Question

QUESTION 4

You are given the following data about expected returns on a security on the LUSE where different states of the economy have the same probability of occurrence:

State                                           Return

Strong growth                              9.0%

Normal growth                             6.5%

Weak growth                                2.5%

Recession                                    -4.5%

Required:

Compute and fully interpret the following for the investment:

1. The Expected return for the security.

                                                                                             [3 Marks]

2. The volatility of the security returns using the semi deviation.

                                                                                             [6 Marks]

3. Evaluate the security’s performance assuming a benchmark target rate of 3.5%.

                                                                                             [4 Marks]

4. Explain the rationale behind the security performance evaluation method used in (c) above.

                                                                                             [7 Marks]

Total 20 Marks

Answer 1

a.The Expected return for the security=

Sum of (individual probability of occurrence *Returns at different states)

ie.(25%*9%)+(25%*6.5%)+(25%*2.5%)+(25%*-4.5%)=

3.375%

so,the Expected return for the security= 3.375% or 3.38%

b. The volatility ,ie. Standard deviation of the security returns using the semi deviation

Semi deviation=SQ. RT.of (1/n*Sum Prob.*(Actual return-Expected Return)^2)

where,

n= the no.of deviations below the expected return found out above, ie.2 ( 2.5% & -4.5%)

So, semi-deviation=(1/2*((25%*(9%-3.375%)^2)+(25%*(6.5%-3.375%)^2)+(25%*(2.5%-3.375%)^2)+(25%*(-4.5%-3.375%)^2)))^(1/2)=

3.61%

c. Evaluation of the security’s performance assuming a benchmark target rate of 3.5%.

SQ. Rt of Sum of prob.* (Squared deviations of every actual return from the benchmark return of 3.5%)

ie.(25%*(((9%-3.5%)^2+(6.5%-3.5%)^2+(2.5%-3.5%)^2+(-4.5%-3.5%)^2))))^(1/2)=

5.11%

d.Rationale behind this is to know how far the actual returns,in different states of growth , under the given probabilities ,will sway away from what is the benchmark return planned to be compared with.This has been done like a normal standard deviation, instead of semi-deviation.