Suppose that we have identified two important systemic risk factors: the growth

Question

Suppose that we have identified two important systemic risk factors: the growth rate of gross domestic product, labeled GDP, and the 30-year bond interest rate, labeled BR. Whole Hog Farms, Inc. has a beta of 1.1 on GDP and 0.9 on BR. Whole Hog has an expected stock return on 12%. GDP is expected to be 5.5% and BR 6%. If gross domestic product grows by 3% and 30-year bond rate turns out to be 9%, and no unexpected news specifically concerning Whole Hog occurs, within the Arbitrage Pricing Theory framework, what is your best guess for realized rate of return on Whole Hog stock?

Explanation / Answer

Percentage of increase in GDP = Change in rate / Base rate = 3/5.5 = 0.54

Percentage of increase in BR = Change in rate / Base rate = (9-6) / 6 = .50

As beta is 1.1 and 0.9 the percentage of increase in whole hog stock return would be :

( 0.54 * 1.1 ) + ( 0.50 * 0.9) / ( 1.1 + 0.9) = 0.522 ie 52.20 %

Now new expected return would be 12 % + 12(.522) = 18.26%

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