Question

a) i. Determine the expected return and risk of a portfolio made up of 70 per cent of security X and 30 per cent of security Y if the correlation coefficient for the returns on X and Y is +0.2 Security Expected Return Standard Deviation of Return

X 12 per cent 15 per cent

Y 18 per cent 22 per cent

ii. Explain briefly why the risk of the portfolio specified above is below the weighted average of the risk of securities of X and Y.

b) Explain how increasing the number of securities in a portfolio is likely to reduce the risk of the portfolio but it is unlikely to eliminate all of the risk.

Answer 1

a(i) Expected return of the portfolio = (expected return of security X*proportion of portfolio invested in security X) + (expected return of security Y*proportion of portfolio invested in security Y) = 12*0.7 + 18%*0.3

= 13.80%.

Expected risk of the portfolio = [(proportion of portfolio invested in security X^2*standard deviation of return of X^2) + (proportion of portfolio invested in security Y^2*standard deviation of return of Y^2) + (2* proportion of portfolio invested in security X* proportion of portfolio invested in security Y*coefficient of correlation* standard deviation of return of X* standard deviation of return of Y)]^0.5

= [(0.7^2*0.15^2)+(0.3^2*0.22^2)+(2*0.7*0.3*0.2*0.15*0.22)]^0.5

= 13.47%

(ii) Risk of the portfolio is below the weighted average of the risks of securities X and Y due to the fact that portfolio risk is a function of proportion invested in the two securities, the risk component of the two securities and lastly the correlation of return between X and Y. As we can see that the portfolio majorly (70%) consists of security X which has a much lower standard deviation of 15% (compared to Y’s figure of 22%). Also the correlation coefficient is low at 0.2. These factors cause the risk of the portfolio to fall below the weighted average of the risks of securities X and Y.

(iii) Increasing the number of securities in a portfolio reduces the risk of the portfolio. Total risk = unique risk+market risk. Unique risk is also known as diversifiable risk or unsystematic risk and represents that portion of a security’s risk which comes from different firm specific factors like introduction of a new product, increase in competitive force etc. Such factors only affect the risk of that particular security in the portfolio. Increasing the number of securities in a portfolio helps in lowering the unique risk or the unsystematic risk. This leads to lowering of the portfolio risk. However it will not eliminate all risk as market risk (also known as systematic risk) cannot be avoided.