# Lecture Five

```Asset Management
Lecture 5
1st case study
 The question set is available online
 The case is due on Feb 27.

Outline for today
Tracking portfolio
 Beta

 estimation

CAPM vs. single-factor index model
 Structural multifactor model

Tracking Portfolio



A Tracking Portfolio (T) is designed to match the
systematic component of a portfolio (P)’s return, and
has as little nonsystematic risk as possible.
This procedure is called Beta Capture.
Example:



R(P) = 0.04 + 1.4R(S&amp;P500) + e(P)
R(T) = 1.4R(S&amp;P500)
A long position in P + a short position in T





R(C) = R(P) – R(T)
= 0.04 + 1.4R(S&amp;P500) + e(P) -1.4R(S&amp;P500)
= 0.04 + e(P)
Long-Short Strategy to achieve a Market Neutral position
Alpha Transport
Beta



Beta coefficients seem to move to 1 over time
Example by Merrill Lynch


Adjusted beta=2/3 sample beta + 1/3 (1)
Prediction

Simple approach



Current beta = a + b (Past beta)
Forecast beta= a + b (current beta)
An expanded version


Current beta = a + b1 (Past beta) + b2 (Size) + b3 (debt
ratio)
Variance of earnings, growth in earnings, dividend yield
etc.
CAPM vs.
the Single-Factor Index Model

For the index model
cov( Ri , RM )  cov( ai  i RM  ei , RM )
cov( Ri , RM )   i cov( RM , RM )  cov( ei , RM )   i M2
i 

 M2
For the CAPM model
i 

cov( Ri , RM )
cov( ri , rM )
 M2
What is different?
CAPM vs.
the Single-Factor Index Model
CAPM
Single-Factor
Index Model
Returns
Expected
Realized
Equilibrium
Yes
No
Residual returns Not
uncorrelated
Expression

E (ri )  rf   i E (rM )  rf
Uncorrelated
 Ri  ai  i RM  ei
The CAPM and Reality

Is the condition of zero alphas for all stocks
as implied by the CAPM met
 Not perfect but one of the best available
Figure 9.4 Estimates of Individual
Mutual Fund Alphas, 1972-1991
The CAPM and Reality



Is the condition of zero alphas for all stocks
as implied by the CAPM met
 Not perfect but one of the best available
Is the CAPM testable
 Proxies must be used for the market
portfolio
CAPM is still considered the best available
description of security pricing and is widely
accepted
Structural Multifactor Models
Return structure:
ri (t )   X i ,k  bk (t )  ei (t )
k
ri (t )
X i , k (t )
Excess return of stock i from time t to t+1
time t.
For industry: 0/1
bk (t )
For other factors: standardized with mean=0 and SD=1
ei (t )
Stock i’s idiosyncratic return from time t to t+1
Structural Multifactor Models
Risk structure:
Vi , j 
k
X
k 1, k 2 1
i ,k1
 Fk1,k 2  X j ,k 2   i , j
Vi , j
Covariance of stock i with stock j
X i ,k 1
estimated at time t.
Fk 1,k 2
 i, j
Covariance of factor k1 with factor k2
idiosyncratic covariance of stock i with stock j
Structural Multifactor Models

The choice of factors


A priori factors
Three categories

Response to external influences (macro factors)





inflation
oil price
Exchange rates
GDP
Problems:
Estimation error (error in variable)
Nonstationary response coefficients
Poor data quality



Structural Multifactor Models

The choice of factors


A priori factors
Three categories


Response to external influences (macro factors)
Cross-sectional comparisons of asset attributes


Compare attributes of the stocks
Fundamental
Ratios (dividend yield etc)
analysts forecasts
Market
Volatility, return, share turnover, etc.
Problem:
Error in variable
Nonstationary coefficient







Structural Multifactor Models

The choice of factors


A priori factors
Three categories



Response to external influences (macro factors)
Cross-sectional comparisons of asset attributes
Internal or statistical factors

Factors produced by statistical methods:
Principal component analysis
Maximum likelihood analysis
Expectations maximization analysis
Problems:
Very difficult to interpret
Spurious correlations
Cannot capture changes over time







Structural Multifactor Models

The choice of factors


A priori factors
Three categories




Response to external influences (macro factors)
Cross-sectional comparisons of asset attributes
Internal or statistical factors
Criteria:


Incisive: distinguish returns
Intuitive: interpretable and recognizable


Recognizable investment themes: industry, size, value,
growth etc.
Interesting: help to explain alpha or beta or volatility
Structural Multifactor Models

Typical factors


Industry factors : 0/1 factors
Risk indices








Volatility
Momentum
Size
Liquidity
Growth
Value
Earnings volatility
Financial leverage
Example: The Relationship Between
Illiquidity and Average Returns
Another Example:
Fama-French Three-Factor Model

The factors chosen are variables that on
past evidence seem to predict average
returns well and may capture the risk