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  1. 1. CH10 Introduction to Risk, Return and Opportunity Cost of Capital FINA3313 Business Finance Spring 2006 Instructor: Bing Y. Du ©2006
  2. 2. Topics Covered <ul><li>Calculation of rate of return </li></ul><ul><li>History of capital market </li></ul><ul><li>What is risk? </li></ul><ul><li>Methods to measure risks:, variance, standard deviation, volatility </li></ul><ul><li>Calculation of standard deviation of returns for an individual common stock or for a stock portfolio </li></ul><ul><li>Diversification and risks, understand why diversification reduces risks; </li></ul><ul><li>Distinguish unique risk, which can be diversified, and market risk, which can not be diversified; </li></ul>
  3. 3. Review: Rate of Return (ROR) <ul><li>When you buy a stock or a bond, return from your investment includes two parts: 1) a dividend or interest payment; 2) a capital gain or capital loss incurred by price changes. </li></ul><ul><li>Annual Percentage Return on your investment </li></ul><ul><li>Example: You bought a PepsiCo stock at the beginning of 2001 at the price of $43 then. By the end of year 2001 the stock price had appreciated to $49, and also you received a dividend of $0.56/Share. </li></ul>
  4. 4. Rate of Return (ROR): A Review
  5. 5. Review: Rates of Return (ROR) <ul><li>Nominal rate of return measures how much more money you will have at the end of year if you invest today. </li></ul><ul><li>Real rate of return tells you how much more you will be able to buy with your money at the end of year. </li></ul><ul><li>Example: In 2001 inflation was 2.8%. The real rate of return on your PepsiCo investment is </li></ul>
  6. 6. Measure Stock Market Performance -Market Index <ul><li>Market index : The measurement of the investment performance of the overall market. </li></ul><ul><li>Dow Jones Industry Average : tracks the performance of a portfolio that holds one share in each of 30 large firms. </li></ul><ul><li>1)The Dow Jones Industrial Average was first computed in 1896 </li></ul><ul><li>2)An equal share index of thirty industrial stocks. </li></ul><ul><li>3) It is not the best measurement of the stock market performance. First, its portfolio only includes 30 large industrial stocks, not representative of the performance of stocks generally. </li></ul><ul><li>Second, investors usually do not hold an equal number of shares in each company. </li></ul>
  7. 7. Measure Stock Market Performance -Market Index <ul><li>The Standard and Poor’s composite index (S&P500), is a market value weighted index of 500 firms, covering about 70 percent of the value of stocks traded. Compared to the Dow, the S&P 500 is a broader index and is adjusted for the relative market value of each company. </li></ul><ul><li>It measures the performance of a portfolio that holds shares in each firm in proportion to the number of shares that have been issued to investors. Holdings are proportional to the number of shares in the issues. </li></ul><ul><li>For example, SP portfolio would hold 10 times as many shares in GE as DuPont. Thus the SP500 shows the average performance of investors in the 500 firms (it is a weighted average index) </li></ul><ul><li>Success for professional investors usually means “ Beating the SP500 ”. </li></ul>
  8. 8. Measure Stock Market Performance -Market Index <ul><li>Some other market indexes </li></ul><ul><li>Wilshire 5000 - referred to as the Total Stock Market Index, track the returns of practically all publicly traded, U.S.-headquartered stocks that trade on the major exchanges. </li></ul><ul><li>Russell 1000 -Large cap( over 5 billion) index </li></ul><ul><li>Russell 2000 -Small cap (250 million to 1 billion) index </li></ul><ul><li>Nikkei Index for Tokyo </li></ul><ul><li>Financial Times (FT) Index for London. </li></ul><ul><li>Morgan Stanley Capital International (MSCI ) computes a world stock market index. </li></ul>
