Page 314 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Unit 12: Models

Factors are compared using the following formula: Notes
R = a + (m) R + (1)F + (2)F + ...... + (N)F + e
i i i m i 1 i 2 i N i
Where,
R i is the returns of security i

R m is the market return

F(1,2,3…N) is each of the factors used
is the beta with respect to each factor including the market (m)

e is the error term
a is the intercept
Multi-factor models are used to construct portfolios with certain characteristics, such as risk, or
to track indexes. When constructing a multi-factor model, it is difficult to decide how many and
which factors to include. One example, the Fama and French model, has three factors: size of
firms, book-to-market values and excess return on the market. Also, models will be judged on
historical numbers, which might not accurately predict future values.
Multi-factor models can be divided into three categories: macroeconomic, fundamental and
statistical models. Macroeconomic models compare a security’s return to such factors as
employment, inflation and interest. Fundamental models analyze the relationship between a
security’s return and its underlying financials (such as earnings). Statistical models are used to
compare the returns of different securities based on the statistical performance of each security
in and of itself.

Task Analyse the utility of Multi Factor Model and discuss the advantages in
details.

12.5 Summary

The application of Markowitz’s model requires estimation of large number of co-variances.
And without having estimates of co-variances, one cannot compute the variance of portfolio
returns.

This makes the task of delineating efficient set extremely difficult.
However, William Sharpe’s single-index model’ simplifies the task to a great extent.
Even with a large population of assets from which to select portfolios, the numbers of
required estimates are amazingly less than what are required in Markowitz’s model.
But how accurate is the portfolio variance estimate as provided by the single-index model’s
simplified formula? While the Markowitz’s model makes no assumption regarding the
source of the co-variances, the single-index model does so.
Obviously, the accuracy of the latter model’s formula for portfolio variance is as good as
the accuracy of its underlying assumptions.
Some other portfolio selection models that seem to hold great promises to practical
applications are also looked at here.

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