Question one
The paper used three stocks of AGL Energy (AGL), Asciano Limited (AIO), and AMCOR Limited (AMC). Monthly histories of prices for the stocks for 1^{st} October 2009 t0 31^{st} October 2014 listed in ASX
- Compute the individual monthly returns, average monthly return, variance and standard deviation of the monthly returns for the stocks of the companies you have chosen.
To compute the return on individual month, the prices of the month and that of the previous month was adjusted. In constructing the table below, the price of the preceding month of the first month is not available in the table. Therefore, the price of the first month was not calculated, and the price for the second month was calculated as
r_{2}= = 1
Where p*= adjusted prices incorporating the effects of stock dividends, cash dividends and stock splits. The adjustable prices are readily available from the “DatAnalysis Premium” link in Deakin Online Library.
Solution 1
In computing the return on individual month, I used the formula = 1 in which
- P*2 is the adjustable closing stock price at beginning of a particular month
- P*1 is the adjustable closing stock price at the end of the particular month
- I divided the P*2 by P*1 and then subtracted 1. The result was then converted to percentage by multiplying by 100
- For example, P*2 of AGL Energy company in 30/09/2014 was 13.49, and on 31/10/2014 P*1 was 13.59
- Calculate: – 1= -0.00735835
- Converted to percentage =-0.74% as return on individual month.
- Using Ms Excel and using the formula, it was =C3/C2-1
- The same formula was used in calculating return on individual month for all the months from October 2009 to October 2014 for the three companies of AGL Energy (AGL), Asciano Limited (AIO), and AMCOR Limited (AMC) as shown in the embedded Excel document (double click on the embedded excel work book to read see the figures).
Solution 2
In calculating average monthly return, standard deviation and variance, I used Ms Excel software of finding average
In my worksheet, I listed the returns in the following ranges
AGL=C2:C62
AIO=D2:D62
AMC=E2:E62
- Therefore the formula of finding average monthly return in excel for AGL was =Average (C2:C62) = 8.01%
- The formula for Standard deviation for AGL also was =STDEV (C2:C62) =0.623542
- Standard deviation is square root of variance, therefore in calculating variance, I squared the standard deviation figures as shown in the excel embedded below
(Double click on the embedded excel work book to read see the figures).
b) Using the various statistics calculated in a), state which stock has the highest expected return, which stock has the highest total risk and which one has the highest expected return per unit of total risk.
Highest expected return- AMCOR Limited (AMC) because it has a the lowest standard deviation of 0.1169 making it less volatile
Highest total risk- AGL Energy because it has the highest standard deviation of 0.6235 making it a volatile stock. According to Hassett (2011), a volatile stock has a higher standard deviation
Highest expected return per unit of total risk- AGL energy has the highest risk and also the highest expected return. From the computation, its average return from the past 61 months indicate an average of 8.01% which makes the highest expected return stock per unit of the total risk.
c) Would the stock with the highest total risk in b) necessarily be the ‘riskiest’ of the three stocks? Explain
No, as much as AGL energy has the highest risk because of its high value of standard deviation which makes it highly volatile, it has the highest average return of 8.01% compared to Asciano Limited (AIO) of 1.17% and AMCOR Limited (AMC) of -2.48%. From the three companies, the riskiest company in terms of making investments is AMCOR Limited (AMC) since its average return is negative and also the lowest. As much as its historical volatility is the lowest, its average return is not impressive to an investor (Barenblat & Mesler, 2002).
d) Use the month-end adjusted closing values of the AORD to compute individual monthly returns on the market index.
Similar to part (a), I used the formula of = 1 in calculating the individual monthly returns on the market index. The closing value of AORD were also already adjusted. Moreover, applying the same formula in excel, I computed the monthly returns as shown in the attached excel workbook below named “SHARES 2”. The file is too big to be embedded
e) Briefly describe the beta estimation process as per the CAPM. Using the information in d) along with the individual monthly returns on each of the three stocks calculated in a), estimate their betas. What do these betas tell you about the riskiness of these three stocks relative to the market? Assuming a 3% p.a. risk-‐free rate, calculate the expected return on each of the three stocks using CAPM.
CAPM is a model describing the relationship between the expected return and risk and is used in the pricing of the securities that are risky. Beta is a measure of the systematic risk, volatility of a portfolio or a security in comparison to the whole market (Harrington & Harrington, 2007).
The paper used SLOPE method in excel in estimating the beta. The SLOPE method is available function in Ms excel for calculating beta values. The formula is =SLOPE (range of stock values of a company, range of market values).
For instance, in computing the beta value of AGL Company in relation to AORD market values using the slope method, the formula was as follows
=SLOPE (J3:J62, I3:I62) = 0.587251
The same method was used in computing beta values for AIO and AMC as shown in the embedded spreadsheet below
(Double click on the embedded excel work book to read see the figures).
From the estimation of the beta values relative to the market, the following information can be deduced about riskiness:
The estimation of the betas for AORD &AGL=0.587251 and AORD &AIO=0.980865 was less than 1 and greater than zero. This implies that the prices of the stock will move with the market in overall, however, the prices of the stock will remain volatile and less risky. For AORD&AMC=-0.06169 which had a negative value indicate a more stable stock prices compared to the other companies in the market.
