WOW Limited & QAN Limited

ZHANG Yanni

ZHANG Yanni

LIU Shicheng

LI Zhuochen

WANG Yueyao

ZHU Qianwen

Table of Contents

EXECUTIVE SUMMARY This report is first going to utilize the Mean-Variance theory and Capital Asset Pricing Model

(CAPM) approach to calculate the expected risk and return of two stocks that are listed on the

ASX- Woolworths Limited (ASX: WOW) and Qantas Airway Limited (ASX: QAN). It later critically examined and discussed rationales and assumptions of the two methods, including the limitations on each method. Finally, the various portfolio combinations will be assessed and a recommendation will be made to the investor on the portfolio combination that has the lowest level of risk.

1. INTRODUCTION

Mean-Variance approach and capital asset pricing model (CAPM) are two important quantitative finance theories that enable investors to select portfolio by assessing its risk and return (Varian 1993). In this report, two companies from different industries are chosen to construct the portfolio, which are Woolworths Limited (WOW) and Qantas Airways Limited (QAN). The two approaches will be implemented to determine the expected return and risk of this two-stock portfolio under various weight allocation conditions. Furthermore, recommendations of portfolio selection are presented after the risk-return analysis based on the critical examination of the rational and assumptions under the two approaches.

2. MEAN VARIANCE APPROACH

2.1 Justification of Data Selection

Our data will be based on the daily stock price of Woolworth (AXS: WOW) and Qantas (ASX: QAN) during a 5 year interval from 17th April 2008 to 17th April 2013.

2.1.1 Five-year Period

Here we use 5 years daily data to calculate the expected return and standard deviation of the WOW and QAN. The data from 17th April 2008 to 17th April 2013 presented a recently momentum of the two stocks, take company recent change into consideration, for instance, merge and acquisition (Sit 2011). Furthermore, it provided a reasonable sample size, which ensures to reflect a more accurate fluctuation of their returns (Sit 2011).

2.1.2 Daily Data

In order to ensure the sample size and reflect a more precisely distribution of the stock return, we use daily data to calculate the stock expected return and the standard deviation, make sure the result is presented a lower standard error (Pruzzo, Cantet & Fioretti 2003).

2.1.3 Adjusted Close Price

To calculate the daily return, the adjusted close price is used to eliminate any price change that is resulted from dividend payment, stock splits and rights offering (Pruzzo, Cantet & Fioretti 2003).

2.2 Calculation of ER and SD of Individual Stock

The daily returns of WOW and QAN are calculated based on the following formula. To calculate the expected return, we average all the historic returns.

The expected return and standard deviation for WOW and QAN are presented in the Table 2.1.

Table 2.1: Expected Return and Standard Deviation for WOW and QAN

The expected return of WOW and QAN are 0.04% and -0.02% respectively. This illustrates that WOW presented a higher future expected return. While the standard deviation of return for WOW and QAN are 0.012671173 and 0.023593466 respectively, this figure indicates that QAN is more volatile than WOW.

2.3 Calculation of ER and SD of Portfolios

2.3.1 Calculation of Covariance

The covariance between WOW and QAN is 0.0000943, which is calculated based on the following formula. The positive result indicated the two stocks are positively correlated, which means that when price of WOW rise, the price of QAN will goes up as well.

2.3.2 Portfolio Returns and Risk Combinations

The portfolios by varying the weights of each stock at 2.5% intervals are presented in Table 6.1 in Appendix A1. The calculation of expected returns and variances of the portfolios are