% -1.5% 6.2% 3.7% March 10.0% 12.6% 11.3% 0.4% 10.1% 5.2% April -4.6% 3.1% -1.6% -0.4% -1.0% May 0.3% 2% 1.7% Average 0.63% 1.70% 1.16% 0.68% 1.90% 1.29% S.D. 5.24% 5.96% 5.44% 5.02% 4.79% 2.84% Covariance 0.25% -0.07% Data Source: http://finance.yahoo.com (6/1/07 to 6/1/08).

Computing standard deviation of a portfolio Portfolio A is half Exxon (std=5.24%) and half Chevron (std=5.96%) with a covariance of 0.25%. This doesn’t offer much risk reduction! Portfolio B is half P&G (std=5.02%) and half Wal-mart (std=4.79%) with a covariance of -0.07%. This does give us risk reduction!

Possible 2-stock portfolios Figure 4.4 Possible Portfolios of Two 2-Stock Portfolios Possible 2-stock portfolios

Investor Perceptions of Risk Portfolio theory is based on the statistics of how investment returns co-move over time. Do people really view risk from this statistical perspective? No, people tend to see high returns as safe. When the markets go up, people jump in. Risk is felt after returns turn negative Myopic view (short-term perspective) After 3-years of losses, long-term investors become 3-year investors—they want out! House Money Effect After experiencing a gain, or profit, gamblers become willing to take more risk.

In Panel A, pick the retirement plan option for your pension plan investment. Option A Option B Option C Good Market Conditions (50% chance) $900 $1,100 $1,260 Bad Market Conditions (50% chance) $800 $700 Panel B Program 1 Program 2 Program 3 $1,380 $600 Then, in Panel B, pick the retirement plan program for your pension plan investment. Who picked what?

Notice that Option C appears to be a “high” risk investment in Panel A. Program 2 is the same as Option C, but it appears to be a “middle” risk investment. In a study… People seemed to prefer Option B over Option C when choosing from Panel A. People seemed to prefer Option C over Option B when they were shown in Panel B. In short… People don’t really know what level of risk they want to take. People measure risk in relative, not absolute, terms.

Investor Risk Perceptions Make the Use of Portfolio Theory Difficult for Real Investors People mentally keep track of things in separate mental “file folders,” called mental accounting. The profits, losses, return of each investment are considered separately. This makes thinking in terms of the interaction between investments difficult. The result, is that people frequently fail to diversify.