# STA457 Time Series

Time：2022-5-8

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.

1. Assignment and solution (Fall 2018)
2. Moskowitz et al. (2012), “Time series momentum”, Journal of Financial Economics
General instruction
§ Download daily and monthly data of 30 constituents in the Dow Jones (DJ) index from 1999
December to 2018 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
annually at the end of each year.
Questions:
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.
2) Construct the equally weighted (EW) and risk-parity (RP) weighted portfolio using all
3. 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.
2
B. Time Series Momentum
1) Calculate the ex-ante volatility estimate ” for all 30 DJ constituents using the
following formula:”# = 261 )(1 ).(2)
where the weights add up to one, and
” is the exponentially weighted
average return computed similarly.
2) Consider the predictive regression that regresses the (excess) return in month on
its return lagged months, i.e. (4)
where :,” denotes the -th stock in the DJ constituents and in the prediction
regression, returns are scaled by their ex-ante volatilities :,”01. Determine the
optimal for both predictive regressions for all 30 DJ constituents.
3) Consider a time series momentum trading strategy by constructing the following
portfolios:”,”P1
QRSTS = 130):,”0>V:”L (5)
where :,”0>V:”L :,”L is our position for the -th constituent at time and

V:”0>V:” denote the :-month lagged returns observed at time. Summarize the
performance of the portfolio.
Hint: For simplicity, assume : = 12 for all 30 DJ constituents.
C. Dynamic position sizing for technical trading rules
1) Consider a technical indicator “, where the technical indicator may be given by ” = ) “0^_0#>45
. (6).
Suppose that our position to the trading rule is determined by the strength (or
magnitude) of the signal. The -period holding period return is then given by. (7)
Calculate the expected -period holding period return, i.e.,.
Remark: In this question, we assume that our position changes linearly with the
strength of the signal. We can generalize it by replacing “P.01 with(“P.01) in
Equation (7).
2) Find the optimal double MA trading rule for all 30 DJ constituents that maximize the
12-period holding period return.
WX：codehelp

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