you are given the following data: Probability Expected return of stock A Expecte
ID: 2728673 • Letter: Y
Question
you are given the following data:
Probability Expected return of stock A Expected return of stock B
30 13 15
20 14 13
20 15 12
30 16 11
Using these stocks you have identified two investments portfolio alternatives:
Alternatives Portfolios
1 100% A
2 40% A and 60% B
Required:
1. Calculate the portfolio return and standard deviation for each alternatives
2. Based on the findings above, which of the two (2) alternatives would you choose? give reason.
3. What do your answers in Part (2) imply about diversification?
4. The most important factor which determines the portfolio's risk is the expected returns and standard deviations of the individual securities in the portfolio. Is this statement corect or incorrect ? discuss.
Explanation / Answer
Calculations:
Answers to questions: 1) Return of portfolio 1 (A 100%) = 14.5; Standard deviation = 1.2% Return of portfolio 2 (A 40% B 60%) = 14.5*0.4+12.8*.6 = 13.48% Standard deviation = (0.4^2*1.2^2+0.6^2*1.6^2+2*.4*.6*1.2*1.6*-.99)^0.5 = 0.49% 2) I would chose Alternative 2, as it has a return of 13.48% with a much lower standard deviation of 0.49%. The expected return of Alternative 1 is higher at 14.5% but the standard deviation is higher at 1.2% 3) For diversification one should choose assets that are negatively correlated as in the case of Stock A Stock B, which have a negative correlation of 0.99. Negative correlation will reduce the standard deviation (risk) of the portfolio. 4) It is incorrect. The formula for two assets is (W1^2*SD1^2+W2^2*SD2^2+2*W1*W2*SD1*SD2*CORRELATION12)^(1/2) where W1 AND W2 are the weights of the two securities in the portfolio and SD1 and SD2 their standard deviations. Though the weights and stanadard deviations of individual securities are important, the third expression is more important as it contains the correlation coefficient of the two assets. The correlation coefficient ranges between -1 and +1. Any value less than +1 will reduce the portfolio standard deviation. Negative value for correlation coefficient will produce higher diversification benefits. Hence, the correlation coefficient of the two assets is more important.Related Questions
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