Valley Fruit Limited is currently assessing the riskiness of the market with an
ID: 2774605 • Letter: V
Question
Valley Fruit Limited is currently assessing the riskiness of the market with an intention of investing. The company currently has excess cash on its balance sheet to invest. Senior management wants to invest the excess cash. As a result, the chief financial officer is analysing the treasury market. However, he is seeking advice to differentiate among a treasury bill, note or a bond. On the other hand, he thinks the returns on treasury securities are insufficient. Hence, he is contemplating corporate securities. However, the risks on corporate securities are greater as indicated by the company’s financial analyst. The following below are the expected returns and probabilities on the company’s stock for the recent four year period: Probabilities Returns 0.4 10% 0.3 20% 0.2 40% 0.1 -10% Required: a. Calculate the expected returns [ 4 marks ] b. Calculate the standard deviation of the returns [ 11 marks ]
Explanation / Answer
Expected Return = 17%
Standard Deviation of Returns = 6.091% (rounded off)
Probabilities
Returns
0.40
10%
0.30
20%
0.20
40%
0.10
-10%
Expected return = 0.40 * 10% + 0.30 * 20% + 0.20 * 40% + 0.10 * -10%
= 4% + 6% + 8% - 1% = 17%
Variance of returns = Sum of (probability * (return – expected return))^2
Variance of returns = {(0.40*(10-17)^2 + (0.30*(20-17)^2 + (0.20*(40-17)^2 + (0.10*(-10-17)^2}
= {( 0.40 * -7)^2 + (0.30 * 3)^2 + (0.20 * 23)^2 + (0.10 * -27)^2}
= {(-2.8)^2 + (0.9)^2 + (4.6)^2 + (-2.7)^2}
= 7.84 + 0.81 + 21.16 + 7.29
= 37.10
Standard Deviation of Returns = Square root of (329) = 37.10^1/2 = 6.090977 or 6.091%
Probabilities
Returns
0.40
10%
0.30
20%
0.20
40%
0.10
-10%
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