Portfolio Analysis Revisited
Equity-Style Investment
Factor Models
Asset Allocation
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Equity-Style Portfolio Construction
• In the 1970s, James Ferrel introduced an approach
to portfolio construction known as cluster
analysis.
• A cluster is a portfolio of stocks that are highly
correlated with each other, but uncorrelated with
other clusters or groups.
• Form clusters for:
–
–
–
–
Cyclical Stocks
Stable Stocks
Growth Stocks
Energy Stocks
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• Today cluster analysis is referred to as
equity-style management.
• Clusters are typically broken into two major
categories:
– Value Stocks
– Growth Stocks
• Sub-categories are often formed within
these two groups: Small Cap, Large Cap,
low P/e, high P/e, etc.
• Managers are described by their style: value
style, growth style, etc.
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Construction of Value-Stock and
Growth-Stock Portfolios
• The most common way to classify value
and growth stocks is to use stock price to
book value ratio – P/B.
– Growth: high P/B
– Value: Low P/B
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Methodology
1. Select a large sample of stocks (1000).
2. Determine the sample’s total market
value.
3. Compute each stock’s P/B ratio.
4. Rank stock from low to high by P/B.
5. Define value stocks as all those stocks that
encompass the first half of the market
value (or some defined percentage).
6. Define growth stocks as all those stocks
that encompass the second half of the
market value (or some percentage).
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Methodology
• Alternative to P/B method is to use a
mutiple-index measure that provides a
score.
• The index score is constructed so that the
higher the score the greater the growth
stock. For Example:
D
Si  w1   w 2 ROE i  w 3 Variationin Earningsi
 P i
• This is the approach used by Salomon-S-B
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Sub-styles
•
•
Within a style, portfolio managers create other
groupings known as sub-styles.
Examples:
1. Within either value or growth style, one could have
sub-styles based on size: Small-Size Value, LargeSize Value, Small-Size Growth, Large-Size Growth.
2. Within either value or growth style, one could have
sub-styles based on P/e, BV/MV, etc.
3. Within growth, one could have sub-styles based on
high growth, low growth, above-average growth,
volatility, etc.
4. Use factor models.
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Empirical Research
•
•
•
•
Study by Leinweber, Arnolt, and Luck looked at the
performance of value and growth style investments.
They defined value and growth by P/B.
They looked monthly returns from 1975 to 1995.
They found:
1. In the U.S. from 1975 to 1995 that $1 invested in a valuegrouped portfolio would have grown to $23, while $1
invested in a growth-grouped portfolio would have grown
to $14.
2. In 45% of the months in the sample, growth stocks
outperformed value; with perfect foresight, one switching
from growth to value would have realized $45.
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Other Styles
• S&P Mid Caps
• S&P Small Caps
• PEG Portfolios
• Reference: Handbook of Equity Style
Management, Editors: Coggin, Fabozzi, and
Arnoldt.
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Factor Models
•
Portfolios constructed from multifactor/APT
analysis are called factor models. Two general
types: statistical, macro and fundamental.
–
–
–
Statistical Factor Models: Based on explaining
security and portfolio returns based on artificial
factors created from factor analysis.
Macroeconomic Factor Models: Developing
portfolios based on macroeconomic factors. These
models are rooted in the works of Chen, Roll, and
Ross and Burnmeister and McElroy. Most are
proprietary models. One published model is
Salomon-Smith-Barney’s Risk Attributes Model
(RAM).
Fundamental Models: Use a cross-sectional approach.
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RAM Model
•
Step 1
Stock returns are explain by a set of
macroeconomc variables.
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•
Variable
•
RAM
1.
Investors’ Confidence
1.
RCorp – Rgovt
2.
Interest Rates
2.
(LT Rate – ST Rate)
3.
Inflation Shock
3.
4.
4.
5.
Aggregate Business
Fluctuations
Foreign Variables
Actual minus expected
inflation rate
 (Industrial Production)
5.
(Exchange Rate)
6.
Market Factors
6.
Residual Market Beta
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RAM
• Step 2: Run a time-series regression of the
stock returns against the six macroeconomic
variables. Salomon-Smith-Barney regresses
the returns of 3500 stocks against the above
macroeconomic factors.
ri  ai  bi1F1  bi2F2      bi6F6  i
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RAM
• Step 3: Standardize the coefficients. For each coefficient,
calculate the average coefficient and average standard
deviation.
• For example, for b1:
3500

