In: Finance
Astrid has the following two investments in her portfolio:
Investment | Expected Return | Standard Deviation | Beta | % Weighting |
M | 12% | 3.1% | 1.40 | 55% |
N | 19% | 3.9 | 0.85 | 45 |
Which investment is riskier by itself and in a portfolio sense?
What is the expected return of the portfolio?
With a correlation coefficient of +0.30, what is the standard deviation of the portfolio?
What is the beta of the portfolio?
What is the significance of the results in parts a through d?
Ans.
a) Which investment is riskier by itself and in a portfolio sense?
It can be calculated by Coefficient of Variation( risk as a percentage of return i.e lower the better )
Coefficient of Variation of Stock M = SD of M / Expected Return of M* 100
= 3.1% / 12% * 100 = 25.8333 or 25.83%
Coefficient of Variation of Stock N = SD of N / Expected Return of N * 100
= 3.9% / 19% * 100 = 20.5263 or 20.53%
Investment in Stock M is riskier as it has higher Coefficient of Variation than N.
b) What is the expected return of the portfolio?
Expected return of the portfolio = Weight of M * Expected return of M + Weight of N * Expected return of N
Expected return of the portfolio = 0.55 * 12% + 0.45 * 19%
= 6.6% + 8.55% = 15.15%
c) With a correlation coefficient of +0.30, what is the standard deviation of the portfolio?
Standard deviation of the portfolio
= Square root of [(Weight of M)2 * (SD of M)2 + (Weight of N)2 * (SD of N)2 + ( 2 * Weight of M * Weight of N * r * SD of M * SD of N)]
= Square root of [(0.55)2 * (3.1)2 + (0.45)2 * (3.9)2 + ( 2 * 0.55 * 0.45 * 0.30 * 3.1 *3.9)]
= Square root of [2.907025 + 3.080025 + 1.795365]
=Square root of [7.782415] = 2.7896 or 2.79%
Standard deviation of the portfolio = 2.79%
d) What is the beta of the portfolio?
Beta of the portfolio = Weight of M * Beta of M + Weight of N * Beta of N
Beta of the portfolio = 0.55 * 1.40 + 0.45 * 0.85 = 0.77 + 0.3825 = 1.1525
e) What is the significance of the results in parts a through d?
Now we calculate the Coefficient of Variation of Portfolio as
SD of Portfolio / Expected Return of Portfolio * 100
= 2.79% / 15.15% * 100 = 18.415 or 18.42%
Now we conclude that this portfolio is less riskier than the above two stocks. Hence, this portfolio will provide us the diversification benefits.