Analyzing portfolio risk and return involve the understanding of expected returns from a portfolio. consider the following case: andre is an amateur investor who holds a small portfolio consisting of only four stocks. the stock holdings in his portfolio are shown in the following table: artemis (20% of portfolio, 6.00% expected return, 34.00% standard deviation) babish & co. (30% of portfolio, 14.00% expected return, 38.00% standard deviation) cornell industries (35% of portfolio, 12.00% expected return, 41.00 standard deviation) danforth motors (15% of portfolio, 3.00% expected return, 43.00% standard deviation) what is the expected return of andre's stock portfolio? a. 15.08, b. 13.57, c. 10.05 d. 7.54 suppose each stock in the preceding portfolio has a correlation coefficient of 0.4 (p=0.4) with each of the other stocks. if the weighted average of the risk (standard deviation) of the individual securities in the partially diversified portfolio of four stocks is 39%, the portfolio's standard deviation most likely is 39%.
a. equal to.
b. more than.
c. less than.

In order to find expected portfolio return we multiply the weight of each security by its expected return and then add all the values.

Artemis = 0.2*0.06=0.012= 1.2%

Babish= 0.3*0.14=0.042= 4.2%

Cornell = 0.35*0.12= 0.042= 4.2%

Danforth Motors = 0.15*0.03=0.0045= 0.45%

1.2+4.2 + 4.2 +0.45=10.05%

Then in order to find the portfolio variance  the formula is

Variance = (w(1)^2 * SD(1)^2) + (w(2)^2 * SD(2)^2) + (2 * (w(1)*(1)*w(2)*o(2)*q(1,2)))

and we can under root this to find the standard deviation

Variance = (w(1)^2 * SD(1)^2) + (w(2)^2 * SD(2)^2) + (2 * (w(1)*SD(1)*w(2)*SD(2)*CR(1,2)))

W (1): Weight of one stock in the portfolio squared.

SD (1): The standard deviation of one asset in the portfolio squared.

W (2): Weight of second stock in the portfolio squared.

O (2): The standard deviation of the second asset in the portfolio squared.

CR(1,2): The correlation between the two assets in the portfolio has been denoted as q (1,2).

When we use this formula whenever the co relation is less than 1 the portfolio standard deviation is less than the weighted average standard deviation of all the individual stocks.

So in this case as the co relation is less than 1 portfolios standard deviation is less than 39%

Explanation:

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