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Chương Rủi ro tỷ suất lợi nhuận Lợi nhuận :các khái niệm Rủi ro: khái niệm Rủi ro riêng lẻ Rủi ro thị trường (rủi ro danh mục) Rủi ro lợi nhuận: CAPM/SML 1-1 Investment returns The rate of return on an investment can be calculated as follows: Return = (Amount received – Amount invested) Amount invested For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is: ($1,100 - $1,000) / $1,000 = 10% 1-2 What is investment risk? Two types of investment risk Stand-alone risk Portfolio risk Investment risk is related to the probability of earning a low or negative actual return The greater the chance of lower than expected or negative returns, the riskier the investment 1-3 Probability distributions A listing of all possible outcomes, and the probability of each occurrence Can be shown graphically Firm X Firm Y -70 15 Expected Rate of Return 100 Rate of Return (%) 1-4 Selected Realized Returns, 1926 – 2004 Small-company stocks Large-company stocks L-T corporate bonds L-T government bonds U.S Treasury bills Average Return 17.5% 12.4 6.2 5.8 3.8 Standard Deviation 33.1% 20.3 8.6 9.3 3.1 Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2005 Yearbook (Chicago: Ibbotson Associates, 2005), p28 1-5 Investment alternatives Economy Prob T-Bill HT Coll USR MP Recession 0.1 5.5% -27.0% 27.0% 6.0% -17.0% Below avg 0.2 5.5% -7.0% 13.0% -14.0% -3.0% Average 0.4 5.5% 15.0% 0.0% 3.0% 10.0% Above avg 0.2 5.5% 30.0% -11.0% 41.0% 25.0% Boom 0.1 5.5% 45.0% -21.0% 26.0% 38.0% 1-6 Why is the T-bill return independent of the economy? Do T-bills promise a completely risk-free return? T-bills will return the promised 5.5%, regardless of the economy No, T-bills not provide a completely risk-free return, as they are still exposed to inflation Although, very little unexpected inflation is likely to occur over such a short period of time T-bills are also risky in terms of reinvestment rate risk T-bills are risk-free in the default sense of the word 1-7 How the returns of HT and Coll behave in relation to the market? HT – Moves with the economy, and has a positive correlation This is typical Coll – Is countercyclical with the economy, and has a negative correlation This is unusual 1-8 Calculating the expected return ^ r = expected rate of return ^ N r = ∑ ri Pi i =1 ^ r HT = (-27%) (0.1) + (-7%) (0.2) + (15%) (0.4) + (30%) (0.2) + (45%) (0.1) = 12.4% 1-9 Summary of expected returns HT Market USR T-bill Coll Expected return 12.4% 10.5% 9.8% 5.5% 1.0% HT has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk? 1-10 Tính beta ? Đường hồi quy beta, tính EXCELL với hàm “regression” b = 0.83 Thường sử dụng suất sinh lời trung bình tháng hay năm để tạo đường hồi quy Đơi dùng số liệu trung bình 52 tuần năm 1-41 Illustrating the calculation of beta _ ri 20 15 10 Year rM 15% -5 12 ri 18% -10 16 -5 -5 -10 10 15 _ 20 rM Regression line: ^ = -2.59 + 1.44 r^ r i M 1-42 Beta coefficients for HT, Coll, and T-Bills 40 _ ri HT: b = 1.30 20 T-bills: b = -20 20 40 _ kM Coll: b = -0.87 -20 1-43 Comparing expected returns and beta coefficients Security HT Market USR T-Bills Coll Expected Return 12.4% 10.5 9.8 5.5 1.0 Beta 1.32 1.00 0.88 0.00 -0.87 Riskier securities have higher returns, so the rank order is OK 1-44 The Security Market Line (SML): Calculating