  9. 9. Rank the Following Securities According to Their Risks: <ul><li>1. A Portfolio of stocks of the S&P 500 index </li></ul><ul><li>2. A Portfolio of US Treasury Bills (3 month maturity) </li></ul><ul><li>3. A Portfolio of Long Term US T-Bonds </li></ul><ul><li>4. A Portfolio of Long Term Corporate Bonds </li></ul><ul><li>Min. Risk: 2 3 4 1 Max. Risk </li></ul>
  10. 10. Risk <ul><li>Hence: Stocks have the highest risk </li></ul><ul><li>The expected return from stocks is the highest. </li></ul><ul><li>Treasury securities will almost surely make the promised payments: No risk. The expected return for T-bills are the lowest.  </li></ul><ul><li>When you buy high risk securities, you ask for risk premium to compensate for the taking risks. </li></ul><ul><li>Risk Premium: The difference between the expected return of a risky security and the risk-free return. </li></ul>
  11. 11. What is risk made of? <ul><li>Market risk: price changes, such as, stock price changes, interest rate changes, and exchange rate changes; </li></ul><ul><li>Liquidity risk; </li></ul><ul><li>Default risk: certainty of payment, default possibility </li></ul><ul><ul><li>If you want to sell a security which has a higher probability of not making the promised payments, you have to compensate investors for this extra risk. </li></ul></ul>
  12. 12. Stock Market Performance -Historical Record <ul><ul><li>Investment performance of three portfolio of securities since 1900 </li></ul></ul><ul><ul><li>(Compiled by Dimson, Marsh, and Staunton) </li></ul></ul><ul><ul><li>a portfolio of 3 month-loans issued each week by the US government. (Treasury Bills) </li></ul></ul><ul><ul><li>A portfolio of long term Treasury Bonds issued by the US government and maturing in about 10 years (Long T-bonds) </li></ul></ul><ul><ul><li>A portfolio of stocks of large firms that make up the SP index. (Common stocks) </li></ul></ul>
  13. 13. Stock Market Performance -Historical Record <ul><li>These portfolios are not equally risky </li></ul><ul><li>Intuitively, </li></ul><ul><li>1) T-bills are the safest investment, because they are issued by US government, you can be sure that you will get your money back; </li></ul><ul><li>2) T-bonds rare also certain to be repaid when they mature, but their price fluctuate more as interest varies because of the long term. Thus they are more risky than T-bills. </li></ul><ul><li>3) Common stocks are most risky, no promise with your money back. You receive what is left over after the bonds and other debts are debt </li></ul>
  14. 14. Stock Market Performance -Historical Record <ul><ul><li>The safest investment, Treasury bills have the lowest rates of return. </li></ul></ul><ul><ul><li>Long term government bonds gave slightly higher returns than Treasury bills. This differences is called maturity premium , which is extra average return in long-versus short –term treasury bills, this is the reward for the longer holding period). </li></ul></ul><ul><ul><li>Common stocks were in a class by themselves. They have offered the highest average returns, but they have also been the riskier investments. Investors who accepted risk of common stocks received an extra return of 7.7 percent a year over the return on Treasury bills. (See Table10-1,p271) </li></ul></ul>
  15. 15. Stock Market Performance -Historical Record <ul><li>This compensation for taking the risk of common stock ownership is known as the market risk premium , which is the expected return in excess of risk-free return as compensation for risk </li></ul><ul><li>The historical record shows that investors have received a risk premium for holding risky assets . Average returns on high-risk assets are higher than those on low-risk assets </li></ul>
  16. 16. Stock Market Performance -Historical Record <ul><li>Common stocks (1900-2001) </li></ul><ul><li>We need to look back a long period to measure average rates of return, because annual rates of return for common stocks fluctuate so much that averages taken over short periods are extremely unreliable. You can see, stock price very volatile!!! Risky. </li></ul>
  17. 17. Evidence from historical record <ul><li>High returns on investment are the compensations for taking high risks. </li></ul>
