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)

State	Return	Probability	Expected Return
Strong growth	9%	25%	2.25%
Normal growth	7%	25%	1.63%
Weak growth	2.50%	25%	0.63%
Recession	-4.50%	25%	-1.13%
Total			3.38%

Hence total expected return is 3.38%.

b) Downside deviation is a measure of downside risk that focuses on returns that fall below a minimum threshold or target return.

Using average return as target return 3.38% from question a)

Volatility of security return using downside deviation:

State	Return (a)	Probability (b)	Expected Return (c)	Return(a) -target(3.38) (d)	(Return -target)^2
Strong growth	9%	25%	2.25%	0.000%	0.000%
Normal growth	7%	25%	1.63%	0.000%	0.000%
Weak growth	2.50%	25%	0.63%	-0.875%	0.008%
Recession	-4.50%	25%	-1.13%	-7.875%	0.620%
Total			3.38%	-8.750%	0.628%
Target Return			3.38%
Downside Deviation					Sqrt (0.628/4) = 3.96%

You can see in column (d) for strong and normal growth it is 0 as we are using downside deviation hence -ve difference should be used.

Hence volatility is 3.96% using downside deviation.

c)