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# Investment returns

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Investment returns

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• ### Investment returns

1. 1. What are investment returns? <ul><li>Investment returns measure the financial results of an investment. </li></ul><ul><li>Returns may be historical or prospective (anticipated). </li></ul><ul><li>Returns can be expressed in: </li></ul><ul><ul><li>Dollar terms. </li></ul></ul><ul><ul><li>Percentage terms. </li></ul></ul>
2. 2. What is the return on an investment that costs \$1,000 and is sold after 1 year for \$1,100? <ul><li>Dollar return : </li></ul><ul><li>Percentage return : </li></ul>\$ Received - \$ Invested \$1,100 - \$1,000 = \$100 . \$ Return/\$ Invested \$100/\$1,000 = 0.10 = 10% .
3. 3. What is investment risk? <ul><li>Typically, investment returns are not known with certainty. </li></ul><ul><li>Investment risk pertains to the probability of earning a return less than that expected. </li></ul><ul><li>The greater the chance of a return far below the expected return, the greater the risk. </li></ul>
4. 4. Assume the Following Investment Alternatives Economy Prob. T-Bill HT Coll USR MP Recession 0.10 8.0% -22.0% 28.0% 10.0% -13.0% Below avg. 0.20 8.0 -2.0 14.7 -10.0 1.0 Average 0.40 8.0 20.0 0.0 7.0 15.0 Above avg. 0.20 8.0 35.0 -10.0 45.0 29.0 Boom 0.10 8.0 50.0 -20.0 30.0 43.0 1.00
5. 5. What is unique about the T-bill return? <ul><li>The T-bill will return 8% regardless of the state of the economy. </li></ul><ul><li>Is the T-bill riskless? Explain. </li></ul>
6. 6. Calculate the expected rate of return on each alternative. k = expected rate of return. k HT = 0.10(-22%) + 0.20(-2%) + 0.40(20%) + 0.20(35%) + 0.10(50%) = 17.4% . ^ ^
7. 7. <ul><li>HT has the highest rate of return. </li></ul><ul><li>Does that make it best? </li></ul>^ k HT 17.4% Market 15.0 USR 13.8 T-bill 8.0 Collections 1.7
8. 8. What is the standard deviation of returns for each alternative?
9. 9. HT:  = ((-22 - 17.4) 2 0.10 + (-2 - 17.4) 2 0.20 + (20 - 17.4) 2 0.40 + (35 - 17.4) 2 0.20 + (50 - 17.4) 2 0.10) 1/2 = 20.0%.  T-bills = 0.0%.  HT = 20.0%.  Coll = 13.4%.  USR = 18.8%.  M = 15.3%.
10. 10. Expected Return versus Risk <ul><li>Which alternative is best? </li></ul>Expected Security return Risk,  HT 17.4% 20.0% Market 15.0 15.3 USR 13.8 18.8 T-bills 8.0 0.0 Collections 1.7 13.4
11. 11. Portfolio Risk and Return Assume a two-stock portfolio with \$50,000 in HT and \$50,000 in Collections. Calculate k p and  p . ^
12. 12. Portfolio Return, k p k p is a weighted average: k p = 0.5(17.4%) + 0.5(1.7%) = 9.6% . k p is between k HT and k Coll . ^ ^ ^ ^ ^ ^ ^ ^ k p =   w i k i  n i = 1
13. 13. Alternative Method k p = (3.0%)0.10 + (6.4%)0.20 + (10.0%)0.40 + (12.5%)0.20 + (15.0%)0.10 = 9.6% . ^ Estimated Return (More...) 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
14. 14. <ul><li> p = ((3.0 - 9.6) 2 0.10 + (6.4 - 9.6) 2 0.20 + (10.0 - 9.6) 2 0.40 + (12.5 - 9.6) 2 0.20 + (15.0 - 9.6) 2 0.10) 1/2 = 3.3%. </li></ul><ul><li> p is much lower than: </li></ul><ul><ul><li>either stock (20% and 13.4%). </li></ul></ul><ul><ul><li>average of HT and Coll (16.7%). </li></ul></ul><ul><li>The portfolio provides average return but much lower risk. The key here is negative correlation. </li></ul>
15. 15. Risk 1.Unsystematic Risk : Ex. Business Risk, Financial Risk : Managed by Diversification 2.Systematic Risk : Ex. Market Risk , Interest Rate Risk , Purchasing Power Risk Measurement by Beta which is calculated by : 2.1 Regression Analysis 2.2 Slope of Regression Line ค่าเบต้า แสดงถึงการเปลี่ยนแปลงของอัตราผลตอบแทนของหลักทรัพย์แต่ละชนิดเมื่ออัตราผลตอบแทนของตลาดเปลี่ยนแปลงไป ดังนั้นจึงถือเป็นดัชนีแสดงความเสี่ยงของหลักทรัพย์แต่ละชนิดจากความสัมพันธ์กับตลาดโดยรวม
16. 16. How are betas calculated? <ul><li>Run 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. </li></ul><ul><li>The slope of the regression line, which measures relative volatility, is defined as the stock’s beta coefficient , or b . </li></ul>
17. 17. <ul><li>If b = 1.0, stock has average risk. </li></ul><ul><li>If b > 1.0, stock is riskier than average. </li></ul><ul><li>If b < 1.0, stock is less risky than average. </li></ul><ul><li>Most stocks have betas in the range of 0.5 to 1.5. </li></ul><ul><li>Can a stock have a negative beta? </li></ul>How is beta interpreted?
18. 18. Expected Return versus Market Risk <ul><li>Which of the alternatives is best? </li></ul>Expected Security return Risk, b HT 17.4% 1.29 Market 15.0 1.00 USR 13.8 0.68 T-bills 8.0 0.00 Collections 1.7 -0.86
19. 19. Use the SML to calculate each alternative’s required return. <ul><li>The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM). </li></ul><ul><li>SML: k i = k RF + (RP M )b i . </li></ul><ul><li>Assume k RF = 8%; k M = k M = 15%. </li></ul><ul><li>RP M = (k M - k RF ) = 15% - 8% = 7%. </li></ul>^
20. 20. Required Rates of Return k HT = 8.0% + (7%)(1.29) = 8.0% + 9.0% = 17.0%. k M = 8.0% + (7%)(1.00) = 15.0%. k USR = 8.0% + (7%)(0.68) = 12.8%. k T-bill = 8.0% + (7%)(0.00) = 8.0%. k Coll = 8.0% + (7%)(-0.86) = 2.0%.
21. 21. Calculate beta for a portfolio with 50% HT and 50% Collections b p = Weighted average = 0.5(b HT ) + 0.5(b Coll ) = 0.5(1.29) + 0.5(-0.86) = 0.22 .
22. 22. What is the required rate of return on the HT/Collections portfolio? k p = Weighted average k = 0.5(17%) + 0.5(2%) = 9.5% . Or use SML: k p = k RF + (RP M ) b p = 8.0% + 7%(0.22) = 9.5% .