Investment returns

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

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% . ^ ^

8. What is the standard deviation of returns for each alternative?

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%.

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. 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. 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

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

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. 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. 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% .