  18. 18. Using historical evidence to Estimate today’s Cost of Capital <ul><li>The opportunity cost of capital is that the firms’ shareholders are giving up by investing in the project rather than in comparable alternatives. </li></ul><ul><li>If the project is a sure thing, the same as investing in Treasury bill, then the cost of capital is easy to measure. Just use the rate of return on Treasury bill. </li></ul><ul><li>If the project is risky , then the firm needs to at least match the return that shareholders could expect to earn if they invested in securities of similar risk. </li></ul>
  19. 19. Using historical evidence to Estimate today’s Cost of Capital <ul><li>Project’s cost of capital is the expected rate of return on investing similar risky securities. </li></ul><ul><li>If an investment project has the same risk as investing in the portfolio of stocks in SP composite index. We will say that it has the same degree of risk as the market portfolio of common stock. </li></ul><ul><li>Instead of investing in the project, the shareholders could invest directly in this market portfolio of common stocks. The expected rate of return on the market portfolio is opportunity cost investing in this project. </li></ul><ul><li>Now the problem of estimating the project cost of capital boils down to estimating the currently expected rate of return on the market portfolio. </li></ul>
  20. 20. Using historical evidence to Estimate today’s Cost of Capital <ul><li>Remember that we based our calculations of NPV on opportunity cost of capital, and so far we assumed that cost of capital was readily available. </li></ul><ul><li>Now assume that cost of capital is not readily available and we need to calculate it. </li></ul><ul><li>Assume that the project you are evaluating has a risk similar to that of an investment in the portfolio of stocks of the S&P 500 (stock market portfolio). Then, you can take the expected rate of return on S&P 500 as your cost of capital. </li></ul><ul><li>(S&P 500 ~ US Stock market as a whole) </li></ul>
  21. 21. Using historical evidence to Estimate today’s Cost of Capital <ul><li>How to estimate the expected rate of return on market portfolio? </li></ul><ul><li>Example: In 1981, when the rate on Treasury bill was 14%, the expected market return would be </li></ul><ul><li>Thus, in 1981, if you invested in a project which was the same risky as market portfolio, the cost of capital of the project was 21.7% </li></ul>
  22. 22. Using historical evidence to Estimate today’s Cost of Capital <ul><li>If the investment project has no risk, then we can take the rate of interest on 3-month T-Bill as the cost of capital because there should be no risk premium for the project. </li></ul>
  23. 23. Measuring Risk <ul><li>Risk is the degree of uncertainty of return on an asset . They are the deviation from the average returns. </li></ul><ul><li>Variation around a central tendency or mean may be presented visually by constructing a histogram (Figure 10.4) and studying the dispersion or spread of possible outcomes. </li></ul><ul><li>Variance and Standard Deviation </li></ul><ul><li>(BRUSH UP YOUR STATISTICS KNOWLEDGE!!!) </li></ul><ul><li>Risk = volatility in returns (or prices) </li></ul><ul><li>In order to quantify risk, we need to use a measurement for volatility: </li></ul><ul><ul><li>Variance and Standard Deviation </li></ul></ul>
  24. 24. Measuring Risk <ul><li>In statistics, the variance and standard deviation are exactly the measurements of the variation from the average. </li></ul><ul><li>Variance - Average value of squared deviations from mean. A measure of volatility. </li></ul><ul><li>Standard Deviation – Square root of variance. Another measure of volatility. </li></ul><ul><li>Variance Var (X) =  X i    </li></ul><ul><li> X 1    ...  X N    </li></ul><ul><li> mean of X </li></ul><ul><li>N = number of observations </li></ul><ul><li>X can be possible stock returns, for example </li></ul><ul><li>mean = expected return </li></ul><ul><li>Standard Deviation = Var 1/2 </li></ul>
