Question

Julius Berger is the junior portfolio manager of the global equities portfolio at BSC Asset Management based in the City. Akinbowale, a recently hired equity analyst, has been assigned to Julius to assist him with the portfolio.

Julius provided the betas estimated by using the Capital Asset Pricing Model (CAPM) for MSFT (MSFT), Lloyds (LLoyd), and CHevron (CVF) are 1.28, 1.63, and 1.03, respectively. The risk-free rate of return is 2.42 percent and the equity risk premium is 7.15 percent. Julius also considers an equal-weighted portfolio from the three stocks.

A private friend of Julius asked him to educate him about alternative asset pricing models to the CAPM. Julius considers the Fama-French 3-factor model. Akinbowale collated the following information to evaluate the price of 106 and park by using the Fama-French model. Treasury bill rate is 2.42 percent.

Exhibit 1: TerraNova Data

	Factor Sensitivity	Risk Premium (%)
Market factor	1.20	4.5
Size factor	-0.50	2.7
Value factor	-0.15	4.3

Required:

Calculate the individual required rates of return for the three stocks using the CAPM.

Calculate the required rate of return and beta of the portfolio consists of the stocks.

Compare the Fama-French 3-factor model to the CAPM and explain the differences.

Based on the data in Exhibit 1, calculate and compare the required return for 106 and park ltd      using the CAPM and the Fama–French model.

Describe the expected style characteristics of 106 and park based on its factor sensitivities.

Answer 1

CAPM gives the required rate of return from a stock as

Required rate of Return = Risk free rate + Beta of stock * market risk premium

So,

Required rate of Return of MSFT = 2.42% + 1.28*7.15% = 11.572%

Required rate of Return of Lloyd = 2.42% + 1.63*7.15% = 14.0745%

Required rate of Return of CVF = 2.42% + 1.03*7.15% = 9.7845%

Beta of the portfolio is the weighted average beta of individual stocks

So, Beta of equally weighted portfolio = 1/3*1.28 + 1/3*1.63+ 1/3*1.03 = 1.31333.

Required rate of Return of portfolio = 2.42% + 1.31333*7.15% = 11.810333%

As per Fama French Model

Required rate of Return of portfolio = Risk free rate +market factor sensitivity * market Risk premium + size factor sensitivity * size risk premium + value factor sensitivity * value risk premium

= 2.42%+ 1.2*4.5%-0.5*2.7%-0.15*4.3% = 5.825%

  

So, the required return as per Fama French Model is only 5.825% as compared to 11.81% as per CAPM model

The required rate is very less as the size factor and value factors have negative sensitivity to the required rate.

The negative factor sensitivities mean that portfolio manager has included big size stocks and growth stocks in the portfolio and hence the overall required rate of return from the portfolio is less. The required rate is thus lower as compared to CAPM