CAPM
Therefore;
AGL Energy (AGL);
R_{a }= 3% + 0.587251 (8.01%-3%) = 5.942%
Asciano Limited (AIO)
R_{a }= 3% + 0.980865 (1.17%-3%) = 1.205%
AMCOR Limited (AMC)
R_{a }= 3% + -0.06169 (-2.48%-3%)= 3.338%
f) What would happen to the expected rates of return for a risk-free rate of 4.5% per annum? What would they be if the risk‐free rate was 1.5%? Explain your observations in light of the risk-return relationship.
Risk free rate of 4.5% p.a | Risk free rate of 1.5% p.a | |
AGL Energy (AGL); | R_{a } = 4.5% + 0.587251 (8.01%-3%)= 7.942% | R_{a } = 3% + 0.587251 (8.01%-3%)= 4.442% |
Asciano Limited (AIO) | R_{a } = 3% + 0.980865 (1.17%-3%)= 2.705% | R_{a } = 3% + 0.980865 (1.17%-3%)= -0.295% |
AMCOR Limited (AMC) | R_{a } = 3% + -0.06169 (-2.48%-3%)= 4.838% | R_{a } = 3% + -0.06169 (-2.48%-3%)= 1.838% |
From the table, it can be observed that with a risk free rate of 4.5% per annum, the expected rates of returns increased, while with a risk free rate of 1.5% p.a, the expected rates of return decreased. Therefore, it can be concluded that as expected returns increases as the investments gets more free of risks, while the rate of returns on investments decreases when the investments gets more risks (Wang & National Bureau of Economic Research, 2001).
Question two
The application of the CAPM in modern financial markets has been much debated and criticized from an empirical point of view. Does this imply that the theory underlying CAPM is flawed? Outline your argument. Should we reject the model outright? If you think that the model should be rejected, provide alternative model(s) to replace it with empirical studies to support your choice. Otherwise, provide the reasons why CAPM should be kept.
The essay will argue that the numerous empirical evidence produced against CAPM model which are based on returns on stock does not invalidate the use of CAPM model in the estimation of cost of capital for projects in the decisions of capital budgeting. According to Harrington (2003), stocks are backed by the projects existing and the option of modifying the current projects and even undertake the new ones. However, the expected stock returns need to satisfy the CAPM even if the returns on projects expected do.
According to Sincere (2004), CAPM model presents a theory that is simple and also delivers simple results. The theory states that the sole reason an investor, on average, should earn more by making an investment in a particular stock than the other is because a particular stock is riskier.
Hassett (2011) pointed out a study by Professor Kenneth and Eugene on the return on shares on the New York stock Exchange, Nasdaq and the American Stock Exchange between 1963 and 1993. The study revealed that the over a lengthy period, differences in beta did not explain different stocks performance. Moreover, the linear relationship between individual stock returns and beta over a short period of time also breaks down. As much as the findings may suggest that CAPM has some errors or is wrong, in the investment community the model is still widely used. Despite the fact that from beta, it is hard to make predictions on the reactions of the individual stocks to particular movements, , the investors can probably deduce safely that high-beta stocks portfolio will move in either direction more than the market, and the low beta stocks portfolio will move less than the market (Barenblat & Mesler, 2002).
Harrington & Harrington (2007) asserted that this is significant to the investors like the fund managers since they may be prevented or maybe unwilling to hold cash if they have a feeling that the market has a likelihood of falling. If it is that way, then they can opt for holding low beta stocks. Moreover, Wang & National Bureau of Economic Research. (2001) indicated that investors can tailor their portfolios to their risk return requirements that are specific, with an aim of holding securities with betas having excess of 1 when the market is rising, and when the marketing is falling with the securities with less than one betas.
Moreover, CAPM should still be used because of its contribution to the rise of indexing usage. That is assembling a shares portfolios that mimic a specific market by the risk averse investors (Harrington, 2003).
In conclusion, it is true that CAPM is not a perfect theory, buts its spirit is correct. CAPM provides investors with a usable risk measure that assist investors in determining the return they deserve for investing and risking their money.
References
Barenblat, S. G., & Mesler, D. T. (2002). Stock index options: How to use and profit from indexed options in volatile & uncertain markets. Chicago, Ill: Probus Pub. Co.
Harrington, D. R. (2003). Modern portfolio theory and the capital asset pricing model: A user’s guide. Englewood Cliffs, N.J: Prentice-Hall.
Harrington, D. R., & Harrington, D. R. (2007). Modern portfolio theory, the capital asset pricing model, and arbitrage pricing theory: A user’s guide. Englewood Cliffs, N.J: Prentice-Hall.
Hassett, S. D. (2011). The risk premium factor: A new model for understanding the volatile forces that drive stock prices. Hoboken, N.J: John Wiley & Sons.
Sincere, M. (2004). Understanding stocks. New York: McGraw-Hill.
Wang, J., & National Bureau of Economic Research. (2001). Trading volume: Implications of an intertemporal capital asset pricing model. Cambridge, MA: National Bureau of Economic Research.