The table below provides the share return forecasts and associated probabilities

Question

The table below provides the share return forecasts and associated probabilities for Western Innovations Limited (WIL) and Albright Limited (ABL). The share return performance for the companies depends to a great extent on future economic conditions.

              WIL                                     ABL
Return (%) Probability (%)     Return (%) Probability (%)
    20.0          40                      20.3             20
    12.0          20                        10.5             50
      5.0          40                         7.0              30

a. Calculate the expected return on each share (4 marks).
b. Calculate the variance and standard deviation for each share (4 marks).
c. Assuming a correlation coefficient of -0.5 between the returns from the two shares, calculate the expected return and the standard deviation of the following investment allocation strategies:
i. Investing 50% of available funds into WIL and the remaining 50% into ABL (2 marks).
ii. Investing 75% of the available funds into WIL and the remaining 25% into ABL (2 marks).
iii. Assuming no other investment opportunities exist, which of the two strategies would be preferred by a highly risk averse investor? Discuss your recommendation (3 marks).

Explanation / Answer

a) Expected retunr for WIL=(40%*20%)+(20%*12%)+(40%*5%)=12.4%
Expected retunr for WIL=(20%*20.3%)+(50%*10.5%)+(30%*7%)=11.41%

b)for variance
WIL=40%*(12.4%-20%)^2+20%*(12.4%-12%)^2+40%*(12.4%-5%)^2=0.0045
ABL=20%*(11.41%-20.3%)^2+50%*(11.41%-10.5%)^2+30%*(11.41%-7%)^2=0.00221

Std=variance^0.5
WIL=0.0671
ABL=0.047

c)Weight WIL=50% weight ABL=50%

E(R)=0.5*12.4%+0.5*11.41%=11.91%
Var=0.5^2*0.0045+0.5^2*0.00221+(2*.5*.5*-0.5)=-.24832
std=.24832^.5=49.83%

D)c)Weight WIL=75% weight ABL=25%

E(R)=0.75*12.4%+0.25*11.41%=1215%
Var=0.75^2*0.0045+0.25^2*0.00221.+(2*.75*.25*-0.5)=.1848
std=.1848^.5=43.%

III) calcualte coefficent of variation

=std/mean

For 1st portfolio=4.19

For 2nd portfloio=3.54

@nd portfolio is best as it has less value of coefficent of variation

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