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CM2 - Sept 2014 Q2

B

Bharti Singla

Senior Member
An investor wishes to allocate her capital between a service company S and a manufacturing company M. The returns on shares in S have mean 10% and variance 16%% while returns of shares on company M have mean 8% and variance 25%%. The correlation between these is 0.3
(iv) calculate minimum variance portfolio

The minimum variance portfolio is calculated as 65.5% in S and 34.5% in M using a formula. But why not investing 100% in S and 0% in M given that S has higher mean and lower variance?
 
You are correct that if we invested 100% in S our variance is 16%%.

However, you can get lower than this. For example, in part (iii) you discovered that the variance of a portfolio which is invested three quarters in S and one quarter in M is 12.8125%%. This is because V(xA+yB) = x^2*V(A)+y^2*V(B)+2*x*y*Corr(A,B)*SD(A)*SD(B).

The variance of the minimum variance portfolio is:
V(0.655S+0.345M)
= V(0.655S)+V(0.345M)+2*Corr(0.655S,0.345M)*SD(0.655S)*SD(0.345M)
= 0.655^2*16%% + 0.345^2*25%% + 2*0.3*0.655*sqrt(16%%)*0.345*sqrt(25%%)
= 12.55%%.
 
Alvin Kissoon said:
You are correct that if we invested 100% in S our variance is 16%%.

However, you can get lower than this. For example, in part (iii) you discovered that the variance of a portfolio which is invested three quarters in S and one quarter in M is 12.8125%%. This is because V(xA+yB) = x^2*V(A)+y^2*V(B)+2*x*y*Corr(A,B)*SD(A)*SD(B).

The variance of the minimum variance portfolio is:
V(0.655S+0.345M)
= V(0.655S)+V(0.345M)+2*Corr(0.655S,0.345M)*SD(0.655S)*SD(0.345M)
= 0.655^2*16%% + 0.345^2*25%% + 2*0.3*0.655*sqrt(16%%)*0.345*sqrt(25%%)
= 12.55%%.
Click to expand...

Thanks for explaining Alvin. I got your point. But I am just thinking is there any possibility where we can give a simple answer by just looking at the mean and variance(without doing any calculations as you did) maybe if the two assets were not correlated ?
 
Bharti Singla said:
Thanks for explaining Alvin. I got your point. But I am just thinking is there any possibility where we can give a simple answer by just looking at the mean and variance(without doing any calculations as you did) maybe if the two assets were not correlated ?
Click to expand...

Unfortunately not. If the two assets were not correlated, you would still use the formula in the Examiners' Report to determine the proportions to invest in each asset and the resulting variance (which will still be lower than 16%%). On the plus side, it is a straightforward formula to use.
 
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