In order to calculate Avon's Beta and its adjusted Beta stock returns and S&P 500 returns were used by taking monthly data from over the past five years (September 28, 2007 through September 28, 2012), and then daily data was used from over the past year (September 30, 2011 through September 28, 2012). Each of the Betas below are different because the returns and time periods over which these Betas were calculated are different. With different data the results will differ. However, all of Avon's estimated Betas above are between .79 and 1.42 which shows that there is a high probability that the actual Beta of Avon is within that set of numbers.
Using monthly data for the past five years
The Beta is 1.418179214 and the adjusted Beta is 1.278786143.
Using daily data for the past five years
The Beta is 0.79577679 and the adjusted Beta is 0.863851193.
Other Beta Estimates
Value Line's Beta :1
Yahoo's Beta: 1.23
The standard deviation explains the difference in expected return of Avon's stock. Avon's arithmetic average is the sum its monthly returns over the past 5 years divided by the number of inputs. Where as, the geometric mean return does not require knowledge of the amount invested but instead is solely focused on returns.
Using the Monthly Returns
|Type of Return||Return|
|AMR S&P 500||0.006876188|
|GMR S&P 500||-0.011600991|
|10 Year T-Bill||0.2184|
|Market Risk Premium||6%|
Using Daily data for the past five years
|Type of Return||Return|
|AMR S&P 500||36.81%|
|GMR S&P 500||34.67%|
|1 Year T-Bill||64.80%|
|Market Risk Premium||-30.13%|
Over the past year using daily data, Avon significantly under performed the S&P 500 market index with its average and geometric mean returns both indicating negative returns on the stock, while the market index made healthy daily gains. With the adjusted beta for the stock being .864 relative to the market, Avon should have had gains that would be just short of the market return because systematic risk was slightly lower than that of the market. Using monthly data over the past five years it can be seen that Avon again significantly under performed the market, having large negative returns while the market had a smaller negative return. Based on the adjusted beta for the stock at 1.278, we would have expected a larger negative return from the stock compared to the market index because of its higher systematic risk, but we would not expect the stock to lose half of its value, which it did over the five year period. Both monthly and daily alphas indicate that the stock has historically under performed the market and missed its required rate of return for its level of risk.Over and under performance is determined by the significance of alpha. And after the t Stat was compared to the P-value, for both monthly and daily data, it was determined that the t Stat is less than 2 and the p-value is less than .05 so there is no significant return for Avon. This means that we can assume alpha to be 0.
Rates and Risks
The risk-free rate is often attributed to government treasury bonds. This is because the US government is not thought of to have any risk because they will always pay their interest on the bonds. The Market risk premium is the amount that one is expected to receive in addition to the risk free rate as compensation for their riskier investment in the stock market rather than in the T-bill market.
The expected market risk premium historical has been 6%. Our calculations for Avon using monthly data is -1.92% and using daily data is -0.08%.
The risk-free rate for a one year investment is 0.18% and for a 10 year investment is 1.82%.
Using Monthly Adjusted Beta
The required rate of return of Avon for a one-year investment is 0.11% and for a 10 year investment is -0.63%.
Link to Excel Sheets
finance.yahoo.com, Value Line , http://federalreserve.gov
No annualised values for means (arithmetic or geometric). Over and under performance is determined by the significance of alpha. Market risk premium should be a historic value (approx. 6%)