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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. Goal. - PowerPoint PPT Presentation
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1
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
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Goal
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.
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Part 1: Methodology
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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.
We select 01/1983 to 08/1996 (163 months) as in sample, and 09/1996 to 11/2004 (99 months) as out of sample.
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Value and Growth Portfolio (a)
Value portfolio sorting variableBook(t-1)/Price(t-1)
Growth portfolio sorting variableEarnings growth per price dollar
[E(t-1)-E(t-13)]/[│E(t-13) │*P(t-1)]
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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)
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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.
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Conditional Weighted Trading Rule (1)
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)
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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)
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)
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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.
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Trading costs
Use two thresholds to minimize between-portfolio turnover
Need to model within-portfolio turnover
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Logistic Predictive Regression Model
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.
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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 Sorting and portfolio construction Trading/Benchmarking
Periods Step : TTRR(t)Value Growth
Dec-04 F(t,ω(t)): 0/1 Predictor 1 (t-1) Predictor n (t-1) Rb(v,t) Rb(g,t) Provide conditional info TTRR(t)
Out-of SampleTest F(t)
Dec-94
Feedback: change sorting variables, weights?
Feedback: change predictors, model?
Step: F(t,ω(t)) Step: Rb(v/g,t)
Out of sample
test
In the sample
data
Challenge: predictorsChallenge: Sorting variables
Challenge: WeightsTransaction costs
each row is sorted long short return for that period for value or growth.
Optimizer to find out w(v,1), w(g,1) w(v,0), w(g,0)
Generate 0/1
Forecast 0/1
Starting Point
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Part 2: Results
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Selected Predictors in Logistic Regression Model
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.
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Coefficients
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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%.
Step -2 Log
likelihood Cox & Snell R Square
Nagelkerke R Square
1 351.037(a) .049 .066
. The overall correct percentage is 61.2% as shown in the following classification table.
Classification Tablea
88 48 64.7
54 73 57.5
61.2
Observed0
1
ValueBetter
Overall Percentage
Step 10 1
ValueBetter PercentageCorrect
Predicted
The cut value is .500a.
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Conditioning & Weight Optimization
rg results rg result>=threshold H? rg result<threshold L? W(v) to use Turnover0.57876 1 0 1.226843107 00.59554 1 0 1.226843107 00.66772 1 0 1.226843107 00.6069 1 0 1.226843107 0
Analysis and presentation Target cell Changing cellsObjective: max conditional return threshold H 0.55
3.903361619 threshold L 0.45w(v) when rg>=threshold 1.226843107w(v) when rg<threshold -0.672121772
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Performance of MCP
In the sampleOut of sample
Value portfolio Growth portfolio Midas Conditional Market T-bill
Annualized return2.6% 6.7% 10.5% 15.9% 6.3%1.2% 2.0% 26.2% 8.9% 3.6%
Volatility17.5% 16.3% 30.0% 14.1% 0.6%27.1% 24.8% 37.5% 17.0% 0.5%
skewness0.268947156 -0.172674905 -0.452138825 -0.947330467 0.121644780.318139691 -0.876256154 0.181344591 -0.44332867 -0.26165161
Correlation0.176735719 -0.058663088 0.063230298 1 0.0209204040.233018437 -0.139552486 -0.046958957 1 0.04701875
Beta0.219764601 -0.067990626 0.134849794 1 0.0008656830.371168031 -0.20299067 -0.103476132 1 0.001496022
Alpha-5.78% 1.04% 2.97% 0.00% -0.01%-4.39% -0.51% 23.09% 0.00% -0.01%
Sharpe Ratio-0.209427986 0.023896531 0.142303888 0.683493189 0-0.08992208 -0.063678409 0.601034212 0.307982992 0
Midas conditional portfolio turnover times20 8.15 average months per turn over7 14.14285714 one turnover average month
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Performance of MCP (1)
Annualized Return
Annualised Return
0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
Value portfolio Growth portfolio Midas Conditional Market T-bill
Per
cen
tage
In the sample
Out of sample
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Performance of MCP (2)
Volatility
Volatility
0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
35.0%
40.0%
Value portfolio Growth portfolio Midas Conditional Market T-bill
In the sample
Out of sample
22
Performance of MCP (4)
Skewness
Skewness
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
Value portfolio Growth portfolio Midas Conditional Market T-bill
In the sample
Out of sample
23
Performance of MCP (4)
Correlation
Correlation
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Value portfolio Growth portfolio Midas Conditional Market T-bill
In the sample
Out of sample
24
Performance of MCP (5)
Beta
Beta
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Value portfolio Growth portfolio Midas Conditional Market T-bill
In the sample
Out of sample
25
Performance of MCP (6)
Sharpe Ratio
Sharpe Ratio
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Value portfolio Growth portfolio Midas Conditional Market T-bill
In the sample
Out of sample
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Performance of MCP (7)Alpha (at least, in the way we calculated it. Yes, we are still wondering, is this real?)
Alpha
-10.00%
-5.00%
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
Value portfolio Growth portfolio Midas Conditional Market T-bill
In the sample
Out of sample
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The concern of transaction costs
Partially addressedTurnover
0
2
4
6
8
10
12
14
16
average months per turn over
In the sample
Out of sample
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Part 3: Future Research
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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??