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Assume that the rf = 0.06, and E(rm) = 0.14.  The expected required return for the stock is

E(rs) = 0.06 + (0.14 - 0.06)βs = 0.06 + (0.08)(0.875) = 0.13.  

Therefore, 13% is the required rate of return on both the stock and the required rate of return on the portfolio of real assets.

However, given the above asset betas, the required rates of return for each of the asset categories are:

E(rA1) = 0.06 + (0.08)(0.50) = 0.10,

E(rA2) = 0.06 + (0.08)(0.75) = 0.12,

E(rA3) = 0.06 + (0.08)(1.00) = 0.14, and

E(rA4) = 0.06 + (0.08)(1.25) = 0.16.

What's the portfolio expected return on these four real asset categories?

E(rp) = (0.25)(0.10) + (0.25)(0.12) + (0.25)(0.14) + (0.25)(0.16) = 0.13.

Notice that the E(r) of the portfolio of real assets equals the E(r) of the stock.  This observation should come as no surprise.  Why?

What if the firm's managers used the overall E(r), or 13%, to evaluate expansion of the four asset categories, i.e., more assets of the same four types?

Let's answer this question in the context of the SML.

E(r)

0.13=E(rS)

   rf

beta

βA1βA2βA3βA4

s = 0.875

8

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