Question

1. An investment analyst estimates the following probabilities of return depending on the state of the economy.

Business conditions	Boom	Good	Normal	Recession	Poor
Probability	0.05	0.25	0.40	0.25	0.05
Petronas share return %	12	10	4	-2	-7
Maxis share return %	26	12	8	-6	-22
Berjaya share return %	41	23	12	-27	-55

1. Compute the expected rate of return and
2. Expected risk of the above shares   
3. What are their Shape Ratios?             (1Mark)

Answer 1

The data about stocks and probability of returns according to the economic condition is given here.

a) The expected return is calculated by adding the return of specific stock multiplied by its probability.

Expected Return = ( Return * Probability)

Petronas Stock
Boom > (12 * 0.05) = 0.6%
Good > (10 * 0.25) = 2.5%
Normal > (4 * 0.4) = 1.6%

So we can create a table here

Business conditions	Boom	Good	Normal	Recession	Poor
Probability	0.05	0.25	0.4	0.25	0.05
Petronas %	12	10	4	-2	-7
Maxis %	26	12	8	-6	-22
Berjaya %	41	23	12	-27	-55
Expected Return						Stock Return
Petronas %	0.6	2.5	1.6	-0.5	-0.35	3.85
Maxis %	1.3	3	3.2	-1.5	-1.1	4.9
Berjaya %	2.05	5.75	4.8	-6.75	-2.75	3.1
Portfolio	3.95	11.25	9.6	-8.75	-4.2

b) Expected risk of the shares is nothing but the standard deviation.

Standard Deviation = (((Observation Value - Mean)^ 2) / Number of Observations)) ^ 0.5

Mean return for Petronas Shares
(0.6 + 2.5 + 1.6 - 0.5 - 0.35) / 5 = 0.77%

We can also use Excel function for calculating standard deviation

						Expected Return	Mean	Standard Deviation
Petronas %	0.6	2.5	1.6	-0.5	-0.35	3.85%	0.77%	1.28
Maxis %	1.3	3	3.2	-1.5	-1.1	4.9%	0.98%	2.21
Berjaya %	2.05	5.75	4.8	-6.75	-2.75	3.1%	0.62%	5.28

c) The Sharpe Ratio can be calculated by the following formula

Sharpe Ratio = (Average Return - Risk-Free Return) / Standard Deviation

The risk free rate is not given in the information.
If the risk free rate is assumed to be 0.5%

Petronas Sharpe Ratio
(0.77 - 0.50) / 1.28 = 0.2105

Maxis Sharpe Ratio
(0.98 - 0.5) / 2.21 = 0.2169

Barjaya Sharpe Ratio
(0.62 - 0.5) / 5.28 = 0.0227