Give the following hypothetical end- of - period prices for shares of the Drill -on- Corporation, and

assuming a current price of sh. 50 per share

Probability 0.15 0.1 0.3 0.2 0.25

End of Period Price per Share 35 42 50 55 60

i) Calculate the rate of return for each probability; what is the expected return? The variance

of end- of- period return; The range and semi-interquartile range

ii) Suppose forecasting is refined such that probabilities of end- of- period prices can be

broken down further, resulting in the following

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Probability 0.01 0.05 0.07 0.02 0.1 0.3 0.2 0.15 0.05 0.05

End of period

price per share 0 35 38.57 40 42 50 55 57 60 69

a) Calculate and explain the change in the expected returns, the range of returns and the semiinterquartile

range of returns.

b) Calculate the semi variance of the end - of period returns. Why might some investors be

concerned with semi variance as a measure of risk

QUESTION FOUR (B)

Given two random variables x and y

State of Nature Probability variable x variable y

I 0.2 18 0

II 0.2 5 -3

III 0.2 12 15

IV 0.2 4 12

V 0.2 6 1

(i) Calculate the mean and variance of each of these variables and the covariance between them

(ii) Suppose x and y represent the returns from two assets. Calculate the mean and variance for the

following part folios.

(iii)Find the portfolio that has the minimum variance.

(iv) Let portfolio A have 75% in x and portfolio B have 25% in x. Calculate the covariance between

the two portfolios.

(v) Calculate the covariance between the minimum variance portfolio and portfolio A.