Investments: Analysis and Behavior Chapter 4- Risk and Return ©2008 McGraw-Hill/Irwin

4-2 Learning Objectives Know the risk and return characteristics of different asset classes. Compute the impact of taxes on investment returns. 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.

4-3 Components of Return Required Return  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

4-4 Annual Rates of Return on Common Stocks Approximate a Normal Distribution, 1950-present

4-5 Computing Returns Arithmetic average return  Example 1: ( )/3 = or 4.67%  Example 2: ( )/2 = 0 or 0% Geometric mean return  Example 1: (1.1×1.08×0.96) 1/3 – 1 = or 4.48%  Example 2: (1.5×0.5) 1/2 – 1 = or -13.4%

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4-7 Risk Variation, or volatility of return  Most investors probably are more interested the chance of losing money  Standard deviation  Example 1: {[( ) 2 + ( ) 2 + ( ) 2 ] / (3-1) } 1/2 = or 7.57%

4-8 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

4-9 Annual data, 1950 to 2005 Long-TermShort-term CommonTreasury Inflation StocksBondsBillsRate Arithmetic average13.27%6.39%4.92%3.89% Median15.40%3.65%4.85%3.19% Geometric mean11.93%5.92%4.92%3.85% Standard deviation17.24%10.51%2.71%2.99% Coefficent of variation

4-10 More Returns Total Return  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

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4-12 Impact of Taxes Capital Gains  Only realized gains are taxed  Short-term (less than one year) taxed at marginal income tax rate  Long-term (over one year) Taxed at 20% Dividends  Taxed at 15% Interest Income  Taxed at marginal income tax rate

4-13 The tax man cometh After-tax value of a $4,000 investment per year Number earning 12% with annual income taxes paid at a rate of of Years0%30%40%50% 1$4,000$2,800$2,400$2, ,41116,55813,85711, ,19541,34133,47426, ,11978,43561,24746, ,210133,955100,56573, ,335217,053156,227109, ,331341,430235,029158,116

4-14 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 main goal of diversification is to reduce overall investment risk.

4-15 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

4-16 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 Return t – Stock Average)  (Gold Return t – Gold Average)} = (1/3){( )  (5-4)+(8-4.67)  (-3-4)+( )  (10-4)} = Correlation = Covariance / (Standard Deviation Stock  Standard Deviation Gold) = / (7.57  6.6) = A negative correlation means that stocks and gold tend to move in opposite directions.

4-17 Correlations in Total Returns for Stocks, Bonds, Bills and Inflation, 1950-present StocksBondsBillsInflation Stocks1.00 Bonds Bills Inflation

4-18 Portfolio Risk and Return Expected Portfolio Return Standard Deviation of Portfolio Returns

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4-20 Combining these investments allows for the possibility of 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)

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4-23 Combining similar assets don’t produce much risk reduction… MonthGMFordPortfolio A November0.0%-2.0%-1.0% December22.8%2.3%12.1% January11.7%17.1%14.4% February11.7%1.1%6.3% March6.2%7.7%6.9% April-7.7%-5.6%-6.6% May-7.3%-2.5%-4.9% June-16.7%-8.7%-12.8% July10.2%23.0%16.4% August21.3%11.7%16.4% September1.9%4.1%3.0% October8.8%10%9.6% Mean4.62%4.50%4.56% S.D.11.81%9.43%9.61% Covariance0.66%

4-24 Combining very different firms does provide risk reduction… MonthMicrosoftCitigroupPortfolio B November2.9%-1.7%0.6% December-7.4%-6.6%-7.0% January0.1%-0.6%-0.2% February6.4%-3.8%1.2% March-6.7%-0.6%-3.7% April-3.0%5.2%1.0% May3.9%1.9%2.9% June-2.3%-0.3%-1.3% July-4.5%-5.2%-4.8% August4.1%6.2%5.1% September4.1%1.9%3.0% October1.7%-1.8%0.0% Mean-0.16%-0.52%-0.34% S.D.4.64%3.84%3.49% Covariance0.06%

4-25 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.

4-26 In Panel A, pick the retirement plan option for your pension plan investment. Panel AOption AOption BOption C Good Market Conditions (50% chance)$900$1,100$1,260 Bad Market Conditions (50% chance)$900$800$700 Panel BProgram 1Program 2Program 3 Good Market Conditions (50% chance)$1,100$1,260$1,380 Bad Market Conditions (50% chance)$800$700$600 Then, in Panel B, pick the retirement plan program for your pension plan investment. Who picked what?

4-27 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.

4-28 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.