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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 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/dow30/ 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:

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.

2) Construct the equally weighted (EW) and risk-parity (RP) weighted portfolio using all

30 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.

Copyright ? Jen-Wen Lin 2019

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.

Copyright Jen-Wen Lin 2019

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.