Question

Consider the following information on two securities Expected rate of return on Security Ri = 0.10 Expected rate of return on Security Rj = 0.20 Variance of ROR of security Ri = 0.16 Variance of ROR of security Rj = 0.25 Covariance between Ri and Rj = -0.04 (minus 0.04)

Obtain the

1. the investment fractions to obtain the Global Minimum Variance Portfolio
2. Expected rate of return on Global Minimum Variance Portfolio
3. Variance of Global Minimum Variance Portfolio
4. Is your portfolio diversified? Whatever your answer you must explain the reason for your answer.
5. If you need to draw a graph how the graph of the efficient frontier will look for the correlation structure given above. (

   Obtain the

6. the investment fractions to obtain the Global Minimum Variance Portfolio
7. Expected rate of return on Global Minimum Variance Portfolio
8. Variance of Global Minimum Variance Portfolio
9. Is your portfolio diversified? Whatever your answer you must explain the reason for your answer.
10. If you need to draw a graph how the graph of the efficient frontier will look for the correlation structure given above. (Draw a graph to discuss your answer). Do not forget to write down the legends on X and Y axis)
11. What is the threshold coefficient of correlation above which diversification will not be possible?
12. a graph to discuss your answer). Do not forget to write down the legends on X and Y axis)
13. What is the threshold coefficient of correlation above which diversification will not be possible?

Answer 1

Asset Expected Return Variance

Ri 0.1 0.16

Rj 0.2 0.25

covariance(Ri,RJ)=-0.04

let Xi amount invest in asset Ri and Xj amount in asset Rj so required return on the portfolio will be

Rp = Xi*Ri+Xj*Rj

Vp=Xi^2*variance(Ri)+Xj^2*variance(Rj)+2*covariance(Ri,Rj)*Xi*Xj

(i) investment fraction for minimum variance

Xi=variance(Rj)-cov(Ri,Rj)/var(Ri)+var(Rj)+var(Rj)-2*cov(Ri,Rj)

=0.25+0.04/0.16+0.25+0.08

=0.59

Xi=0.59

Xj=0.41

(ii)

expected return on minimum variance portfolio

=0.59*0.1+0.41*0.2

=14.1%

(iii) variance on portfolio

=0.59^2*0.16+0.41^2*0.25-0.08*0.41*0.59

=7.8369%

(iv) As we look at the variance of the portfolio it is below the variance of both the securities and the aim of the diversification is to minimise the risk factor so we can say that our portfolio is diversified.

(v) We can see that correlation coefficient is -0.04 . Negative correlation means that both the securities moves in opposite direction so that we can avle to make diversified portfolio if the correlation between the security would be positive then it is difficult to make minimise the risk. threshold to the covariance is 0 as covariance above the 0 it isnot possible to minimise the risk .