Expected Return and Risk of Portfolios Consisting of Stocks Listed on Woolmart Limited - Example

1. executive summary This report provides an overview of the expected return and risk of portfolios consisting of stocks listed on ASX, which is the woolmart limited. Firstly, the risk and return of the combined portfolio will be examined by applying mean-variance approach, followed by the portfolio analysis using the capm approach including the justification of data selection, information of the rationale and calculated results. Then, the recommendation will be provided with consideration of assumptions and limitations under the two approaches and analyzing the results of the calculations 2. Mean variance A portfolio under Markowitz’s mean-variance framework] is characterized by the reward, measured by the expected return, and the risk, measured by the variance of return (anagnostopoulos and mamanis 2013).’ the expected return, which determines the reward of a portfolio, would be more likely to be maximized by investors. Historical data is collected as the basic information for further calculation. 2.1 data selection The data, which is selected to calculate the expected return and variance, is a recent five-year monthly data (from 2008 mar to 2013 mar). 2.2 stock expected returns (see appendix 1) The formula used in calculating historical returns is: =percentage return on the securities =price of the share at the month t+1 Price of the share at the month t dividends on ex-dividend date on the The mean return, which is the expected return, is measured as: The expected return of woolmart limited is 0.92594%, 2.3 stock standard deviation (see appendix in excel) Standard deviation describes the risk of each stock and portfolio by measuring distance from the mean (Frederick and Larry 2011). According to frino, hill and Chen (2009), ‘the risk of a security is the extent to which payoffs on the security are expected to vary from their expected value.’ the measure of standard deviation gives a good picture in describing portfolio’s risk. rt = the observed during interval t n = the number of available observation = the expected return according to our calculation, the variance of woolmart limited is 0.0057294; standard deviation of woolmart limited is 0.0756928.According to the frino, hill and chen (2009), ‘the higher the standard deviation of returns, the higher the range of possible outcomes, and hence the more risk that is associated with stock market investment.’ from the calculation results, the standard deviation of woolmart limited is high, which indicates that the investment of woolmart limited will generate a higher return associated with a higher risk. 3. Calculation of beta (see appendix) There are two types of risks presumed in the capm, which are unsystematic risk and systematic risk. According to frino, hill and Chen (2009, p.173), unsystematic risk is ‘the movement in the price of a security which results from an event specific to the security. Systematic risk is ‘the movement in the price of a security which is driven by broad market related factors’. In short, unsystematic risk can be eliminated by a sufficient diversified investment; hence, investors cannot be allowed a risk premium for the risk. In contrast, systematic risk can be eliminated by a sufficient diversified investment; therefore, some risk premium can be provided for investors as compensation. Beta coefficient is the tool of assessment for the systematic risk of stock, which measures the volatility of an individual share or stock portfolio. Beta coefficient is a regression coefficient that can be calculated from historical data. Basic formula: = = Which implies the coefficient a=zero, beta is given by: Where: =the dividend over the holding every 6 months \ = closing price at month t; pt-1 = closing price at month t-1 = index level at month t; it-1 = index level at month t-1 = the return on stock i, earned over period t = the risk-free rate of return = the market rate of return =the number of periods (n = 60 in this case) For woolmart limited: total covariance(x, y) = 0.0023003 variance (x) = 0.0024042 Beta of woolmart limited = total covariance(x, y) / variance (x) = 0.9568 3.1 calculation of individual stock return (see appendix 6) Frino (2009) indicates that return on an individual stock can be presented through the following basic formula: = risk free rate = beta coefficient of individual stock or stock portfolio = expected market return = equity market premium In this formula, ‘rm - rf’ is the market premium. It is clear that equity market premium is the result of expected market return minus risk free rate. Security risk premium is the product between beta coefficient and equity market premium. If investor takes more risks, the more risk premium will be added when holding other factors constant. Therefore, the expected return on an individual stock will be increased as well. Average risk free rate = 0.0089% average market risk premium = 0.0418% Beta of woolmart limited = 0.9568 individual stock return = 0.0489% 4. Market index all ordinaries index, which is commonly known as market index and includes about 97.7% of market capitalisation, covers a parcel of 500 securities (frino 2009). Although, there are other market proxy, such as s&p/ASX 200 accumulation index and s&p/ASX 200 index, which are very popular. Not the all ords index ignores the dividends paid through not considering the dividends when giving the index. Therefore, the all ordinaries index represents market index. 5. risk-free rate For determination of beta of CAPM, the risk-free rate should be firstly determined. Generally, the government bond is always be chosen as assumed zero risk asset when calculating beta and pricing capital (frino, 2009). There are many different kinds of bonds, such as 5-year, 10-year, and 30-year. However, the 10-year government bond rate is most acceptable because of its less sensitivity to unexpected change in inflation (Campbell & viceira, 1998). bowman (2001) also said that “the most commonly used estimation in Australia is based upon the ten-year risk free rate of government bonds, which represents a low risk investment.” therefore, 10-year government bonds are used as a measure of the risk-free rate in this report Read More