Question

You are interest in investing in two firms in Wisconsin, Harley Davidson (HOG) and Alliant Energy (LNT).

LNT has an expected return of 10.4% and a volatility of 16.0%.

HOG has an expected return of 12.0% and a volatility of 30.0%.

The correlation between the two is 0.08.

Risk-free rate is 3.8.

Suppose you want to create the "optimal risky portfolio" (see page 162 in the book), what is weight you need to put into LNT? You can review the video on the Optimal Risky Portfolio.

Answer 1

Weight in LNT = (Expected return of LNT - Risk free rate) * (Standard Deviation of HOG)² - (Expected return of HOG - Risk free rate) * (Standard Deviation of HOG * Standard Deviation of LNT * Correlation between HOG & LNT) / ((Expected return of LNT - Risk free rate) * (Standard Deviation of HOG)² + (Expected return of HOG- Risk free rate) * (Standard Deviation of LNT)² - ((Expected return of LNT - Risk free rate + Expected return of LNT - Risk free rate) * Standard Deviation of HOG * Standard Deviation of LNT * Correlation between HOG & LNT))

Weight in LNT = (10.4% - 3.8%) * (30%)² - (12% - 3.8%) * (30% * 16% * 0.008) / ((10.4% - 3.8%) * (30%)² + (12% - 3.8%) * (16%)² - (10.4% - 3.8% + 12% - 3.8%) * (30% * 16% * 0.008)

Weight in LNT = 75.29%