Description

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=

ÃÆ’=

CV = ÃÆ’/r

r = r(RF)+[r(m) Ã¢â‚¬â€œ r(rf)]ÃŽÂ²

Portfolio Beta = weight * (beta1) + weight * (Beta 2) + Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦…

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