  25. 25. Measuring Risks <ul><li>You play the following game: You put in $100 at the beginning of the game and you flip a coin twice. Each time you get a Head you get 20% on your $100. Each time you get a Tail, you loose 10% of your $100. </li></ul><ul><li>Let’s calculate the expected return: </li></ul><ul><li>Head + Head: +40%, probability = 1/4 </li></ul><ul><li>Head + Tail: +10%, probability = 1/4 </li></ul><ul><li>Tail + Head: +10%, probability = 1/4 </li></ul><ul><li>Tail + Tail: -20%, probability = 1/4 </li></ul>
  26. 26. Measuring Risks <ul><li>Expected return (Average return) </li></ul><ul><li>= probability weighted average of all possible outcomes </li></ul><ul><li>=(1/4)*40%+(1/4)*10%+(1/4)*10% +(1/4)(-20%) = +10% </li></ul><ul><li>% return dev. from exp. ret . Squared deviation </li></ul><ul><li>+40% 40%-10%=30% (40%-10%) 2 =900(%) 2 </li></ul><ul><li>+10% 10%-10%= 0% (10%-10%) 2 =0(%) 2 </li></ul><ul><li>+10% 10%-10%=0% (10%-10%) 2 =0(%) 2 </li></ul><ul><li>-20% -20%-10%= -30% (-20%-10%) 2 = 900 (%) 2 </li></ul><ul><li>sum = 1800 (%) 2 </li></ul><ul><li>Variance of returns = 1800/4 = 450 (%) 2 </li></ul><ul><li>Standard deviation of returns = 21.21% </li></ul>
  27. 27. Measuring the Variation in Stock Returns Standard deviation=squared root of variance=18.36% Variance=Average of squared deviations=1685.39/5=337.08 (%) 2 11.284 Average 1685.3924 (%) 2 56.42 Total 495.0625 (%) 2 -10.97 -11.28= -22.25 -10.97 2001 491.5089 (%) 2 -10.89 -11.28= -22.17 -10.89 2000 150.7984 (%) 2 23.56 -11.28= 12.28 23.56 1999 147.6225 (%) 2 23.43 -11.28= 12.15 23.43 1998 400.4001 (%) 2 31.29 -11.28=20.01 31.29 1997 Squared deviation(%) 2 Deviation from Average Return Rate of return (%) Year Example: Measuring variation in stock returns
  28. 28. Stock Market Volatility 1926-2001
  29. 29. Measuring the Variation in Stock Returns <ul><li>The comparison of average returns and volatility indicates that historical risk and return are directly related . </li></ul><ul><li>Higher risk is associated with higher average returns . </li></ul>
  30. 30. Risk and Diversification <ul><li>The measures of variation can apply to groupings of securities or portfolios as well as single securities. </li></ul><ul><li>The variability or risk of a portfolio, or a market portfolio such as the S&P 500, is not the simple average of the individual stock variability. </li></ul><ul><li>The portfolio risk is less than the average risk of the individual securities. </li></ul><ul><li>Diversification reduces variability. </li></ul>
  31. 31. Risk and Diversification <ul><li>Market portfolio is less risky than the individual stocks included in the market portfolio. Why? </li></ul><ul><li>Assume there are two companies: Company one sells ice cream and company two sells umbrellas. They both have same level of earnings. How would the variability of the sales change for these two companies? </li></ul>
  32. 32. Risk and Diversification <ul><li>Company 1 will sell more when it is sunny and will sell less when it is rainy. </li></ul><ul><li>Company 2 will sell more when it is rainy and will sell less when it is sunny. </li></ul><ul><li>(i.e. weather conditions affect the two companies in opposite ways ) </li></ul><ul><li>If you invest in company 1 you can loose if the weather stays rainy and cold </li></ul><ul><li>If you invest in company 2 you can loose if the weather stays sunny. </li></ul><ul><li>What-if you invest in both ? </li></ul><ul><li>By spreading your investment, you are following a strategy called diversification . </li></ul>
  33. 33. Risk and Diversification <ul><li>Definition of Diversification : Reducing risk by spreading the portfolio across many investments </li></ul><ul><li>By diversifying on the two companies, you make an average level of profit if the weather is rainy or shiny. </li></ul><ul><li>Obviously, we do not limit our discussion to only weather conditions. There are numerous variables in an economy that may affect different companies differently. </li></ul>
