Question

11. Sophie is a highly risk-averse investor. She wants to invest in the following two stocks: stock A has expected return of 4% and standard deviation of 40%, stock B has expected return of 12% and standard deviation of 30%. The correlation coefficient between the two stocks is (-1), Sophie's friend advises her to invest 50% in stock A and 50% in stock B. Calculate and explain if you agree or disagree with the advice (7 points).

Answer 1

Calculation of Expected Return and Standard Deviation if invested 50% in A and 50% in B
Expected return = (Weight of Stock A in the portfolio * Expected Return of Stock A) + (Weight of Stock B in the portfolio * Expected Return of Stock B)
= 0.5*4% + .5*12% = 8%

Portfolio Standard Deviation is calculated by (WAOW 2 2WAW3O0PAB)2 OP ww + + Where gis the portfolio standard deviation; WA=weight of asset A in the portfolio; w=weight of asset B in the portfolio; =standard deviation of asset A; ga standard deviation of asset B; and PA Correlation coefficient between returns on asset A and asset B. = = [((0.5)2(.40)2) t(0.5)2 (.30)2)+2* 0.5 0.5* (-1)]1/2 [4%+2.25% - .5%]/2 = [5.75 % )/2 2.40%

Since sophie is a high risk averse investor she will prefer lower standard deviation. Since the corelation coefficient is -1 the standard deviation of the portfolio consisting of 50% investment in Stock A and 50% in Stock B is 2.40% and quite low comparative to individual stocks, we agree with Sophie Friend Advice. Also this portfolio will have comparatively how Sharpe Ratio to justify this.