Question

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

1. Which investment is riskier by itself and in a portfolio sense?

2. What is the expected return of the portfolio?

3. With a correlation coefficient of +0.30, what is the standard deviation of the portfolio?

4. What is the beta of the portfolio?

5. What is the significance of the results in parts a through d?

Answer 1

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.