STA457 Time Series Analysis Assignment 1 (Winter 2019)
Jen-Wen Lin, PhD, CFA
Date: February 07, 2019
Please check in Quercus regularly for the update of the assignment.
Background reading:

1. Assignment and solution (Fall 2018)
2. Moskowitz et al. (2012),“Time series momentum”, Journal of Financial Economics
   General instruction
   § Download daily data of 30 constituents in the Dow Jones (DJ) index from 1999 December to
3. December. Please see https://money.cnn.com/data/do… for the list of DJ
   constituents.
   § Calculate the performance based on a 60-month rolling window and rebalance the portfolio
   monthly but calibrate/estimate parameters () at the end of each year.
   § Performance: Annualized expected return, annualized volatility (standard deviation), and
   Annualized Sharpe ratio. Annualization is done using the squared root of time. Use Sharpe
   ratio as example
   where assume that annual risk free rate , = 0.02 and ) is the sample mean of monthly
   strategy returns and ./ is the monthly volatility.
   Questions:
   A. Technical trading rule
   1) Find the optimal double moving average (MA) trading rules for all 30 DJ constituents
   (stocks) using monthly data.
   Hint: see Assignment (Fall 2018) for more details.
   Copyright Jen-Wen Lin 2019
   2) Construct the equally weighted (EW) and risk-parity (RP) weighted portfolio using all

4. DJ constituents. Summarize the performances of EW and RP portfolios (trading
   strategies).
   Hint: For simplicity, assume the correlations among stocks are zero when
   constructing the risk-parity portfolio.

   BCD #D3B#E

   /G = ∑ H IJKL
   ∑ IM NO KL M; is defined in Equation (1) (see question B)
   B. Time Series Momentum
   1) Calculate the ex-ante volatility estimate 3 for all 30 DJ constituents using the
   following formula:
   R = 261 T(1)X(2)
   where the weights X
   (1) add up to one, and
   ;,3 is the exponentially weighted
   average return computed similarly.
   Hint: Solve using
   T(1XR\8XF8= 1and;,3 = T(1)XR\8XF8
   ;,3=6=X.
   Copyright Jen-Wen Lin 201932) Consider the predictive regression that regresses the (excess) return in month on
   its return lagged months, i.e.
   (4)
   where ;,3 denotes the -th stock in the DJ constituents and in the prediction
   regression, returns are scaled by their ex-ante volatilities ;,3=6. Determine the
   optimal for both predictive regressions for all 30 DJ constituents.
   Remark: For simplicity, students only need to consider Equation (4) in this question
   and use R-squared to evaluate the predictive regression.
   3) Consider a time series momentum trading strategy by constructing the following