The Financial Advisor’s Investment Case “Inferior Investment Decisions” This case essentially repeats the material on the risk and return, and helps determine is a particular combination of risk and return is inefficient. The expected returns and betas are 1. Position Expected Return Beta All in T-Bill 7% 0.0 All in A 9% 0.6 All in B 11% 1.3 All in C 14% 1.5 25% in each alternative: Expected return= (.25)(.07)+(.25)(.11)+(.25)(.14)+(.25)(.09)=10.25% Beta= (.25)(.00)+(.25)(.6)+(.25)(1.3)+(.25)(1.5)= 0.85% 50% in A and 50% in C: Expected return= (.5)(.09)+(.5)(.14)=11.5% Beta= (.5)(.6)+(.5)(1.5)= 1.05% 33 1/3% in each stock: Expected return= (.33)(.09)+(.33)(.11)+(.33)(.14)=11.22% Beta= (.33)(.6)+(.33)(1.3)+(.33)(1.5)= 1.12% Summary of the portfolios returns and their betas: Return Beta All in T-Bill 7% 0.0 All in A 9% 0.6 All in B 11% 1.3 All in C 14% 1.5 25% in each 10.25% .85 50% in A and B 11.5% 1.05 1/3 in each 11.22% 1.12 2. All that has to be shown is that a portfolio offers an inferior return for a given amount of risk (or for a given return requires more risk) to determine an inefficient portfolio. For example, all in B produces a return of 11% with a beta of 1.3 while 50% in A and 50% in C produces a higher return (11% and lower risk (beta of 1.05). A portfolio invested entirely in B is inefficient. 3. Combination of half the funds in A and half the funds in C generates a return of 11.5% and has a beta of 1.05%. What combination of the T-Bill and stock C offers a beta of 1.05% Answer: (X%)(0) + (Y%)(1.5) = 1.05 (Y%)(1.5)= 1.05 Y% = 1.05/1.5 = 70% A combination of 30% in the T-Bill and 70% in stock C generates a beta of 1.05%. That combination of the stock and T-Bill generates a return of (.3)(7%) + (.7)(14%) = 11.9%. 11.9% exceeds 11.5%, so that portfolio is superior to 50% invested in A and C. (30%) in the T-Bill and 70% in stock A produces a point that lies above the point representing 50% in Stock A and 50% in stock C, so that latter combination is inefficient. 4. To illustrate a return of 12% and a beta of 1.4 is inefficient, all that is necessary is to find a portfolio with either a higher return with a beta of 1.4 or a lower beta with a higher return. For example: 89% in stock C and 11% in stock A generates a beta of (.89)(1.5) + (.11)(.06) = 1.4 and a return of (.89)(14%) + (.11)(9%) = 13.67% which is superior and indicates the client’s suggestion is an inferior portfolio. In this project you are asked to find the betas for the stocks. The assignment also asks you to compute the average beta for the portfolio. As you can see proper weighing with a beta less than 1.0 should be less volatile than the market as a whole and should earn a lower return than the market. Lower returns are not necessarily inferior since it may be the result of less risk and not necessarily the result of inferior portfolio management.