1 CHAPTER 8 Risk and Rates of Return Stand-alone risk (statistics review) Portfolio risk (investor view) -- diversification important Risk & return: CAPM/SML (market equilibrium) Risk is viewed primarily from the 2 stockholder perspective Management cares about risk because stockholders care about risk. If stockholders like or dislike something about a company (like risk) it affects the stock price. Risk affects the discount rate for future returns -- directly affecting the multiple (P/E ratio) Thus, the concern is still about the stock price. Stockholders have portfolios of investments – they have stock in more than just one company and a great deal of flexibility in which stocks they buy. 3 What is investment risk? Investment risk pertains to the uncertainty regarding the rate of return. Especially when it is less than the expected (mean) return. The greater the chance of low or negative returns, the riskier the investment. 4 Return = dividend + capital gain or loss Dividends are relatively stable Stock price changes (capital gains/losses) are the major uncertain component There is a range of possible outcomes and a likelihood of each -- a probability distribution. 5 Expected Rate of Return The mean value of the probability distribution of possible returns It is a weighted average of the outcomes, where the weights are the probabilities 6 Expected Rate of Return (k hat) ˆ k p1k1 p2 k 2 ... pn k n n pi k i i 1 7 Investment Alternatives Economy Prob. T-bill HT Coll USR MP Recession 0.1 8.0% -22.0% 28.0% 10.0% -13.0% Below avg 0.2 8.0 -2.0 14.7 -10.0 1.0 Average 0.4 8.0 20.0 0.0 7.0 15.0 Above avg 0.2 8.0 35.0 -10.0 45.0 29.0 Boom 0.1 8.0 50.0 -20.0 30.0 43.0 1.0 8 Why is the T-bill return independent of the economy? Will return be 8% regardless of the economy? 9 Do T-bills really promise a completely risk-free return? No, T-bills are still exposed to the risk of inflation. However, not much unexpected inflation is likely to occur over a relatively short period. 10 Do the returns of HT and Coll. move with or counter to the economy? High Tech: With. Positive correlation. Typical. Collections: Countercyclical. Negative correlation. Unusual. 11 Calculate the expected rate of return for each alternative: ^ = expected rate of return k n k = k i pi ^ i=1 ^ = (-22%)0.1 + (-2%)0.20 kHT + (20%)0.40 + (35%)0.20 + (50%)0.1 = 17.4% 12 Calculate others on your own ^ k HT 17.4% Market 15.0 USR 13.8 T-bill 8.0 Coll. 1.7 HT appears to be the best, but is it really? 13 What‟s the standard deviation of returns for each alternative? = standard deviation = Variance = 2 n = (ki k i ˆ )2 p i =1 14 Normal Distribution 15 In a sample of observations One often assumes that data are from an approximately normally distributed population. then about 68.26% of the values are at within 1 standard deviation away from the mean, 95.46% of the values are within two standard deviations and 99.73% lie within 3 standard deviations. 16 n = ^2 (k i k) Pi i=1 HT = [- 22 - 17.4 2 0.1 + - 2 - 17.4 2 0.2 20 - 17.4 2 0.4 + 35 - 17.4 2 0.20 50 17.4 2 0.1]0.5 0.5 20.0748599 T-bills = 0.0%. HT = 20.0%. Coll = 13.4%. USR = 18.8%. M = 15.3%. 17 Standard deviation (i) measures total, or stand- alone, risk. The larger the i , the lower the probability that actual returns will be close to the expected return. 18 Expected Returns vs. Risk: Security Expected Risk, return High Tech 17.4% 20.0 Market 15.0 15.3 US Rubber 13.8* 18.8* T-bills 8.0 0.0 Collections 1.7* 13.4* *Return looks low relative to 19 Coefficient of variation (CV): Standardized measure of dispersion about the expected value: Std dev CV = = Mean k Shows risk per unit of return. 