Question

Question 6 Amelia Investment Fund has total capital of R100 000 invested in three shares Return 4% 24% 14% Shares Invested R30 000 R25 000 R45 000 The current risk-free rate is 8%. Market returns have the following estimated probability distribution for the next period Probability 0,2 0,4 0,2 Market return 10% 12% 13% 16% What is the beta coefficient of the investment fund? 1. 0,5 2. 1,4 3. 3,8 4. 5,5

Answer 1

E(rP) = $\sum_{i=1}^{n}$ [Wi x Ri]

= [(R30,000 / R100,000) x 4%] + [(R25,000 / R100,000) x 24%] + [(R45,000 / R100,000) x 14%]

= 1.20% + 6.00% + 6.30% = 13.50%

E(rM) = $\sum_{i=1}^{n}$ [Pi x Ri]

= [0.1 x 10%] + [0.2 x 12%] + [0.4 x 13%] + [0.2 x 16%] = 1% + 2.4% + 5.2% + 3.2% = 11.8%

According to the CAPM,

E(rP) = rF + beta[E(rM) - rF]

0.1350 = 0.08 + beta[0.1180 - 0.08]

0.0550 = beta[0.0380]

beta = 0.0550 / 0.0380 = 1.4

Hence, Option "2" is correct.