 3500


b1  i 1
and  b1  

3500



bi1
1/ 2

(bi1  b1 ) 2 


i 1

3500




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• Next, for stock i measure the adjusted
standardized coefficient as:
bi1  b1
b̂i1 
b1
• Interpretation:
– If adjusted b = 0  Stock’s sensitivity to factor 1 is
no different than the average.
– If adjusted b > 0  Above average responsiveness
to factor 1.
– If adjusted b < 0  Below average responsiveness
to factor 1.
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RAM
• Step 4: For each stock determine its score,
Si. The score is obtained by multiplying the
stock’s adjusted coefficients by an estimate
of the macroeconomic factors, then
summing the products.
Si  a i  b̂i1(E(F1))  b̂i 2 (E(F2 ))      b̂i6 (E(F6 ))
• Step 5: Construct a portfolio with the
highest score.
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RAM
•
•
Alternative: Monte Carlo Simulation
Construct different portfolios based on the
portfolio’s sensitivity to different economic
scenarios, then select the best.
Steps:
1. Identify different economic scenarios and their
probabilities. For example, a scenario in which there
is an exogenous supply side increase (low inflation,
high gdp growth, and low rates), one in which there is
a negative exogenous demand change (low gdp, low
inflation, and high interest rates), or one in which
there is both.
– Use econometric forecasting, economic indicators, etc., and
define the scenarios in terms of factors value.
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RAM
2. Construct different portfolios with different
sensitivities.
3. For each economic scenario calculate the
portfolio’s score and probability.
4. For each portfolio, calculate its expected score
and standard deviation based on all scenarios.
5. Rank each portfolio, S/.
6. Select the best.
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Scenario
Factor
Prob.
1. High energy
prices, slow
down in tech:
Low gdp, high
inflation, etc.
F1 = .02
F2 = .01
F3 = 5%
F4 = 2%
F5 = -1%
F6 = .25
.02
.01
.02
.05
.10
.005
F1 = .02
F2 = .01
Etc.
.01
.005
2. High gdp,
low rates, etc
ETC
Portfolio 1 Portfolio 2 Portfolio 3
Score
Score
Score
10
15
20
12
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10
E(S) = 10
(S) = 5
=2
E(S) = 15
(S) = 8
 = 1.875
E(S) = 12
(S) = 10
 = 1.2
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Fundamental Factor Models
Example: BARRA Model (Barra Consulting Firm)
Features:
– Regress 1300 stocks against 13 factors: P/e, P/B, size,
ROE, etc.
– Construct portfolios with different sensitivities.
– Define portfolios with different styles: Value, growth,
Value-low cap, etc.
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Asset Allocation Strategies
• Asset allocation refers to determining the
portfolio mix among different asset classes:
– Stocks, Bonds, Money Market
– Value, Growth
• There are two general assets allocation
strategies:
– Passive
– Active
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Passive Asset Allocation
• Set long-run objectives in terms of return
and risk, then determine the equity, bond,
and money mix to achieve that.
• Strategies of pensions, LICs, etc.
• Use a Markowitz strategy to determine
equity, bond, and money mix.
• Determine mix of value and growth using a
P/B approach.
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Active Asset Allocation
Examples: Tactical Asset Allocation (TAA) and
Dynamic Asset Allocation (DAA).
• TAA
– TAA strategy is aimed at enhancing returns by
changing the asset mix in response to changing market
conditions or return patterns. Uses indicators.
• Value/Growth Stock Changing: Change or tilt portfolio from
value to growth or growth to value when conditions dictate.
Key is to forecast this.
• Use factor model to change a portfolio based on a security’s
sensitivity to factors: inflation, interest rates, gdp, etc.
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• TAA
Valuation approach to determine stock, bond, and
money mix.
• Use Indicators as signals to change allocations.
• Often the indicators are risk premiums:
– Stock/Bill RP = RS – RTB
– Bond/Bill RP = RB – RTB
– Stock/Bond RP = RS – RB
• There is historical evidence to support this approach.
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TAA
• Study by DuBois
• Time Period: 1951-1989
• Looked at historical RP of Stock/Bills and the
average stock returns (S&P 500) over T-Bill
returns for 1, 3, and 12 Months.
•
Stock / Bill
No. of Months
RP Range
ObservedRP
1 Mo.
3 Mo.
12 Mo.
10
2.5%
6.8%
26.1%
8%  10%
64
.7%
1.6%
4.8%
2%  4%
96
 1%
 1.4%
2.8%
 2%
25
 1.8%
 10%
 1.7%
 6.9%
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Dynamic Asset Allocation:
• DAA is an active strategy of changing a bond and
equity mix over time and in response to stock
market changes in order to achieve a certain return
distribution at the end of a period.
• For example, at the end of five years the objetive
may be to have a return on the portfolio that
matches the market’s return if the market has
increased, but has a certain minimum return is the
market has declined.
• DAA is a dynamic portfolio insurance strategy.
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