20 Portfolio Risk & Return Assume a two-stock portfolio with $50,000 in HighTech and $50,000 in Collections. Calculate kp and p. 21 ^ Portfolio Return,kp ^ kp is a weighted average: n ˆ ˆ kp = w i k i . i =1 ^ kp = 0.5(17.4%) + 0.5(1.7%) = 9.6% ^ ^ ^ kp is between kHT and kCOLL. 22 Alternative Method: Estimated Return Economy Prob. HT Coll. Port. Recession 0.10 -22.0% 28.0% 3.0% Below avg. 0.20 -2.0 14.7 6.4 Average 0.40 20.0 0.0 10.0 Above avg. 0.20 35.0 -10.0 12.5 Boom 0.10 50.0 -20.0 15.0 ^ kp = (3.0%)0.1 + (6.4%)0.20 + (10.0%)0.4 + (12.5%)0.20 + (15.0%)0.1 = 9.6% 23 3.0 - 9.6 0.1 6.4 9.6 0.20 1/ 2 2 2 P = 10.0 9.6 0.4 12.5 9.6 0.20 2 2 15.0 9.6 0.1 2 = 3.3% 3.3% CVP = = 0.34. 9.6% 24 p = 3.3% is much lower than that of either stock (20% and 13.4%). p = 3.3% is also lower than avg. of HT and Coll, which is 16.7%. Portfolio provides avg. return but lower risk. Reason: diversification. Negative correlation is present between HT and Coll but is not required to have a diversification effect 25 General Statements about risk: Most stocks are positively correlated. rk,m 0.65. You still get a lot of diversification effect at .65 correlation 35% for an average stock. Combining stocks generally lowers risk. 26 What would happen to the riskiness of a 1-stock portfolio as more randomly selected stocks were added? p would decrease because the added stocks would not be perfectly correlated 27 p % 35 Company Specific risk Total Risk, P 20 Market Risk 0 10 20 30 40 ...... 1500+ # stocks in portfolio 28 As more stocks are added, each new stock has a smaller risk- reducing impact. p falls very slowly after about 40 stocks are included. The lower limit for p is about 20% = M . 29 Decomposing Risk—Systematic (Market) and Unsystematic (Business-Specific) Risk Fundamental truth of the investment world – The returns on securities tend to move up and down together • Not exactly together or proportionately Events and Conditions Causing Movement in Returns – Some things influence all stocks (market risk) • Political news, inflation, interest rates, war, etc. – Some things influence only particular firms (business-specific risk) • Earnings reports, unexpected death of key executive, etc. – Some things affect all companies within an industry • A labor dispute, shortage of a raw material 30 Total = Market + Firm specific risk risk risk Market risk is that part of a security‟s risk that cannot be eliminated by diversification. Firm-specific risk is that part of a security‟s risk which can be eliminated with diversification. 31 By forming portfolios, we can eliminate nearly half the riskiness of individual stocks (35% vs. 20%). (actually35% vs. 20% is a 43%reduction) 32 CAPM -- Capital Asset Pricing Model If you chose to hold a one- stock portfolio and thus are exposed to more risk than diversified investors, would you be compensated for all the risk you bear? 33 NO! Stand-alone risk as measured by a stock‟s or CV is not important to well-diversified investors. Rational, risk averse investors are concerned with p , which is based on market risk. Beta measures a stock‟s 34 market risk. It shows a stock‟s volatility relative to the market. Beta shows how risky a stock is when the stock is held in a well-diversified portfolio. The higher beta, the higher the expected rate of return. 35 How are betas calculated? Run a regression of past returns on Stock i versus returns on the market. The slope coefficient is the beta coefficient. 36 Illustration of beta = slope: Regression line ki 20 . 15 . Year 1 kM 15% ki 18% 2 -5 -10 10 3 12 16 5 -5 0 5 10 15 20 kM -5 ki = -2.59 + 1.44 kM . -10 37 Find beta: “By Eye.” Plot points, draw in „regression‟ line, get slope as b = Rise/Run. The “rise” is the difference in ki , the “run” is the difference in kM . For example, how much does ki increase or decrease when kM increases from 0% to 10%? 