Kế toán, kiểm toán - Chapter 2: Risk and return: part I

CHAPTER 2Risk and Return: Part I1Topics in ChapterBasic return conceptsBasic risk conceptsStand-alone riskPortfolio (market) riskRisk and return: CAPM/SML2What are investment returns?Investment returns measure the financial results of an investment.Returns may be historical or prospective (anticipated).Returns can be expressed in:Dollar terms.Percentage terms. 3An investment costs $1,000 and is sold after 1 year for $1,100.Dollar return:Percentage return:$ Received - $ Invested $1,100 - $1,000 = $100.$ Return/$ Invested $100/$1,000 = 0.10 = 10%.4What is investment risk?Typically, investment returns are not known with certainty.Investment risk pertains to the probability of earning a return less than that expected.The greater the chance of a return far below the expected return, the greater the risk.5Probability Distribution: Which stock is riskier? Why?6Consider the FollowingInvestment AlternativesEcon.Prob.T-BillAltaRepoAm F.MPBust 0.108.0%-22.0% 28.0% 10.0%-13.0%Below avg. 0.20 8.0 -2.0 14.7-10.0 1.0Avg. 0.40 8.0 20.0 0.0 7.0 15.0Above avg. 0.20 8.0 35.0-10.0 45.0 29.0Boom 0.10 8.0 50.0-20.0 30.0 43.0 1.007What is unique about the T-bill return?The T-bill will return 8% regardless of the state of the economy.Is the T-bill riskless? Explain.8Alta Inds. and Repo Men vs. the EconomyAlta Inds. moves with the economy, so it is positively correlated with the economy. This is the typical situation.Repo Men moves counter to the economy. Such negative correlation is unusual.9Calculate the expected rate of return on each alternative.r = expected rate of return.rAlta = 0.10(-22%) + 0.20(-2%) + 0.40(20%) + 0.20(35%) + 0.10(50%) = 17.4%.^^n∑r = ^i=1riPi.10Alta has the highest rate of return. Does that make it best?^rAlta17.4%Market15.0Am. Foam13.8T-bill 8.0Repo Men 1.711What is the standard deviationof returns for each alternative?σ = Standard deviationσ = √ Variance = √ σ2n∑i=1= √(ri – r)2 Pi.^12 = [(-22 - 17.4)20.10 + (-2 - 17.4)20.20 + (20 - 17.4)20.40 + (35 - 17.4)20.20 + (50 - 17.4)20.10]1/2 = 20.0%.Standard Deviation of Alta Industries13T-bills = 0.0%. Alta = 20.0%. Repo = 13.4%. Am Foam = 18.8%.Market = 15.3%.Standard Deviation of Alternatives14Stand-Alone RiskStandard deviation measures the stand-alone risk of an investment.The larger the standard deviation, the higher the probability that returns will be far below the expected return.15Expected Return versus RiskSecurityExpectedreturnRisk, Alta Inds. 17.4% 20.0%Market 15.0 15.3Am. Foam 13.8 18.8T-bills 8.0 0.0Repo Men 1.7 13.416Coefficient of Variation (CV)CV = Standard deviation / expected returnCVT-BILLS = 0.0% / 8.0% = 0.0.CVAlta Inds = 20.0% / 17.4% = 1.1.CVRepo Men = 13.4% / 1.7% = 7.9.CVAm. Foam = 18.8% / 13.8% = 1.4.CVM = 15.3% / 15.0% = 1.0.17Expected Return versus Coefficient of VariationSecurityExpectedreturnRisk:Risk:CVAlta Inds 17.4% 20.0%1.1Market 15.0 15.31.0Am. Foam 13.8 18.81.4T-bills 8.0 0.00.0Repo Men 1.7 13.47.918Return vs. Risk (Std. Dev.): Which investment is best?19Portfolio Risk and ReturnAssume a two-stock portfolio with $50,000 in Alta Inds. and $50,000 in Repo Men.Calculate rp and p.^20Portfolio Expected Returnrp = Σ wi rirp is a weighted average (wi is % ofportfolio in stock i):rp = 0.5(17.4%) + 0.5(1.7%) = 9.6%.^^^^ni = 121Alternative Method: Find portfolio return in each economic stateEconomyProb.AltaRepoPort.= 0.5(Alta) + 0.5(Repo)Bust 0.10-22.0% 28.0% 3.0%Below avg. 0.20 -2.0 14.7 6.4Average 0.40 20.0 0.0 10.0Above avg. 0.20 35.0 -10.0 12.5Boom 0.10 50.0 -20.0 15.022Use portfolio outcomes to estimate risk and expected returnrp = (3.0%)0.10 + (6.4%)0.20 + (10.0%)0.40 + (12.5%)0.20 + (15.0%)0.10 = 9.6%^p = ((3.0 - 9.6)20.10 + (6.4 - 9.6)20.20 +(10.0 - 9.6)20.40 + (12.5 -9.6)20.20 + (15.0 - 9.6)20.10)1/2 = 3.3%CVp = 3.3%/9.6% = .3423Portfolio vs. Its ComponentsPortfolio expected return (9.6%) is between Alta (17.4%) and Repo (1.7%)Portfolio standard deviation is much lower than:either stock (20% and 13.4%).average of Alta and Repo (16.7%).The reason is due to negative correlation (r) between Alta and Repo.24Two-Stock PortfoliosTwo stocks can be combined to form a riskless portfolio if r = -1.0.Risk is not reduced at all if the two stocks have r = +1.0. In general, stocks have r ≈ 0.35, so risk is lowered but not eliminated.Investors typically hold many stocks.What happens when r = 0?25Adding Stocks to a PortfolioWhat would happen to the risk of an average 1-stock portfolio as more randomly selected stocks were added?sp would decrease because the added stocks would not be perfectly correlated, but the expected portfolio return would remain relatively constant.26s1 stock ≈ 35%sMany stocks ≈ 20%2710 20 30 40 2,000 stocksCompany Specific (Diversifiable) RiskMarket Risk20% 0Stand-Alone Risk, pp35%Risk vs. Number of Stock in Portfolio28Stand-alone risk = Market risk + Diversifiable riskMarket risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification.Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification.29ConclusionsAs more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio.sp falls very slowly after about 40 stocks are included. The lower limit for sp is about 20%=sM .By forming well-diversified portfolios, investors can eliminate about half the risk of owning a single stock.30Can an investor holding one stock earn a return commensurate with its risk?No. Rational investors will minimize risk by holding portfolios.They bear only market risk, so prices and returns reflect this lower risk.The one-stock investor bears higher (stand-alone) risk, so the return is less than that required by the risk.31How is market risk measured for individual securities?Market risk, which is relevant for stocks held in well-diversified portfolios, is defined as the contribution of a security to the overall riskiness of the portfolio.It is measured by a stock’s beta coefficient. For stock i, its beta is:bi = (ri,M si) / sM32How are betas calculated? In addition to measuring a stock’s contribution of risk to a portfolio, beta also which measures the stock’s volatility relative to the market.33Using a Regression to Estimate BetaRun a regression with returns on the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis.The slope of the regression line, which measures relative volatility, is defined as the stock’s beta coefficient, or b.34Use the historical stock returns to calculate the beta for PQU.YearMarketPQU1 25.7% 40.0%2 8.0%-15.0%3-11.0%-15.0%4 15.0% 35.0%5 32.5% 10.0%6 13.7% 30.0%7 40.0% 42.0%8 10.0%-10.0%9-10.8%-25.0%10-13.1% 25.0%35Calculating Beta for PQU36What is beta for PQU?The regression line, and hence beta, can be found using a calculator with a regression function or a spreadsheet program. In this example, b = 0.83.37Calculating Beta in PracticeMany analysts use the S&P 500 to find the market return.Analysts typically use four or five years’ of monthly returns to establish the regression line. Some analysts use 52 weeks of weekly returns.38How is beta interpreted?If b = 1.0, stock has average risk.If b > 1.0, stock is riskier than average.If b < 1.0, stock is less risky than average.Most stocks have betas in the range of 0.5 to 1.5.Can a stock have a negative beta?39Finding Beta Estimates on the WebGo to Thomson ONE—Business School Edition using the information on the card that comes with your book.Enter the ticker symbol for a “Stock Quote”, such as IBM or Dell, then click GO.40Other Web Sites for BetaGo to the ticker symbol for a “Stock Quote”, such as IBM or Dell, then click GO.When the quote comes up, select Key Statistics from panel on left.41Expected Return versus Market Risk: Which investment is best?SecurityExpectedReturn (%)Risk, bAlta 17.4 1.29Market 15.0 1.00Am. Foam 13.8 0.68T-bills 8.0 0.00Repo Men 1.7 -0.8642Use the SML to calculate eachalternative’s required return.The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM). SML: ri = rRF + (RPM)bi .Assume rRF = 8%; rM = rM = 15%.RPM = (rM - rRF) = 15% - 8% = 7%.43Required Rates of ReturnrAlta = 8.0% + (7%)(1.29) = 17%.rM = 8.0% + (7%)(1.00) = 15.0%.rAm. F. = 8.0% + (7%)(0.68) = 12.8%.rT-bill = 8.0% + (7%)(0.00) = 8.0%.rRepo = 8.0% + (7%)(-0.86) = 2.0%.44Expected versus Required Returns (%)Exp.Req. rrAlta 17.4 17.0 Undervalued Market 15.0 15.0 Fairly valuedAm. F. 13.8 12.8 UndervaluedT-bills 8.0 8.0 Fairly valuedRepo 1.7 2.0 Overvalued45SML: ri = rRF + (RPM) bi ri = 8% + (7%) bi..Repo.AltaT-bills.Am. FoamrM = 15 rRF = 8-1 0 1 2 .ri (%)Risk, biMarket46Calculate beta for a portfolio with 50% Alta and 50% Repobp = Weighted average = 0.5(bAlta) + 0.5(bRepo) = 0.5(1.29) + 0.5(-0.86) = 0.22.47Required Return on the Alta/Repo Portfolio?rp = Weighted average r = 0.5(17%) + 0.5(2%) = 9.5%.Or use SML:rp = rRF + (RPM) bp = 8.0% + 7%(0.22) = 9.5%.48SML1Original situationr (%)SML20 0.5 1.0 1.5 Risk, bi181511 8New SML I = 3%Impact of Inflation Change on SML49SML1Original situationr (%)SML2After changeRisk, bi181581.0 RPM = 3%Impact of Risk Aversion Change50Has the CAPM been completely confirmed or refuted?No. The statistical tests have problems that make empirical verification or rejection virtually impossible.Investors’ required returns are based on future risk, but betas are calculated with historical data.Investors may be concerned about both stand-alone and market risk.51