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

T OPIC 8 P ORTFOLIO M ANAGEMENT

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.

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.

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

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?

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

In the case of Stock A EventsProbabilityRatio of Return Better Normal Worse % 12% 4%

 Expectation value of stock A Expectation value of stock A

Then we get

Assume that stock B EventProbabilityRatio of Return Better Normal Worse % 11%

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

Then we get Covariance of A and B

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

Best answer (differentiate) Then we get

M E(Rp) RFRF σ(Rp) G H

Then we get RFM …… capital market line

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

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

RFRF βｋβｋ E(R ｋ )

Situa- tions Prob. Ratio of returns of market portfolio Ratio of returns of each projects Project １ Project ２ Project ３ Very good Better Normal Worse Worst

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×( ) ２＋ 0.2×( ) ２ ＋ 0.4×( ) ２＋ 0.2×(0-0.08) ２ ＋ 0.1×( ) ２ =0.0071

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 E(R 1 )=0.06COV(R 1,R M )= Project ２ E(R 2 )=0.12COV(R 2,R M )= Project ３ E(R 3 )=0.085COV(R 3,R M )=0.0062

THANK YOU FOR YOUR ATTENTION!