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1
p
r
0.1
0.2
0.4
0.2
0.1
-50%
-5%
16%
25%
60%
return
p*r
r-r^
-0.05 -61.400%
-0.01 -16.400%
0.064
4.600%
0.05 13.600%
0.06 48.600%
######
(r-r^)^2
0.376996
0.026896
0.002116
0.018496
0.236196
S.D.
CV
2.34
2
stock 1
35000
0.8
stock 2
40000
1.4
beta of the portfolio = weighted average of the individual assets
1.12
3
r rf
rm
required
r of stock
beta of the stock
r of stock
6%
13%
??
0.7
10.90%
4
r rf
r m – r rf
expected
rm
required
r of stock
beta of stock
5
required
r of stock
r rf
r m – r rf
a
beta
beta
b
r of stock
r rf
???
???
5% t-bill
6%
11%
12.20%
1.2
11%
7%
4%
???
1.00
???
7%
((r-r^)^2)*p
0.0377
0.005379
0.000846
0.003699
0.02362
0.071244
26.69%
r m – r rf
beta
r of stock
6%
1.00
13.00%
6
p
x
0.1
0.2
0.4
0.2
0.1
y
-10%
-35%
2%
0
12%
20%
20%
25%
38%
45%
12% r^y
p*y
r-r^x
-0.035
0
0.08
0.05
0.045
14.00%
b
cv for x
1.02
cv for y
1.4536
stock y is more risky than x.
7 r of the fund
rm
r rf
CAPM r of the fund
beta
beta of the fund
or portfolio
??
14%
6%
r rf + beta *(r m – r rf)
??
is the weighted average of the individual assets
0.7625
r of the fund
8 beta
required r
r rf
rm
capm required r
beta
-22%
-10%
0%
8%
26%
(r-r^)^2
((r-r^)^2)*p
0.0484 0.00484
0.01
0.002
0
0
0.0064 0.00128
0.0676 0.00676
0.01488
12.20%
12.10% capm formula
???
12.50% capm r
4.50%
10.50%
is equal to r rf + beta *(r m – r rf)
1.3333333
11 required r
exp inf.
real r rf
r m – r rf
beta
realized r
nom. R rf
required r
14
???
capm r
3.50%
2.50%
6.50%
1.70
13.50%
6.00%
17.05%
no of stocks
20
inv. Per stock
7500
beta of 20 old stock portfolio
1.12
selling price of 1 stock
7500
beta of the stock sold
1
cost of the new stock
7500
beta of the new stock
1.75
b 20 old stock portfolio
is weighted average of +
weighted average
beta of 19 stocks
of the beta of 1
find beta of 19 stocks
stock sold
1.12 ((7500)*19)/(7500*20)*beta 19)+(7500*1/(7500*20))*1
beta of 19 stocks
1.1263158
beta of 20 new stocks
1.1575
16 old portfolio
5000000
beta of old portfolio
1.25
required r on 5 m portfolio
12% capm r
r rf
5.25%
money received
500000 buy a new stock with this money received
beta of the new stock bought
0.75
required r on the new 5.5 m
portfolio
????
required r on 5 m portfolio
r rf + beta *(rm – r rf)
12% 5.25% + 1.25 *(rm – 5.25%)
rm
10.6500%
beta of the new portfolio
???
beta of the 5.5 m portfolio
beta 5.5 m
required r on the new 5.5 m
portfolio
13
weighted average of
beta of 5 m portfolio
1.2045455
11.755%
+
weighted average of
beta of 500000 investment
Economy
ProbabilityT-Bill
Land
Gold
Recession
0.1
5.50%
-20%
20%
Below Average
0.2
5.50%
-5%
10%
Average
0.4
5.50%
10%
1%
Above Average
0.2
5.50%
25%
-7%
Boom
0.1
5.50%
30%
-15%
A
B
Assuming Jay is a risk averse investor, which are the two best assets you recommend him to buy?
In Addition, Jay “the idiot” decides to invest in the following
Asset
Amount Beta
T-Bill
$40,000
0.4
Land
$30,000
0.75
Gold
$30,000
(1.25)
Market risk premium
10%
Calculate the required rate of return of the portfolio containing all the above three securities
C
10 points
end him to buy?
An hedge fund manager is managing a portfolio of 20 million dollars. The portfolio has a beta of 1.5, risk free rate of
The manager expects that next month he will have to sell some assets worth 5 million dollars. After the sale, the requ
What should be the beta of the assets that will be sold next month???
(5 points)
Consider the following information about three stocks
state of economy
Boom
Normal
Bust
probability stock A stock B stock C
0.3
0.2
0.25
0.6
0.45
0.15
0.11
0.05
0.25
0.01
-0.15
-0.5
A
B
C
If your portfolio invested 40 percent each in A and B and 20 percent in C, what is the portfolio ex
If the expected T-Bill rate is 3.8%, what is the risk premium?
If the expected inflation is 3.5% what is the approximate real returns on the portfolio?
(5 points)
nt in C, what is the portfolio expected return?? The risk??
Stock
X
Y
Z
A
Expected Return
9%
10.75%
12.50%
Standard Deviation
15%
15%
15%
5%
15%
Beta
0.8
1.2
1.6
1
(5 points)
r=
σ=
CV = σ/r
r = r(RF)+[r(m) – r(rf)]β
Portfolio Beta = weight * (beta1) + weight * (Beta 2) + …………

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