Ch. 19 Capital Asset Pricing

Chapter 19: Capital Asset Pricing Theory and Arbitrage Pricing Theory Q. 11. The risk free rate of return is 9 per cent, the expected return on NSE-Nifty is 20 per cent and the variance of the index is 25 per cent. Portfolio return is 15 per cent. Estimate the risk of it. If the investor borrows 25 per cent funds at the risk free rate of return, what will be the return and risk of the portfolio? Solution:

Rf = 9,

Rm = 20,

σm = 25,

Ri = 15

 Rm − R f  Ri = Rf +   σi σ m  

 20 − 9  15 = 9 +  σi  25  15 – 9 = (0.44 σi)

6 = σi 0.44 σi = 13.636

Borrows 25 per cent of funds at risk free rate of return Return = – (0.25 × 9) + 1 × 15 = 12.75 Risk = 13.636 ×1 = 13.636.

Q. 12. The stock market analyst has analysed the stock market and given his opinion regarding J.J. Steel company and the market in the follow table. Growth

Likely Return

Probability

J.J. Steel

Market

Boom

20 %

24 %

0.4

Fair

13%

15%

0.5

Depression

5%

– 7%

0.1

The risk free rate is 7 per cent. It is advisable to buy J.J. Steel company’s stock?

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Solution: J.J. Steel and Market return: Pr

(Rj – Rf)

Pr (Rj – Rf)

(Rm – Rf)

Pr (Rm – Rf)

0.4

20 – 7 = 13

5.2

24 – 7 = 17

6.8

0.5

13 – 7 = 5

2.5

15 – 7 = 8

4.0

0.1

5–7=–2

– 02

– 7 – 7 = – 14

7.5

– 1.4 9.4

J.J. Steel return 7.5 is less than market return of 9.4, hence, it is not advisable to by J.J. Steel stock. Q. 13. The CAPM was estimated for some period in the market. The actual return of two portfolios is given below: Portfolio A: Actual return = 14 per cent Beta = 0.8 Portfolio B: Actual return = 20 per cent Beta = 1.2 The equation of the CAPM is Ri = .07 + 10 βi What can be said about the portfolio’s performance? Solution:

Ri = α + β Rm RA = 0.07 + β 0.10

Portfolio RA = 0.07 + 0.8 × 0.10 = 0.07 + 0.08 = 0.15 = 0.15 × 100 = 15 per cent Portfolio RB = 0.07 + 1.2 × 0.10 = 0.07 + 0.12 = 0.19 × 100 = 19 per cent Portfolio A’s expected return is 15 per cent but the actual return is 14 per cent. It is an under performed portfolio. B’s expected return is 19 per cent. But actual return is 20 per cent. The performance is higher than the expected return. Portfolio B has performed well than the portfolio A. Q. 14. If the following assets are correctly priced on the security market line, what is the return of the market portfolio? What is risk free rate of return? R1 = 10 per cent, R = 14 per cent, β = 0.9, β2 = 1.2

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Solution:

Rm = ?, Rf = ? Ri = Rf + β (Rm)

15 = Rf + 0.9 (Rm) 17 = Rf + 1.2 (Rm) – 2 = – 0.3 Rm Rm = 6.67

The Market portfolio return is 6.67 per cent. 15 = Rf + 0.9 (6.67) 15 = Rf + 6.003 15 – 6.003 = Rf Rf = 9 %

Q. 16. The XY company stock’s return depends heavily on the market return, the beta being 1.4, the risk free rate of return is 8 per cent and the market return is 15 per cent. (a)

Determine the expected return for XY stock.

(b)

What happens to expected return, if the market return increases to 20 per cent?

(c)

What happens to the return if beta falls to .90 while the other inputs remain the same?

Solution:

β = 1.4,

Rt = .8 per cent,

Rm = 15 per cent

E ( R) = Rf + β (Rm – Rf) = 8 + 1.4 (15 – 8) = 8 + 1.4 (7) = 8 + 9.8 = 17.8 If the market return increases to 20 per cent E(R) = 8 + 1.4 (20 – 8)

= 8 + 1.4 (12) = 8 + 16.8 E(R) = 24.8

If the β value falls to 0.90

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E(R) = 8 + 0.9 (15 – 8)

= 8 + 6.3 = 14.3 Q. 17. If the AB company’s expected return is 18 per cent, the market return is 20 per cent and the risk free rate is 6 per cent. (a) Determine the beta value for the stock AB. (b) What is stock’s return if beta value for the stock is 1.1? Solution: Ri = 18, Rm = 20, Rf = 15 per cent, β = ? Ri = Rf + β (Rm – Rf)

(a)

18 = 6 + β (20 – 6) 18 – 6 = β 14 12 =β 14 β = 0.86

(b) If the β value is 1.1, E(R) = 6 + 1.1 (20 – 6) E(R) = 21.4

Q.18. The Broad Way Investment Company manages equity fund consisting of five stocks with the following market values and betas. Stock

Market Value

Beta

A

Rs 3,00,000

1.3

B

Rs 2,50,000

1.2

C

Rs 2,00,000

0.9

D

Rs 1,50,000

0.5

E

Rs 1,00,000

1.6

If Rf is 9 per cent and Rm is 6 per cent. What is Portfolio’s expected return?

Solution:

Total investment A = 3,00,000 B = 2,50,000 C = 2,00,000 D = 1,50,000 E = 1,00,000

10,00,000

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X1 =

3, 00, 000 = 0.3 10, 00, 000

X2 =

2, 50, 000 = 0.25 10, 00, 000

X3 =

2, 00, 000 = 0.2 10, 00, 000

X4 =

1,50, 000 = 0.15 10, 00, 000

X5 =

1, 00, 000 = 0.1 10, 00, 000 1.0 N

βp =

∑

X1 βi

i =1

= (0.3 × 1.3) + (0.25 × 1.2) + (0.2 × 0.9) + (0.15 × 0.5) + (0.1 × 1.6) = 0.39 + 0.3 + 0.18 + 0.075 + 0.16 = 1.105 Rp = Rf + β (Rm – Rf)

= 9 + 1.105 (16 – 9) = 9 + 1.105 (7) = 9 + 7.735 = 16.735

Q. 19. Mr. X is considering investing in the stock of the BHIL Corporation. X expects a positive return of 18 per cent from the BHIL Corp. If the β value is 1.6, Rf is 7 per cent and Rm is 15 per cent, should X invest in the BHIL Corporation? (b) If the beta value is 1.3, should he invest his money in the stock? Solution: (a) E(R) = 18 per cent, β = 1.6, Rf = 7 per cent, Rm = 15 per cent Rf = Rf + β (Rm – Rf)

= 7 + 1.6 (15 – 7) = 7 + 1.6 (8) = 7 + 12.8 = 19.8

Estimated return is higher than the expected return hence the Mr. X can invest.

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(b) Rf β value is

1.3 = 7 + 1.3 (15 – 7) = 7 + 1.3 (8) = 7 + 10.4 = 17.4

Estimated return is lower than the expected return hence the Mr. X should not invest.

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