Page 312 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Unit 12: Models

X = ( 30 × 150)/( 18,500) = 0.24 Notes
B
X = ( 20 × 75)/( 18,500) = 0.08
C
X = ( 25 × 100)/( 18,500) = 0.14
D
X = ( 40 × 125)/( 18,500) = 0.27
E
The expected returns on the portfolio securities are:
~ R = ( 65 – 50)/ 50 + 30.0%
A
~ R = ( 40 – 30)/ 30 + 33.3%
B
~ R = ( 25 – 20)/ 20 + 25.0%
A
~ R = ( 32 – 25)/ 25 + 28.0%
A
~ R = ( 47 – 40)/ 40 + 17.5%
A
The expected return on a portfolio is given by:
N

R = (X × R )
p i x
i 1
In the case of RKV’s portfolios

R =(0.27 × 30.0%) + (0.24 × 33.3%) + (0.08 × 25.0%) + (1.4 × 28.0%) + (0.27 × 17.5%)
p
= (0.81%) + (7.992%) + (2.0%) + (3.92%) + (4.725%)
= (19.447%)

12.3 Two Factor Model

The two factor model has been derived from Fama and French’s three factor model, it is important
that we understand in principle the Fama-French Model. It’s a model that compares a portfolio
to three distinctive types of risk found in the equity market to assist in categorizing returns.
Prior to the three-factor model, the Capital Asset Pricing Model (CAPM) was used as a “single
factor” way to explain portfolio returns.

However, several shortcomings of the CAPM model exist. Incorrectly predicting results
compared to realize returns and the affect of other risk factors have put this model under
criticism. The assumption of a single risk factor limits the usefulness of this model.
In June 1992, Eugene F. Fama and Kenneth R. French published a paper that found that on average,
a portfolio’s beta only explains about 70% of its actual returns. For example, if a portfolio was up
10%, about 70% of the return can be explained by the advance of all stocks and the other 30% is
due to other factors not related to beta.

1. “Beta,” the measure of market exposure of a given stock or portfolio, which was previously
thought to be the be-all/end-all measurement of stock risk/return, is of only limited use.
Fama/French showed that this parameter did not predict the returns of all equity portfolios,
although it is still useful in predicting the return of stock/bond and stock/cash mixes.
2. The return of any stock portfolio can be explained almost entirely by two factors: Market
cap (“size”) and book/market ratio (“value”). The smaller and the median market cap of
your portfolio, the higher its expected return.

To represent the market cap (“size”) and book/market ratio (“value”) returns, Fama and French
modified the original CAPM with two additional risk factors: size risk and value risk.

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