38 Computer: statistics program or spreadsheet regression program Calculator. Enter data points, and calculator does least squares regression: ki = a + bkM = -2.59 + 1.44kM . r = corr. coefficient = 0.997. Find someone‟s estimate of beta for a given stock on the web In the real world, we would use weekly or monthly returns, with at least a year of data, and would always use a computer. 39 If beta = 1.0, average risk stock. (The „market‟ portfolio has a beta of 1.0.) If beta > 1.0, stock riskier than average. If beta < 1.0, stock less risky than average. Most stocks have betas in the range of 0.5 to 1.5. Some ag. related companies have betas less than 0.5 40 =1, get the market expected return <1, earn less than the market expected return >1, get an expected return greater than the market 41 Can a beta be negative? Answer: Yes, if the correlation between ki and kM is negative. Then in a “beta graph” the regression line will slope downward. Negative beta -- rare 42 ki b = 1.29 HT 40 b=0 20 T-bills -20 0 20 40 kM Coll -20 b = -0.86 43 Expected Risk Security Return (Beta) HighTech 17.4% 1.29 “Market” 15.0 1.00 US Rubber 13.8 0.68 T-bills 8.0 0.00 Collections 1.7 -0.86 Riskier securities have higher returns, so the rank order is O.K. 44 Given the beta of a stock, a theoretical required rate of return can be calculated. The Security Market Line (SML) is used. SML: ki = kRF + (kM - kRF)bi MRP MRP= market risk premium 45 ki = kRF + (kM - kRF)bi 46 For Term Projects Use KRF = 2.5%; this is the 10 year treasury rate. Often it is argued to use a shorter term rate, but we are going to use 2.5%. Use MRP = 5% The historical average MRP is about 5%. Find your own beta from the web On Yahoo Finance look up your company and then the “key statistics” tab on the left will give you their beta 47 Use the SML to calculate the required returns (for the example) SML: ki = kRF + (kM - kRF)bi . Assume kRF = 8%. ^ Note that kM = kM is 15%. MRP = kM - kRF = 15% - 8% = 7% 48 Required rates of return: kHT = 8.0% + (15.0% - 8.0%) 1.29 = 8.0% + (7%)1.29 = 8.0% + 9.0% = 17.0% kM = 8.0% + (7%)1.00 = 15.0% kUSR = 8.0% + (7%)0.68 = 12.8% kTbill = 8.0% + (7%)0.00 = 8.0% kColl = 8.0% + (7%)(-0.86) = 2.0% 49 Calculate beta for a portfolio with 50% HT and 50% Collections: Portfolio Beta bP = weighted average of the betas of the stocks in the portfolio = 0.5(bHT) + 0.5(bColl) = 0.5(1.29) + 0.5(-0.86) = 0.22 . Weights are the proportions invested in each stock. 50 The required return on the HT/Coll. portfolio is: kP = Weighted average k = 0.5(17%) + 0.5(2%) = 9.5% . Or use SML for the portfolio: kP = kRF + (kM - kRF) bP = 8.0% + (15.0% - 8.0%) (0.22) = 8.0% + 7%(0.22) = 9.5% . 51 Using Beta—The Capital Asset Pricing Model (CAPM) The CAPM helps us determine how stock prices are set in the market Developed in 1950s and 1960s by Harry Markowitz and William Sharpe The CAPM's Approach People won't invest unless a stock's expected return is at least equal to their required return The CAPM attempts to explain how investors' required returns are determined 52 Has the CAPM been verified through empirical tests? Not completely. Because statistical tests have problems which make verification almost impossible. 53 Investors seem to be concerned with both market risk and total risk. Therefore, the SML may not produce a correct estimate of ki: ki = kRF + (kM - kRF)b + ? 54 Also, CAPM/SML concepts are based on expectations, yet betas are calculated using historical data. A company‟s historical data may not reflect investors‟ expectations about future riskiness.
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