# Risk and Return

**Topics:**Capital asset pricing model, Modern portfolio theory, Portfolio

**Pages:**9 (518 words)

**Published:**February 2, 2014

c) Because Diversifiable risk can be eliminated through portfolio diversification, the more relevant risk is the Nondiversifiable risk. This kind of risk can be attributed to market forces and factors that affect ALL the firms and cannot be eliminated through portfolio diversification. In this case, the nondiversifiable risk is about 6.00%. Notice that the area between the red curve and the green line (which represents the diversifiable risk) diminishes as it approaches the green line.

P8-18 Graphical Derivation of Beta

c) Looking at the graph we can see that the best-fit line of returns for Asset B is steeper (has greater slope) than Asset A The slopes of these lines are the betas for each asset: 2.61 for Asset B and 1.48 for Asset A. The greater beta value of Asset B signifies that it is more responsive to market factors and therefore makes it more risky than Asset A.

P8-20 Interpreting Beta

a. A 15% increase in market return would lead to an 18% (15% x 1.20) increase in the asset’s return. b. An 8% decrease in market return would lead to a 9.6% (8% x 1.20) decrease in the asset’s return. c. If the market return doesn’t change, the asset’s return more or else stays the same holding other things constant. d. This asset has a beta of 1.20 signifying that it is 1.2x more responsive than the market. This means that the asset is riskier than the market.

P8-23 Portfolio Betas

Asset (j)

Asset beta (bj)

Portfolio A weights (wja)

wja x bj

Portfolio B weights (wjb)

wj x bj

1

1.30

0.1

0.13

0.3

0.39

2

0.70

0.3

0.21

0.1

0.07

3

1.25

0.1

0.125

0.2

0.25

4

1.10

0.1

0.11

0.2

0.22

5

0.90

0.4

0.36

0.2

0.18

Totals

1

0.935

1

1.11

b. Portfolio B has a beta of 1.11 which is greater than Portfolio A’s beta of only 0.935. This makes Portfolio B more responsive the changes in the market and therefore riskier than Portfolio A.

P8-24 Capital Asset Pricing Model (CAPM)

Case

Risk-free Rate (Rf)

Market Return (rm)

Beta (b)

Risk Premium (rm-Rf)

b x (rm - Rf)

Required Rate of Return (rj)

A

5%

8%

1.30

3%

0.039

8.90%

B

8%

13%

0.90

5%

0.045

12.50%

C

9%

12%

-0.20

3%

-0.006

8.40%

D

10%

15%

1.00

5%

0.05

15.00%

E

6%

10%

0.60

4%

0.024

8.40%

We use the formula for the required return in the CAPM model:

P8-26 Manipulating CAPM

Using the formula for the required return in the CAPM model:

Case

Risk-free Rate (Rf)

Market Return (rm)

Beta (b)

Required Rate of Return (rj)

A

8%

12.0%

0.90

11.60%

B

?

14.0%

1.25

15.00%

C

9%

?

1.10

16.00%

D

10%

12.5%

?

15.00%

We derive the missing values:

a. 11.60%; 8% + [0.90*(12.0%-8%)] =11.60%

b. 10%; 15% = x + [1.25 *(14% - x)]

c. 15.36%; 16% = 9% + [1.10 * ( x – 9%)]

d. 2.0; 15% = 10% + [ x * ( 12.5% - 10%)]

P8-28 Security Market Line

Case

Risk-free Rate (Rf)

Market Return (rm)

Beta (b)

Risk Premium

Required Rate of Return (rj)

Asset A

9%

13%

0.80

3.2%

12.2%

Asset B

9%

13%

1.30

5.2%

14.2%

P8-29 Shifts in the Security Market Line

16

14

12

10

8

6

4

2

00.51 1.11.5

Case

Risk-free Rate (Rf) %

Market Return (rm)%

Beta (b)

Risk Premium

Required Rate of Return (rj) %

a

8

12

1.1

4.4

12.4

b

6

10

1.1

4.4

10.4

c

8

13

1.1

5.5

13.5

P8-30 Integrative Risk, return and CAPM

A.)

Case

Risk-free Rate (Rf)

Market Return (rm)

Beta (b)

Risk Premium

Required Rate of Return (rj)

project a

9%

14%

1.50

7.50%

16.50%

project b

9%

14%

0.75

3.75%

12.75%

project c

9%

14%

2.00

10.00%

19.00%

project d

9%

14%

0.00

0.00%

9.00%

project e

9%

14%

-0.50

-2.50%

6.50%

20

18

16

14

12

10

8

6

4

2

0

0.250.50.751.01.251.5 1.75 2.0

d.) decline in risk aversion

Case

Risk-free Rate (Rf)

Market Return (rm)...

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