Question

QUESTION FOUR You are given the folowing data about expected retums on a security on the LUSE where different states of the economy have the same probability of occurrencs State Retun Strong growth 9.0% Normal growth 6.5% Weak growth 2.5% 4.5 % Recession Required: Compute and fully interpret the following for the investment a) The Expected retum for the security b) The volatility of the security retums using the standard deviation. c) Evaluate the security's performance assuming a benchmark target rate of 3.5 %. [3 Marks] [6 Marks] [4 Marks] d) Explain the rationale behind the security performance evaluation method used in 7 Marks] (c) above. [TOTAL: 20 Marks

investment analysis

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

Answer 1

Following are the calculations:

State	Probability	Return	Probability weighted return	P x (r-Er)^2
Strong	0.25	9.00%	0.25 x 9 = 2.25%	0.25 x (9-3.38)^2 = 0.08%
Normal	0.25	6.50%	0.25 x 6.50 = 1.63%	0.25 x (6.50-3.38)^2 = 0.02%
Weak	0.25	2.50%	0.25 x 2.50 = 0.63%	0.25 x (2.50-3.38)^2 = 0.00%
Recession	0.25	-4.50%	0.25 x -4.50 = -1.13%	0.25 x (-4.50-3.38)^2 = 0.16%
		Expected return	2.25+1.63+0.63-1.13 = 3.38%
			Variance	0.08+0.02+0+0.16 = 0.260%
			Standard Deviation	0.260^0.5 = 5.104%

We find the sharpe ratio to evaluate the performance:

Er – Ro Sharpe ratio =

Sharpe ratio = 3.38 – 3.5 5.104

Sharpe ratio = -0.02

So the risk adjusted return of this asset under performed the benchmark.

We used this method because it gives us a comparison on a risk adjusted level.