4.2 THREE-FIRM CASE: PORTFOLIOS
In this topic, you will see how changing portfolio weights affects both the risk and return of a portfolio in the Three-Firm case. We recommend that you read this topic in conjunction with CAPM Tutor using the default data set.
Assume there are three firms in which you can invest. They have the individual risk and return characteristics shown in Table 4.1 (also see computations). The last line in the table gives the characteristics of a portfolio consisting of Firms 1 and 3 only, with weights 0.487 and 0.513, respectively.
Table 4.1
Three-Firm Case
Firm |
Expected Return |
Standard Deviation |
Firm1 |
0.229 |
0.961 |
Firm2 |
0.138 |
0.928 |
Firm3 |
0.052 |
0.727 |
Portfolio (1,3) |
0.138 |
0.259 |
You can see in the table that no firm gives you both a higher expected return and a lower standard deviation than any other firm. (You can see this on CAPM Tutor, using the default dataset, by clicking the button marked Indiv.)
The portfolio of Firms 1 and 3 with weights 0.487 and 0.513, however, has the same expected return as Firm 2, but with less portfolio risk. The portfolio risk from holding Firm 2 by itself is 0.928 and the portfolio risk from holding 0.487 of Firm 1, 0 of Firm 2, and 0.513 of Firm 3 is 0.259. That is, choosing this portfolio results in less risk than choosing Firm 2 by itself.
Using CAPM Tutor you can try out various portfolio combinations to examine how different portfolio weights influence the risk and return characteristics of the portfolio.
For example, using CAPM Tutor, contrast the following two portfolios. Portfolio A is the naively diversified portfolio (one-third in each Firm). Observe that this portfolio provides an expected return of 13.97% and a portfolio risk equal to 0.249. Contrast this with portfolio B with weights 0.416, 0.178, and 0.405, respectively, for shares in firms 1,2, and 3. This portfolio provides an expected return equal to 14.1% and has portfolio risk equal to 0.180. That is, portfolio B dominates portfolio A along the dimensions of both risk and return.
In the next topic you will read about characterizing the investment opportunity set.
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