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In: Finance

Portfolio expected return and risk A collection of financial assets and securities is referred to as...

Portfolio expected return and risk

A collection of financial assets and securities is referred to as a portfolio. Most individuals and institutions invest in a portfolio, making portfolio risk analysis an integral part of finance. Just like standalone assets and securities, portfolios are also exposed to risk. Portfolio risk refers to the possibility that an investment portfolio will not generate the expected rate of return.

Analyzing portfolio risk and return involves the understanding of expected returns from a portfolio.

Consider the following case:

Bob 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:

Stock

Percentage of Portfolio

Expected Return

Standard Deviation
Artemis Inc. 20% 6.00% 23.00%
Babish & Co. 30% 14.00% 27.00%
Cornell Industries 35% 13.00% 30.00%
Danforth Motors 15% 5.00% 32.00%

The expected return on Bob’s stock portfolio is   .

Suppose each stock in the preceding portfolio has a correlation coefficient of 0.4 (ρ = 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 28%, the portfolio’s standard deviation (σpσp) most likely is   28%.

Solutions

Expert Solution

Solution: (a)

RP = 0.2∗0.06+0.3∗0.14+0.35∗0.13+0.15∗0.05

RP = 10.7%

Solution (b)

Let

  • w1 = weight of stock 1
  • w2 = weight of stock 2
  • sigma1 = standard deviation of stock 1
  • sigma2 = standard deviation of stock 2
  • sigma = standard deviation of portfolio
  • r1,2 = correlation coefficient between the two stocks.

The standard deviation of a portfolio of 2 stocks is:

As the formula indicates, the portfolio standard deviation will be the weighted average of the standard deviations of its stocks if and only if the correlation coefficient between the two stocks is 1. If its is less than 1, the portfolio standard deviation will be smaller due to the effect of diversification. So, if you keep adding 40 more stocks with correlations coefficients less than 1, the portfolio standard deviation will keep going down and will approach the market standard deviation of 20%.

jeff jeffy answered 1 year ago
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