Question

You have the following assets available to you:

Asset	Expected Return
Riskless debt	3.8%
Portfolio of small cap stocks	9.0%
Portfolio of large cap stocks	7.3%
Portfolio of growth stocks	13.3%
Portfolio of value stocks	8.8%
S&P500 index fund	9.9%

What is the cost of equity for a firm with a market beta of 3.4, a SMB beta of 1.9, and a HML beta of 2.4? You may assume this firm has an alpha of zero. Please give your answers to four decimal places - an answer of 9.54% would be represented as 0.0954.

Answer 1

Assuming Alpha as zero, the cost of Equity is calculated using the following equation of Fama-French model three factor model

Cost of Equity

Where, r_f is risk free rate

is Beta or factor coefficients

r_m is market return

SMB is size premium (Small minus Big)

HML is value premium (High minus low)

Cost of Equity = 0.038 + 3.4*(0.099-0.038) + 1.9*(0.09-0.073) + 2.4*(0.088-0.133)

= 0.038 + 0.2074 + 0.0323 - 0.108

= 0.1697