t he mot and v enture b usiness prof. takao ito, doctor of economics, ph.d. of engineering, graduate...
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THE MOT AND VENTURE BUSINESS
Prof. Takao Ito, Doctor of Economics, PH.D. of Engineering, Graduate School of Engineering, Hiroshima University
Thursday, October 16, 2014
TOPIC 8 CAPM BASICS 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
0
01
P
DPPR
P0……Initial priceP1……trading priceD…….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
%5.1416.0%7510.0%25
][][)(
NNTTP RExRExRE
Expectation value of stock A
l
kkiki PRRE
1
)(
Expectation value of stock AExpectation value of stock A
l
kkiiki PRERR
1
2))(()(
Assume that stock B
Event Probability Ratio of Return
BetterNormalWorse
0.250.5
0.25
7%7%
11%
%81125.075.0725.0)( BRE
%3
)811(25.0)87(5.0)87(25.0)( 222
BR
In the case of two stocks: Stock A and stock B, the expectation value and risk
;1 BA XX
);()()( BBAAi REXREXRE
),(2)()(
)(
2222BABABBAA
i
RRCovXXRXRX
R
Then we getBAp XXRE 812)(
BABA
BABAp
XXXX
XXXXR
16332
)8(2332)(
22
22
Covariance of A and BCovariance of A and B
8
25.0)811)(124(5.0)87)(1212(25.0)87)(1220(
)]}()][({[),(
BBAABA RERRERERRCov
Correlation ratio of A and B
816.0332
8
)()(
),(
BA
BAAB RR
RRCov
Risk of stocks A and BRisk of stocks A and B
32251
)1(16)1(332
16332)(
2
22
22
AA
AAAA
BABAp
XX
XXXX
XXXXR
Best answer (differentiate)
%5.78;215.0102/22 BA XX
0)(
A
p
dX
Rd
032251
22102
2
1)(
2
AA
A
A
p
XX
X
dX
Rd
Then we getThen we get
)()1()()1()()( SFSFP REXRXREXRXERE
)()1(
)0)(()()1(
)()()1(2)()1()()(
22
2222
S
FS
SFFSSFP
RX
RRX
RRXXRXRXR
Then we getThen we get
)()(
)()( p
M
FMFP R
R
RRERRE
RFM……capital market line
STOCK J AND STOCK MARKET
)()1()()( MjjjP REXREXRE
),()1(2)()1()()( 2222MjjjMjjjP RRCovXXRXRXR
M
E(Rp)
RF
σ(Rp)
G
H
),()(
)()(
2 MjM
FMFj RRCov
R
RRERRE
)(
),(2
M
Mj
R
RRCov
])([)( FMjFj RRERRE
Let
We can easy to get
RF
COV(Rj,RM)
E(R j )
Situa-tions
Prob.
Ratio of returns of market portfolio
Ratio of returns of each projects
Project 1
Project 2
Project3
Very good
0.1 0.2 0.4 0.6 0.2
Better 0.2 0.15 0.3 0.4 0.15
Normal
0.4 0.1 0 0.1 0.1
Worse 0.2 0 -0.1 -0.1 0
Worst 0.1 -0.1 -0.2 -0.4 -0.05
E(RM)=0.1×0.2 + 0.2×0.15 + 0.4×0.1 + 0.2×0 + 0.1× ( -0.1 ) = 0.08
σ 2( RM )= 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
① ② ③ ④ ⑤ ⑥
Situations Prob.:PRate of
returns:RK
P*R k
[R k- E(Rk) ] [RM - E(R
M) ] ②×⑤
Project 1
1 0.1 0.4 0.04 0.0408 0.00408
2 0.2 0.3 0.06 0.0168 0.00336
3 0.4 0 0 -0.0012 -0.00048
4 0.2 -0.1 -0.02 0.0128 0.00256
5 0.1 -0.2 -0.02 0.0468 0.00468
E(R1)= 0.06 COV(R1,RM)= 0.0142
Project 2
1 0.1 0.6 0.06 0.0648 0.00648
2 0.2 0.4 0.08 0.0238 0.00476
3 0.4 0.1 0.04 0.0008 0.00032
4 0.2 -0.1 -0.02 0.0128 0.00256
5 0.1 -0.4 -0.04 0.0828 0.00828
E(R2)= 0.12 COV(R2,RM)= 0.0224
Project 3
1 0.1 0.2 0.02 0.0168 0.00168
2 0.2 0.15 0.03 0.0063 0.00126
3 0.4 0.1 0.04 0.0008 0.00032
4 0.2 0 0 0.0048 0.00096
5 0.1 -0.05 -0.005 0.0198 0.00198
E(R3)= 0.085 COV(R3,RM)= 0.0062
20071.0
0142.0
)(
),(2
11
M
M
R
RRCov
15.30071.0
0224.0
)(
),(2
22
M
M
R
RRCov
87.00071.0
0062.0
)(
),(2
33
M
M
R
RRCov
03.005.008.0])([ FM RRE
11.0
)05.008.0(205.0])([)( 11
FMF RRERRE
1445.0
)05.008.0(15.305.0])([)( 22
FMF RRERRE
0761.0
)05.008.0(87.005.0])([)( 33
FMF RRERRE
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