  34. 34. When does diversification work? <ul><li>The reduced risk of the portfolio is caused by diversification effects of spreading the portfolio across many investments. </li></ul><ul><li>Portfolio diversification works because prices of different stocks do not move exactly together or are not perfectly correlated (+1). </li></ul><ul><li>Diversification works best when the stock returns are negatively correlated. </li></ul><ul><li>Diversification reduces the variability of returns on the portfolio compared to the average variability of the individual stocks. </li></ul>
  35. 35. Asset vs. Portfolio Risk: <ul><li>Main idea: An asset that looks unattractive on an individual basis may be attractive as a part of a portfolio. </li></ul><ul><li>Assume there is a stock with high volatility and low average return. This stock sounds like a loser but there will still be a lot of investors interested in the stock. Why? </li></ul><ul><li>Assume that there is a gold stock. Gold stocks do well when other stocks are doing poorly (counter cyclical)). </li></ul><ul><li>Assume that there is also an auto stock (GM, Ford,…) (Auto stocks are cyclical) </li></ul>
  36. 36. Asset vs. Portfolio Risk: Example <ul><li>The below table shows the returns on these two stocks in three different states of the economy: </li></ul><ul><li>State Probability Auto stock Gold stock </li></ul><ul><li>recession 1/3 -8% +20% </li></ul><ul><li>Normal 1/3 +5% +3% </li></ul><ul><li>Boom 1/3 +18% -20% </li></ul>
  37. 37. Asset vs. Portfolio Risk: Example (cont’d) <ul><li>Calculate the expected rate of return and risk for the two stocks separately: </li></ul><ul><li>auto stock: </li></ul><ul><li>Expected return = (1/3)*(-8) + (1/3)*(+5) +(1/3)(+18) = 5% </li></ul><ul><li>Variance = [(-8-5) 2 +(5-5) 2 +(18-5) 2 ]/ 3 = 112.7(%) 2 </li></ul><ul><li>Std. Deviation = 10.6% </li></ul><ul><li>gold stock: </li></ul><ul><li>Expected return =(1/3)*(20) + (1/3)*(+3) +(1/3)(-20) = 1% </li></ul><ul><li>Variance =[(20-1) 2 +(3-1) 2 +(-20-1) 2 ]/ 3 = 268.67(%) 2 </li></ul><ul><li>Std. Deviation = 16.4 % </li></ul>
  38. 38. Asset vs. Portfolio Risk: Example (cont’d) <ul><li>Gold has both lower return and higher risk. It does not look like an attractive alternative by itself, but: </li></ul><ul><li>Assume a portfolio of the two stocks: </li></ul><ul><li>Weight of auto stock = 75% </li></ul><ul><li>Weight of gold stock = 25% </li></ul><ul><li>Portfolio returns will be as follows: </li></ul><ul><li>Portfolio return= </li></ul><ul><li>fraction of portfolio in Asset1 * Rate of return on Asset1 </li></ul><ul><li>+ fraction of portfolio in Asset 2* Rate of return on Asset2 </li></ul><ul><li>In recession: portfolio return = (.75)(-8) +(.25)(20) = -1% </li></ul><ul><li>In normal economy: portfolio return = (.75)(5) +(.25)(3) = 4.5% </li></ul><ul><li>In boom : portfolio return= (.75)(18) +(.25)(-20) = +8.5% </li></ul>
  39. 39. Asset vs. Portfolio Risk: Example (cont’d) <ul><li>Calculate the portfolio values in the same way: </li></ul><ul><ul><li>Expected return of portfolio =(1/3)(-1)+ (1/3)(4.5)+(1/3)(8.5)=4% </li></ul></ul><ul><li>Or Simply portfolio return </li></ul><ul><li>=(0.75)*Expected return on Auto stock + (0.25)*Expected return on Gold stock = 0.75*5%+0.25*1%=4% </li></ul><ul><ul><li>Portfolio Variance </li></ul></ul><ul><ul><li>=[(-1%-4%) 2 -(4.5%-4%) 2 -(8.5%-4%) 2 ]/3= 15.2(%) 2 </li></ul></ul><ul><ul><li>Portfolio standard deviation </li></ul></ul><ul><ul><li>= 3.89% </li></ul></ul>
  40. 40. Asset vs. Portfolio Risk: Summary <ul><li>Conclusion: By adding gold stock to our portfolio, we reduced the best case scenario return and increased the worst case scenario return, i.e. we stabilized the returns. </li></ul><ul><li>Gold stock in this example was a negative risk asset for an investor with auto stocks. The incremental risk of the gold stocks when they are added to the portfolio was negative (reduced the portfolio variance) </li></ul>
  41. 41. Market Risk versus Unique Risk Rule of thumb: If you have a portfolio of over 20 stocks, diversification has done the most it can to eliminate unique risk.
