Conditional Weighted Value + Growth Portfolio
(a.k.a MCP)
Midas Asset Management
Under the instruction of Prof. Campbell Harvey
Feb 2005
Assignment 1 for GAA
1
Goal

2
Optimize weights between value and growth
trading styles periodically (monthly) on basis
of conditional information available at the end
of last period, so that the total returns and/or
risk adjusted returns of our dynamic trading
rule beat those of the benchmark portfolios
and/or other selected benchmarks.
 Part
3
1: Methodology
Security Universe

We select the top 5,000 U.S. stocks in market
capitalization as the universe.
S&P 500: universe size too small
Russell 2000: only small- to mid cap.

4
We select 01/1983 to 08/1996 (163 months) as in
sample, and 09/1996 to 11/2004 (99 months) as
out of sample.
Value and Growth Portfolio (a)
Value portfolio sorting variable
Book(t-1)/Price(t-1)

Growth portfolio sorting variable
Earnings growth per price dollar

[E(t-1)-E(t-13)]/[│E(t-13) │*P(t-1)]
5
Value and Growth Portfolio (b)
• For each period, long F(1) stocks and short
F(10) stocks in our universe.
• Within the two groups (N,N), equally value
weighted.
• Portfolio return for each period:
Rv or Rg=1/N*[Ra-Rz]
Ra=sum of return of top F(1)
Rz=sum of return of bottom F(10)
6
Risk Adjusted Returns
Selected risk factor model: CAPM
 Risk adjusted return for Ra and Rz, for
Ra’(t)=Ra(t)-Rf(t)-β(a)*[Rm(t)-Rf(t)]
Rz’(t)=Rz(t)-Rf(t)-β(z)*[Rm(t)-Rf(t)]

Here a, z represent a stock.
So we have risk adjusted return for each of the
constructed portfolio (value portfolio and
growth portfolio) and each period.
7
Conditional Weighted Trading Rule (1)



8
For each period, assign w(v,t) to the value
portfolio and w(g,t) to the growth portfolio.
w(v,t)+w(g,t)=1
Total trading rule return (TTRR)
TTRR(t)=w(v,t)*Rv(t)+w(g,t)*Rg(t)
Conditional Weighted Trading Rule (2)

Alternatively, we use two sets of weights, one for 1 (value will out-perform growth), one for
0. And then we use in-the-sample R(v,t) and R(g,t) data, and optimizer to maximize positive
excess return (over benchmark trading rule) and minimize negative excess return.
Suppose two sets of weights are
{w(v,1),w(g,1)}, w(v,1)>=w(g,1), w(v,1)+w(g,1)=1
{w(v,0),w(g,0)}, w(v,0)<=w(g,0), w(v,0)+w(g,0)=1

Then,
if F(t,ω(t))=1,
TTRR(t)=w(v,1)*R(v,t)+w(g,1)*R(g,t)
if F(t,ω(t))=0,
TTRR(t)=w(v,0)*R(v,t)+w(g,0)*R(g,t)


9
F(t,ω(t)) stands for the logistic predictive regression model. ω(t) stands for information
set available at time t (at the end of t-1)
Objective Function to Solve for
Weights
 Objective
function for Optimizer
(solve for optimal conditional
weights)
Maximize Midas Conditional Portfolio (MCP) holding
period return over the whole in-the-sample period.
10
Trading costs
Use two thresholds to minimize
between-portfolio turnover
 Need to model within-portfolio turnover

11
Logistic Predictive Regression Model



12
F(t,ω(t)) stands for the logistic predictive
regression model. ω(t) stands for
information set available at time t (at the end
of t-1, lagged predictors).
F(t,ω(t)) takes on a probability between 0
and 1 given the predictors of period t-1.
F(t,ω(t)) conditions MCP.
Map it out: the big picture of the steps
Total Trading Rule Return = if(C4=1,w(v,1)*G4+w(g,1)*H4, w(v,0)*G4+w(g,0)*H4)
Regression
Step: F(t,ω(t))
Periods
Dec-04
Out of
sample
test
Sorting and portfolio construction
F(t,ω(t)): 0/1
Forecast 0/1
Step: Rb(v/g,t)
Value
Growth
Rb(v,t)
Rb(g,t)
Predictor 1 (t-1) Predictor n (t-1)
Challenge:
Sorting variables
Challenge: predictors
Out-of Sample
Test F(t)
Trading/Benchmarking
Step : TTRR(t)
Provide conditional info
each row is sorted
long short return
for that period for
value or growth.
TTRR(t)
Challenge:
Weights
Transaction costs
Dec-94
In the
sample
data
Generate 0/1
Starting
Point
Optimizer to
find out
w(v,1), w(g,1)
w(v,0), w(g,0)
Feedback: change sorting variables, weights?
Feedback: change predictors, model?
13
 Part
14
2: Results
Selected Predictors in Logistic
Regression Model
15
o
3ContMonValBetter (categorical variable): “1” means value portfolio outperforms growth
portfolio in previous three consecutive months.
o
3ContMonGroBetter (categorical variable): “1” means growth portfolio outperforms value
portfolio in previous three consecutive months.
o
ValLessGrow: value portfolio return minus growth portfolio return
o
TenLess3MUpDn (categorical variable): Term structure.
o
BaaLessAaaUpDn (categorical variable): Credit spread
o
PELessMA: P/E minus 12 months moving average
o
Spread10YLessFedUpDn (categorical variable): “1” means10 year bond is higher than fed
fund rate.
Coefficients
16
Model Statistics