required rates of return SML: ri = rRF + (rM – rRF) bi ri = rRF + (RPM) bi Assume the yield curve is flat and that rRF = 5.5% and RPM = 5.0% 1-45 What is the market risk premium? Additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk Its size depends on the perceived risk of the stock market and investors’ degree of risk aversion Varies from year to year, but most estimates suggest that it ranges between 4% and 8% per year 1-46 Calculating required rates of return rHT rM rUSR rT-bill rColl = = = = = = 5.5% 5.5% 5.5% 5.5% 5.5% 5.5% + + + + + + (5.0%)(1.32) 6.6% (5.0%)(1.00) (5.0%)(0.88) (5.0%)(0.00) (5.0%)(-0.87) = = = = = 12.10% 10.50% 9.90% 5.50% 1.15% 1-47 Expected vs Required returns ^ r r ^ HT 12.4% 12.1% Undervalued (r > r) ^ Market 10.5 10.5 Fairly valued (r = r) ^ USR 9.8 9.9 Overvalued (r < r) ^ T - bills 5.5 5.5 Fairly valued (r = r) ^ Coll 1.0 1.2 Overvalued (r < r) 1-48 Illustrating the Security Market Line SML: ri = 5.5% + (5.0%) bi ri (%) SML HT rM = 10.5 rRF = 5.5 -1 Coll T-bills USR Risk, bi 1-49 An example: Equally-weighted two-stock portfolio Create a portfolio with 50% invested in HT and 50% invested in Collections The beta of a portfolio is the weighted average of each of the stock’s betas bP = wHT bHT + wColl bColl bP = 0.5 (1.32) + 0.5 (-0.87) bP = 0.225 1-50 Calculating portfolio required returns The required return of a portfolio is the weighted average of each of the stock’s required returns rP = wHT rHT + wColl rColl rP = 0.5 (12.10%) + 0.5 (1.15%) rP = 6.63% Or, using the portfolio’s beta, CAPM can be used to solve for expected return rP = rRF + (RPM) bP rP = 5.5% + (5.0%) (0.225) rP = 6.63% 1-51 Factors that change the SML What if investors raise inflation expectations by 3%, what would happen to the SML? ri (%) ∆ I = 3% SML2 SML1 13.5 10.5 8.5 5.5 Risk, bi 0.5 1.0 1.5 1-52 Factors that change the SML What if investors’ risk aversion increased, causing the market risk premium to increase by 3%, what would happen to the SML? ri (%) ∆ RPM = 3% SML2 SML1 13.5 10.5 5.5 Risk, bi 0.5 1.0 1.5 1-53 Verifying the CAPM empirically The CAPM has not been verified completely Statistical tests have problems that make verification almost impossible Some argue that there are additional risk factors, other than the market risk premium, that must be considered 1-54 More thoughts on the CAPM Investors seem to be concerned with both market risk and total risk Therefore, the SML may not produce a correct estimate of ri ri = rRF + (rM – rRF) bi + ??? CAPM/SML concepts are based upon expectations, but betas are calculated using historical data A company’s historical data may not reflect investors’ expectations about future riskiness 1-55 ... beta (b) 1- 37 VD: dùng số liệu suất sinh lời khứ cổ phiếu KWE để tính beta Year 10 Market 25.7% 8.0% -11 .0% 15 .0% 32.5% 13 .7% 40.0% 10 .0% -10 .8% -13 .1% KWE 40.0% -15 .0% -15 .0% 35.0% 10 .0% 30.0%... 25 25 15 15 15 0 -10 -10 -10 1- 26 Returns distribution for two perfectly positively correlated stocks (ρ = 1. 0) Stock M’ Stock M Portfolio MM’ 25 25 25 15 15 15 0 -10 -10 -10 1- 27 Creating a portfolio:... + + + + (5.0%) (1. 32) 6.6% (5.0%) (1. 00) (5.0%)(0.88) (5.0%)(0.00) (5.0%)(-0.87) = = = = = 12 .10 % 10 .50% 9.90% 5.50% 1. 15% 1- 47 Expected vs Required returns ^ r r ^ HT 12 .4% 12 .1% Undervalued (r