  42. 42. Market Risk versus Unique Risk
  43. 43. Market Risk versus Unique Risk <ul><li>Unique risk : Risk factors affecting only that firm. Also called diversifiable risk , firm specific risk </li></ul><ul><li>Market risk : Economywide (Macroeconomic) sources of risk that affect the overall stock market. Also called systematic risk which is cannot be diversified. </li></ul><ul><li>By diversification, you are able to eliminate the firm specific risks (unique risks). </li></ul><ul><li>Unique risk is diversifiable . Unique risk consists of risk factors affecting only that firm. </li></ul><ul><li>Market risk is not diversifiable . This is also called systematic risk . It contains economy wide sources of risk. </li></ul><ul><li>As you increase the number of securities in a portfolio, the importance of unique risk diminishes. </li></ul>
  44. 44. Market Risk versus Unique Risk <ul><li>The diversification effect or the reduction in portfolio risk takes place with the addition of added securities until about 20 or 30 are included in the portfolio. Beyond that, the diversification effect of added securities is minimal. </li></ul><ul><li>While diversification eliminates the unique risk of individual securities, one cannot eliminate the market risk or systematic risk , the risks that affect the entire stock market. </li></ul><ul><li>For a diversified portfolio, only the market risk matters . When one discusses securities investment or investors, it is assumed that the security is held in a diversified portfolio and the relevant risk is market risk. </li></ul>
  45. 45. What are these market risks: <ul><li>Macroeconomic factors such as: </li></ul><ul><ul><li>Interest rates </li></ul></ul><ul><ul><li>Inflation </li></ul></ul><ul><ul><li>Exchange rates </li></ul></ul><ul><ul><li>Oil prices </li></ul></ul><ul><ul><li>etc. </li></ul></ul><ul><li>These macroeconomic factors affect the earnings of all companies. Example: When interest rates go up stock prices as a whole suffer. </li></ul><ul><li>Some companies are more exposed to these macroeconomic risks than others. </li></ul>
  46. 46. Macro and Micro Risks: <ul><li>Managers worry about both market risks and firm specific risks. </li></ul><ul><li>Only the market risk affects the cost of capital. </li></ul><ul><li>Investors of diversified portfolios are concerned only with market risk , not the individual unique risks . (macroeconomic risks rather than microeconomic risks), because investors can eliminate firm specific risks by investing diversified portfolios. </li></ul>
  47. 47. How should we measure the risk of an individual stock: <ul><li>Rather than looking at firm-specific risks, we should look at how sensitive the stock price is to the changes of the whole stock market (Beta) </li></ul><ul><li>  How to measure Beta of a stock (CH11) </li></ul>
  48. 48. Think about Risks <ul><li>Message 1: Some Risks Look Big and Dangerous but Really Are Diversifiable </li></ul><ul><li>Individual project risk may not be as high when the project is part of a portfolio of business investments. The individual project risk can be diversified if you hold a portfolio of business investments. </li></ul>
  49. 49. Think about Risks <ul><li>Message 2: Market Risks Are Macro Risks </li></ul><ul><li>A. Investors holding diversified portfolios are only concerned with macroeconomic risks (market risks, systematic risks), or the impact of business cycle, exchange rates, etc. Specific or unique risk is not relevant. </li></ul><ul><li>B. Managers must deal with unique risk exposure in addition to market risk, but only market risk affects the opportunity rate of return of the firm. </li></ul>
  50. 50. Think about Risks <ul><li>Message 3: Risk Can Be Measured </li></ul><ul><li>The risk can be measured by the variance or standard deviation , </li></ul>
  51. 51. Summary <ul><li>Calculation of rates of return </li></ul><ul><li>History of capital market </li></ul><ul><li>What is risk? </li></ul><ul><li>Methods to measure risks: volatility, variance , standard deviation </li></ul><ul><li>Calculation of standard deviation of returns for an individual common stock or for a stock portfolio </li></ul><ul><li>Diversification and risks , understand why diversification reduces risks; </li></ul><ul><li>Distinguish unique risk , which can be diversified, and market risk , which can not be diversified; </li></ul>