Required Return, Opportunity Cost, and Portfolio Diversification
Summary
The document considers whether to accept a new investment by comparing its expected return with its required return, calculated from the risk free rate, market risk premium, and beta. It notes that this comparison can address whether the investment is attractive on a standalone basis, but may not answer whether it improves the investor’s overall portfolio.
The existing holding and proposed investment’s amounts and betas may matter when assessing opportunity cost and diversification. Beta alone does not describe the correlation between the two investments or all information needed to determine the portfolio’s risk and return. If the investments are perfectly positively correlated, the response says the choice can reduce to favoring the investment with the more attractive expected return relative to its required return. With other correlations, more information is needed to assess a combined allocation. The answer therefore treats the problem as either a qualitative portfolio question or a simpler standalone return comparison, depending on the original context.
Key ideas
- A required return can be estimated from the risk free rate, market risk premium, and an investment’s beta.
- Comparing expected return with required return assesses an investment on a standalone basis.
- Whether an investment improves a portfolio depends on its relationship to existing holdings.
- Beta does not provide enough information to determine the diversification benefit between two investments.
- Correlation and portfolio risk information may be needed to choose an allocation across investments.
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Full text
# Required Rate of Return vs Expected Return # Required Rate of Return vs Expected Return 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? ## Answer by Matt Wolf (score 0, accepted) https://quant.stackexchange.com/a/8205 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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