All-in-sample regression
First, we tried to run the regression using all data points as in-sample data. The Cox & Snell R Square is 4.9%
and the Naqelkerke R Square is 6.6%.
-2 Log
likelihood
351.037(a)
Step
1
Cox & Snell
R Square
.049
Nagelkerke R
Square
.066
.
The overall correct percentage is 61.2% as shown in the following classification table.
Classification Tablea
Predicted
ValueBetter
Step 1
Observed
ValueBetter
Overall Percentage
a. The cut value is .500
17
0
0
1
1
88
54
48
73
Percentage
Correct
64.7
57.5
61.2
Conditioning & Weight Optimization
rg results
0.57876
0.59554
0.66772
0.6069
rg result>=threshold H? rg result<threshold L?
1
0
1
0
1
0
1
0
Analysis and presentation
Objective: max conditional return
3.903361619
18
W(v) to use
1.226843107
1.226843107
1.226843107
1.226843107
Target cell
threshold H
threshold L
w(v) when rg>=threshold
w(v) when rg<threshold
Turnover
0
0
0
0
Changing cells
0.55
0.45
1.226843107
-0.672121772
Performance of MCP
In the sample
Out of sample
Value portfolio
Annualized return
2.6%
1.2%
Volatility
17.5%
27.1%
skewness
0.268947156
0.318139691
Correlation
0.176735719
0.233018437
Beta
0.219764601
0.371168031
Alpha
-5.78%
-4.39%
Sharpe Ratio
-0.209427986
-0.08992208
19
Growth portfolio
Midas Conditional
Market
T-bill
6.7%
2.0%
10.5%
26.2%
15.9%
8.9%
6.3%
3.6%
16.3%
24.8%
30.0%
37.5%
14.1%
17.0%
0.6%
0.5%
-0.172674905
-0.876256154
-0.452138825
0.181344591
-0.947330467
-0.44332867
0.12164478
-0.26165161
-0.058663088
-0.139552486
0.063230298
-0.046958957
1
1
0.020920404
0.04701875
-0.067990626
-0.20299067
0.134849794
-0.103476132
1
1
0.000865683
0.001496022
1.04%
-0.51%
2.97%
23.09%
0.00%
0.00%
-0.01%
-0.01%
0.023896531
-0.063678409
0.142303888
0.601034212
0.683493189
0.307982992
0
0
Midas conditional portfolio turnover times
20
8.15
average months per turn over
7
14.14285714
one turnover average month
Performance of MCP (1)
Annualized Return
Annualised Return
30.0%
25.0%
Percentage
20.0%
In the sample
Out of sample
15.0%
10.0%
5.0%
0.0%
Value portfolio
20
Growth portfolio
Midas Conditional
Market
T-bill
Performance of MCP (2)
Volatility
Volatility
40.0%
35.0%
30.0%
25.0%
In the sample
Out of sample
20.0%
15.0%
10.0%
5.0%
0.0%
Value portfolio
21
Growth portfolio
Midas Conditional
Market
T-bill
Performance of MCP (4)
Skewness
Skewness
0.4
0.2
0
Value portfolio
Growth portfolio
Midas Conditional
Market
T-bill
-0.2
-0.4
-0.6
-0.8
-1
-1.2
22
In the sample
Out of sample
Performance of MCP (4)
Correlation
Correlation
1.2
1
0.8
0.6
In the sample
Out of sample
0.4
0.2
0
Value portfolio
-0.2
23
Growth portfolio
Midas Conditional
Market
T-bill
Performance of MCP (5)
Beta
Beta
1.2
1
0.8
0.6
In the sample
Out of sample
0.4
0.2
0
Value portfolio
-0.2
-0.4
24
Growth portfolio
Midas Conditional
Market
T-bill
Performance of MCP (6)
Sharpe Ratio
Sharpe Ratio
0.8
0.7
0.6
0.5
0.4
0.3
In the sample
Out of sample
0.2
0.1
0
Value portfolio
-0.1
-0.2
-0.3
25
Growth portfolio
Midas Conditional
Market
T-bill
Performance of MCP (7)
Alpha (at least, in the way we calculated it. Yes, we
are still wondering, is this real?)
Alpha
25.00%
20.00%
15.00%
10.00%
In the sample
Out of sample
5.00%
0.00%
Value portfolio
-5.00%
-10.00%
26
Growth portfolio
Midas Conditional
Market
T-bill
The concern of transaction costs

Partially addressed
Turnover
16
14
12
10
In the sample
Out of sample
8
6
4
2
0
average months per turn over
27
 Part
28
3: Future Research
Suggested Future Research
Midas is an intriguing figure. Interesting research
topics arise around him.
For example,
Women like gold; but do they like to be turned into
gold??
29