1. T HE MOT AND V ENTURE B USINESS Prof. Takao Ito, Doctor of Economics, PH.D. of Engineering, Graduate School of Engineering, Hiroshima University Thursday, October 16, 2014

2. T OPIC 8 P ORTFOLIO M ANAGEMENT

3. T OPIC 8 CAPM B ASICS  The ROI A performance measure used to evaluate the efficiency of an investment or to compare the efficiency of a number of different investments.

4. The P/E Ratio of a stock (price-to- earnings ratio, "P/E", "PER", "earnings multiple," or simply "multiple") It is a measure of the price paid for a share relative to the annual net income or profit earned by the firm per share.

5.  Basic formula of the ratio of a stock return P 0 …… Initial price P 1 …… trading price D …….Dividend yield

6. Problem: Suppose you invest $10,000 in Toyota, and $30,000 in Nissan international stock. You expect a return of 10% for Toyota and 16% for Nissan. What is the expected return for your portfolio?

7. Solution: You have $40,000 invested in total, so your portfolio weight are 10,000/40,000=25% in Toyota and 30,000/40,000=75% in Nissan. Therefore, the expected return on your portfolio is

8. In the case of Stock A EventsProbabilityRatio of Return Better Normal Worse 0.25 0.5 0.25 20% 12% 4%

9.  Expectation value of stock A Expectation value of stock A

10. Then we get

11. Assume that stock B EventProbabilityRatio of Return Better Normal Worse 0.25 0.5 0.25 7% 11%

12. In the case of two stocks: Stock A and stock B, the expectation value and risk

13. Then we get Covariance of A and B

14. Correlation ratio of A and B Risk of stocks A and B

15. Best answer (differentiate) Then we get

17. M E(Rp) RFRF σ(Rp) G H

18. Then we get RFM …… capital market line

19. S TOCK J AND S TOCK M ARKET M E(Rp) RFRF σ(Rp) G H

20. Let We can easy to get RFRF COV(R j,R M ) E(R ｊ )

21. RFRF βｋβｋ E(R ｋ )

22. Situa- tions Prob. Ratio of returns of market portfolio Ratio of returns of each projects Project １ Project ２ Project ３ Very good 0.10.20.40.60.2 Better0.20.150.30.40.15 Normal0.40.10 Worse0.20-0.1 0 Worst0.1-0.1-0.2-0.4-0.05

23. E(R M )=0.1×0.2 ＋ 0.2×0.15 ＋ 0.4×0.1 ＋ 0.2×0 ＋ 0.1× （ -0.1 ） ＝ 0.08 σ ２ （ R M ）＝ 0.1×(0.2-0.08) ２＋ 0.2×(0.15-0.08) ２ ＋ 0.4×(0.1-0.08) ２＋ 0.2×(0-0.08) ２ ＋ 0.1×(-0.1-0.08) ２ =0.0071

24. ①②③④⑤⑥ SituationsProb.:P Rate of returns:R K P*R ｋ [R ｋ － E(R k ) ］ [R M － E(R M ) ］②×⑤②×⑤ Project １ 10.10.40.040.04080.00408 20.20.30.060.01680.00336 30.400-0.0012-0.00048 40.2-0.1-0.020.01280.00256 50.1-0.2-0.020.04680.00468 E(R 1 )=0.06COV(R 1,R M )=0.0142 Project ２ 10.10.60.060.06480.00648 20.20.40.080.02380.00476 30.40.10.040.00080.00032 40.2-0.1-0.020.01280.00256 50.1-0.4-0.040.08280.00828 E(R 2 )=0.12COV(R 2,R M )=0.0224 Project ３ 10.10.20.020.01680.00168 20.20.150.030.00630.00126 30.40.10.040.00080.00032 40.2000.00480.00096 50.1-0.05-0.0050.01980.00198 E(R 3 )=0.085COV(R 3,R M )=0.0062

28. THANK YOU FOR YOUR ATTENTION!