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

2 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.

3 Part 1: Methodology

4 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.

5 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)]

6 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)

7 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.

8 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)

9 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)

10 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.

11 Trading costs Use two thresholds to minimize between-portfolio turnover Need to model within-portfolio turnover

12 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.

13 Map it out: the big picture of the steps

14 Part 2: Results

15 Selected Predictors in Logistic Regression Model

16 Coefficients

17 Model Statistics

18 Conditioning & Weight Optimization

19 Performance of MCP

20 Performance of MCP (1) Annualized Return

21 Performance of MCP (2) Volatility

22 Performance of MCP (4) Skewness

23 Performance of MCP (4) Correlation

24 Performance of MCP (5) Beta

25 Performance of MCP (6) Sharpe Ratio

26 Performance of MCP (7) Alpha (at least, in the way we calculated it. Yes, we are still wondering, is this real?)

27 The concern of transaction costs Partially addressed

28 Part 3: Future Research

29 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??