Mean Approach & Beta Approach in Stock-Investing

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This report aims at implement two distinct approaches, which can indicate the expected return and risk of a two-stock portfolio, to generate a practical solution to risk-analyzing for stock-investing. The two approaches are Mean-Variance Approach and CAPM Approach. While we apply the Mean-Variance Approach to determine the expected return and standard deviation, we employ the CAPM approach to measure the beta and expected return of each stock. The calculations of the aforesaid mathematical characteristics will contain the weekly returns during a seven-year time period integrated with the ASX all ordinaries Accumulation Index as a substitute for the market index and Official Cash Rate (thereafter, OCR, which is the interest rate paid by banks in the overnight money market in Australia and New Zealand) as a substitute as rate of return on risk-free asset. In this report, the data of stocks are from David Jones Ltd (DJS) and BHP respectively. DJS is Australia's third-largest department store company operating more than 30 stores across Australia, which also stakes the claim as the world's oldest continuously operating department store (Cengage, 2006). BHP Billiton is the world's largest mining company; it is also the largest company in Australia by Market capitalization, which was created in 2001 by the merger of Australia's Broken Hill Proprietary Company (BHP) and the UK's Billiton ( BHP profile, 2010). 2. MEAN-VARIANCE APPROACH

2.1 Selection of Sample Frequency and Sample Period
To calculate the expected return and the standard deviation of each stock, it is necessary to obtain the relevant and accurate data on share price of historical time series. Evidently, the more the observation points and the longer sample period are employed, the more the reliable assessable consequences can be generated.

Ordinarily, the daily data, weekly data and monthly data of share price can be selected for calculating the expected return and the standard deviation of each stock. The considerations for determining the sample frequency are as the following: On the one hand, daily data is quite unstable and affected by massive unrelated factors although it is high in sample frequency. On the other hand, monthly data inconsiderably relies on the choice of reference day (Daniella and Nigel, 2007) although it is relatively stable. And thus, to achieve the reliable analysis, weekly data as a compromise may be the optimal choice.

When it comes to determine the length of sample period, we consider that around seven years the performance of each stock can be assessed reliably. The main reason for the determination is we intend to seek a sample period as long as possible, and BHP was listed on the ASX since 2003. Accordingly, 1st Apr. 2003 was chosen as the beginning time of weekly closing share price of BHP. To keep the consistency, we selected the same time as the beginning for DJS. Furthermore, for the sake of guaranteeing this report in accordance with practical significance, 29th Mar. 2010 was selected as the closing time. Namely, there are 366 data points in total, which provides adequate time series of data. 2.2 Calculation of each parameter

Formula for calculating the risk of a security:
Decision Rule: The higher the standard deviation of returns, the higher the range of possible outcomes and hence the more risk is associated with stock-market investment (Frino et al., 2006).

Method for Calculating parameters of portfolios:
Covariance of two stocks
Decision Rule: If the result of calculation is positive, it means that the returns on two securities are positively correlated. Conversely, if the result of calculation is negative, it means that the returns on two securities are negatively correlated (Frino et al., 2006).

Formula for calculating the risk of portfolios:
Just two stocks are involved in the calculation, thus the calculation is: [pic]
The lowest outcome of σp2 will be favorable in...
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