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I faced a problem that gives the following information:

  • market risk premium, and risk free rate is given
  • You currently have a portfolio of amount of x, beta b1.
  • Now there is a new investment opportunity of amount y, beta b2, expected return r2.

The question is: Under what circumstance should you take the new investment opportunity?

I think the answer is quite simple, just calculate the required rate of return for investment y, and compare that to r2. If it is lower than r2 then take it, else don't.

I am slightly confused because the problem also gave the information on the current investment, and value of the new investment. Is this redundant information?

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  • $\begingroup$ Is it at the expense of the current investment? $\endgroup$
    – Henry
    Jun 10, 2013 at 18:50
  • $\begingroup$ It didn't say. But you can assume it is. $\endgroup$
    – Xiaowen Li
    Jun 10, 2013 at 19:09
  • $\begingroup$ With CFA exams just having taken place, is this a CFA question? $\endgroup$
    – Matt Wolf
    Jun 11, 2013 at 1:25
  • $\begingroup$ No. CFA exams questions are usually worded better than this. $\endgroup$
    – Xiaowen Li
    Jun 11, 2013 at 16:32
  • $\begingroup$ @XiaowenLi, well you can chose your own wording on this site, can't blame my neighbor for failing the exam because I copied the wrong answer off his answer sheet ;-) $\endgroup$
    – Matt Wolf
    Jun 11, 2013 at 21:24

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This question is maybe not just about evaluating whether investment y is profitable in terms of expected return vs. required return but you also may need to consider the opportunity cost, meaning, whether it makes more sense to invest in investment x or y plus whether it may be most beneficial to diversify into investments in x and y.

Without knowing the context in which the question was posed I would say that the answer is supposed to be qualitative in nature and that the correct answer should be that there is missing information in order to fully determine whether a diversification benefit will cause the best investment to be a portfolio of x and y. For example, details on the individuals' risk is only given as betas but the betas are computed through the covariance and individual investment's standard deviation, both of which are missing.

If the two investments are perfectly positively correlated then you would obviously want to invest everything in the investment with the most attractive expected return relative to the required return, but if the investments correlate otherwise then I would say that to give a precise answer you would need more information than what was given.

In summary, either the question looks for a purely qualitative answer and checks whether you understand the bigger picture of investing in different assets or you are simply asked to calculate the expected return of investment x through b1, r-f-rate, and market risk premium and compare with investment y. I would err on the former.

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