Question

A. Christy is considering investing in the ordinary shares of BlueSteel and Ranco. The following data are available for these two securities:

BlueSteel Ranco

Expected return 9.2% 19.1%

Standard deviation of returns 7.8% 14.3% Using these two shares undertake calculations of the expected return and standard deviation of the portfolio, for

: a) A portfolio of 30% Heico, and correlation coefficients of either -0.2 or 0.8 between the two assets

b) A portfolio of 70% Heico, and correlation coefficients of either -0.2 or 0.8 between the two assets Explain using these calculations how diversifying a portfolio benefits an investor, and what key factors contribute to the extent of benefit involved.

Answer 1

A,Portfolio with 30% Blue steel and 70% Ranco

Expected Return of the portfolio =R1*w1+R2*w2

Where R1and R2 are expected returns of Bluesteel and Ranco and w1& W2 are respective weights

Thus expected Return of portfolio=9.2%*0.30+19.1%*0.70

                                                                  =2.76%+13.37%=16.13%

Variance of the portfolio=w1² *Variance of Blue steel+W2² *Variance of                 Ranco+2.W1.W2. Coavriance of Blue steel and Ranco

(covariance =Correlation coeffient*Standard deviation of Bluesteel *Standard deviation of Ranco

=0.30*0.30*7.8*7.8+(0.70*0.70*14.3*14.3)+2*0.30*0.70*7.8*14.3*0.80

=5.4756+96.452+36.7698=138.697

Standard deviation of the portfolio=Square root of 138.697=11.777%

When Correlation coeffient=-0.2,

Variance of portfolio0.30*0.30*7.8*7.8+(0.70*0.70*14.3*14.3)+2*0.30*0.70*7.8*14.3*-0.20

=5.4756+96.452-9.1925=92.7352

Standard deviation of the portfolio=Square root of 92.7352=9.63%

b,Portfolio with 70% Blue steel and 30% Ranco

Expected Return of the portfolio =R1*w1+R2*w2

Where R1and R2 are expected returns of Bluesteel and Ranco and w1& W2 are respective weights

Thus expected Return of portfolio=9.2%*0.70+19.1%*0.30

                                                                  =6.44%+5.71%=12.17%

Variance of the portfolio=w1² *Variance of Blue steel+W2² *Variance of                 Ranco+2.W1.W2. Covariance of Blue steel and Ranco

=0.70*0.70*7.8*7.8+(0.30*0.30*14.3*14.3)+2*0.30*0.70*7.8*14.3*0.80

=29.8116+17.7157+36.7698=84.2971

Standard deviation of the portfolio=Square root of 84.2971=9.18%

When Correlation coeffient=-0.2,

Variance of portfolio=.70*0.70*7.8*7.8+(0.30*0.30*14.3*14.3)+2*0.30*0.70*7.8*14.3*-0.20

29.8116+17.7157-9.1925=38.3348

Standard deviation of the portfolio=Square root of 38.3348=6.19%

Thus ,Both portfolio returns are greater than return of blue steel ,at the same time lesser than return of Ranco.But benefit of the portfolio investment is that it reduces risk. Standard deviation is the measure of the risk.Risk of the portfolio is not simply as measure of its weighted average risk.Blue steel and ranco are associated with each other. So portfolio risk also considers covariance of two securities.

Diversification of unsystematic risk,using two security portfolio,depends upon correlation that exists between the returns of these securities.When correlation coeffient decreases risk of portfolio also decreases.