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STA457 Time Series Analysis Assignment 1 (Winter 2019)Jen-Wen Lin, PhD, CFADate: February 07, 2019Please 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 EconomicsGeneral instruction§ Download daily data of 30 constituents in the Dow Jones (DJ) index from 1999 December to2018 December. Please see https://money.cnn.com/data/dow30/ for the list of DJconstituents.§ Calculate the performance based on a 60-month rolling window and rebalance the portfoliomonthly but calibrate/estimate parameters () at the end of each year.§ Performance: Annualized expected return, annualized volatility (standard deviation), andAnnualized Sharpe ratio. Annualization is done using the squared root of time. Use Sharperatio as examplewhere assume that annual risk free rate , = 0.02 and ) is the sample mean of monthlystrategy returns and ./ is the monthly volatility.Questions:A. Technical trading rule1) 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 20192) Construct the equally weighted (EW) and risk-parity (RP) weighted portfolio using all30 DJ constituents. Summarize the performances of EW and RP portfolios (tradingstrategies).Hint: For simplicity, assume the correlations among stocks are zero whenconstructing 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 Momentum1) Calculate the ex-ante volatility estimate 3 for all 30 DJ constituents using thefollowing formula:R = 261 T(1)X(2)where the weights X(1) add up to one, and ;,3 is the exponentially weightedaverage return computed similarly.Hint: Solve usingT(1XR8XF8= 1and;,3 = T(1)XR8XF8;,3=6=X.Copyright Jen-Wen Lin 201932) Consider the predictive regression that regresses the (excess) return in month onits return lagged months, i.e.(4)where ;,3 denotes the -th stock in the DJ constituents and in the predictionregression, returns are scaled by their ex-ante volatilities ;,3=6. Determine theoptimal for both predictive regressions for all 30 DJ constituents.Remark: For simplicity, students only need to consider Equation (4) in this questionand use R-squared to evaluate the predictive regression.3) Consider a time series momentum trading strategy by constructing the followingportfolios:(5)where ,3=cJ:3[ Y40%;,3[ is our position for the -th constituent at time andcJ:3=cJ:3 denote the ;-month lagged returns observed at time. Summarize theperformance of the portfolio.Hint: For simplicity, assume ; = 12 for all 30 DJ constituents.Copyright Jen-Wen Lin 2019C. Dynamic position sizing for technical trading rules1) Consider a technical indicator 3, where the technical indicator may be given by�(6).Suppose that our position to the trading rule is determined by the strength (ormagnitude) of the signal. The -period holding period return is then given by�(7Calculate the expected -period holding period return, i.e.,(3:3qc).Remark: In this question, we assume that our position changes linearly with thestrength of the signal. We can generalize it by replacing ?3qX=6 with (3qX=6) inEquation (7).2) Find the optimal double MA trading rule for all 30 DJ constituents that maximize the12-period holding period return. 本团队核心人员组成主要包括硅谷工程师、BAT一线工程师，精通德英语！我们主要业务范围是代做编程大作业、课程设计等等。我们的方向领域：window编程 数值算法 AI人工智能 金融统计 计量分析 大数据 网络编程 WEB编程 通讯编程 游戏编程多媒体linux 外挂编程 程序API图像处理 嵌入式/单片机 数据库编程 控制台 进程与线程 网络安全 汇编语言 硬件编程 软件设计 工程标准规等。其中代写编程、代写程序、代写留学生程序作业语言或工具包括但不限于以下范围:C/C++/C#代写Java代写IT代写Python代写辅导编程作业Matlab代写Haskell代写Processing代写Linux环境搭建Rust代写Data Structure Assginment 数据结构代写MIPS代写Machine Learning 作业 代写Oracle/SQL/PostgreSQL/Pig 数据库代写/代做/辅导Web开发、网站开发、网站作业ASP.NET网站开发Finance Insurace Statistics统计、回归、迭代Prolog代写Computer Computational method代做因为专业，所以值得信赖。如有需要，请加QQ：99515681 或邮箱：[email protected] 微信：codehelp