1. Consider the following information about three stocks: State of Economy Probability of State of Economy Rate of Return If State Occurs Stock A Stock B Stock C Boom .25 .21 .36 .55 Normal .60 .17 .13 .09 Bust .15 .00 −.28 −.45 a. If your portfolio is invested 40 percent each in A and B and 20 percent in C, what is the portfolio expected return? The variance? The standard deviation? b. If the expected T-bill rate is 3.80 percent, what is the expected risk premium on the portfolio? c. If the expected inflation rate is 3.50 percent, what are the approximate and exact expected real returns on the portfolio? What are the approximate and exact expected real risk premiums on the portfolio?

Answer and Explanation:

The computation is shown below:

a. For expected return

As we know that

Expected return = Probability × Rate of return

The same formula applies for all of the given stock

For Boom it is

= 0.4(0.21) + 0.4(0.36) + 0.2(0.55)

= 0.33

For Normal it is

= 0.4(0.17) + 0.4(0.13) + 0.2(0.09)

= 0.13

For Bust

= 0.4(0.00) + 0.4(-0.28) + 0.2(-0.45)

= - 0.20

So, the expected rate of return is

= 0.25(0.33) + 0.60(0.13) + 0.15(-0.20)

= 0.1305

Now the variance is

= 0.25 × (0.33 - 0.1305)^2 + 0.60 × (0.13 - 0.1305)^2+ 0.15 × (-0.20 – 0.1305)^2

= 0.053

Now the standard deviation is

= [0.053]^1/2

= 0.23

b.  Risk premium is

= E(Rp) – Rf

= 0.1305 - 0.038

= 0.0925

c.  Expected real return is

= 0.1305 - 0.035

= 0.0955

The Expected real risk premium  is

= risk premium - inflation rate

= 0.0955 - 0.035

= 0.0605

We simply applied the above formulas

c.

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