Question

# The two risky assets you can invest in are Exxon and BP. Exxon has a mean...

The two risky assets you can invest in are Exxon and BP. Exxon has a mean return of 8% and a standard deviation of 10%. BP has mean return of 10 percent and standard deviation of 15 percent. The correlation between the two is 0.25. The tangency portfolio has weight of 55% in Exxon.

The risk free asset has return of 3.0 percent. What is the expected return and standard deviation of the tangency portfolio?

You desire an expected return of 25%. What will be the standard deviation of your portfolio? What fraction of your portfolio will be invested in Exxon?

Tangency Portfolio is the optimally risky portfolio as it is the point of tangency of the CAL to the efficient frontier of risky assets.

Exxon Weight = 0.55 and BP Weight = 0.45

Let the expected return and standard deviation of the tangency portfolio be Rt and St respectively.

Rt = 0.55 x 8 + 0.45 x 10 = 8.9 %

Correlation = 0.25

St = [{0.1 x 0.55}^(2) + {0.15 x 0.45}^(2) + 2 x 0.55 x 0.45 x 0.1 x 0.15 x 0.25]^(1/2) = 9.715 %

Risk-Free Rate = Rf = 3 %

Expected Return = E(r) = 25 %

Let the fraction of investment in risky asset be y

Therefore, E(r) = Rf + y x (Rt - Rf) = 3 + y x (8.9 - 3)

25 = 3 + 5.9y

y = (22/5.9) = 3.73

A value greater than 1 implies that this is a leverage portfolio, one where portfolio investments have been made by borrowing.

Standard deviation of Portfolio = St x y = 9.715 x 3.73 = 36.237 %

Fraction Invested in Exxon = (0.55 x 3.73) / 4.73 = .4337

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