Statistical Analysis for a Portfolio of Two Stocks

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Title: Statistical Analysis for a Portfolio of Two Stocks

CHEN LIU

Course: Computational Statistics in Finance

School: School of Economics

Major: Master in Financial Economics    

   Tutor: Dr. Sutaip SAW Leng Chooi

25th, Nov, 2015

Contents

Introduction        

Part 1        

Part 2        

GMV Portfolio Analysis        

Sharpe ratio Analysis        

Value-at-Risk Analysis        

Summary        

Statistical Analysis for a Portfolio of Two Stocks

Introduction

Study in investment in a portfolio of multiple stocks is always a hot issue for both investors and the government. Most commonly, the unstable returns on stocks are either tempting or risky for the investors who are risk-preferred. Statistics is a robust useful tool for us to analyze the performance of a stock in the capital market. Next, we illustrate how to analyze statistically and empirically the return on stocks through an analysis case on a pair of stocks denoted as HD and DIS.

Part 1

To commence with, we extracted the data of the log-returns of the pair of stocks based on the past 96 months from a pool of stocks. To visualize the performance of the pair of stocks, we graphed the log-returns on the two stocks separately along with time passing, shown in Figure 1.1.              

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Figure 1.1 Log-returns on HD and DIS

To assess whether the log-returns of the stocks have a bivariate normal distribution, we first utilized the graphical techniques to check if the marginal distributions are normal. We graphed the density function by histograms of probability distribution for the stock HD and DIS separately in R with rugs added as shown in Figure 1.2.