ASX Portfolios

Executive summary
The report presents the analysis which is related to the risk and expected return of share portfolios of two stocks from the ASX in Australia. There are two approaches which refer to Mean-Variance and CAPM model to be applied in the analysis of the portfolios in this report. The two stocks which construct the portfolio are Asia Pacific Holdings Limited (AXA) and Caltex Australia Limited (CTX).Each stock occupies a certain proportion in one portfolio and their weights are varied in different portfolios. The rule of the portfolio construction is basis on varying the weights of each portfolio at 2.5% intervals. Then through the calculations and theoretical research which is related to the two approaches, the recommendation can
be illustrated to the investors who desire to invest the portfolio of the two stocks. The report consists of 5 sections, which are:
● The Introduction of the two model
● Justify the selection of data which refer to the share prices of the two companies and the relevant data which satisfy the condition of the calculation under the two approaches.
● Calculation ● The Calculation which is relevant to Mean-Variance model ● The Calculation which is relevant to CAPM model
● Analyze the two models on the basis of their assumptions and present the criticisms of two models.
● The Recommendation for investors

1. Introduction ● Mean-Variance Approach
The classical mean-variance approach was presented by Harry Markowitz is the first systematic treatment of a dilemma which is how to balance the high profit and low risk; meanwhile, it is also the first quantitative treatment of the tradeoff between profit and risk in the analysis of the selection of optimum stock portfolios (Steinbach, (2001)). The theory recognizes that the expected return of an asset can be estimated by the average of its one period returns, namely mean return and the total risk can be estimated by the standard deviation of these returns. Through the estimation of mean return and the standard deviation, the efficient portfolios which are the subset of minimum variance portfolios possessing the highest return for a certain level of risk can be found (Frino, (2009)). In other words, the efficient portfolios includes two meanings which is it provides each expected return with the minimum variance and it maximize the expected return for a given variance, respectively. Britten Jones (1999) illustrates that this approaches plays a pivotal role in the application of portfolio management and it is the basis of a multitude of asset pricing theories, such as CAPM (P.G.Cédric, M.Victoria-Fese, (2004)).

● CAPM Approach
This approach reflects a liner relationship between the expected return of one asset and the premium of market risk. The relationship can be expressed as a linear equation in which the slope is Beta and the intercept is the risk-free rate (Brailsford, (1997)).The application of CAPM approach is based on a series of assumptions, in spite of some criticism of this model which stems form its assumptions (Roll 1977, Fama and French 1992), it is still more prevail in the investment domain (Brailsford, (1997)).

2. Justify the selection of the data under the two approaches. ● The time period and the return internal
In order to get more precise and reliable results, it is necessary to base calculations on a long estimated period with enough observations. However this can be offset by the fact that the firm itself may change its characteristics over that period (Damodaran, (1999)). A short period with more frequent sampling interval was used to resolve this problem, but meanwhile this could bring the bias in estimation of beta due to the non-trading on an asset. The non-trading on an asset during the return period can reduce the correlation with the market index, and consequently with the beta estimates which can be more significantly affected using daily and weekly returns intervals (Damodaran, (1999)). In this report, monthly data for recent five years period (March 2005 to March 2010) are chosen as it is a relatively good reconciliation “between the needs for a sufficiently large sample to obtain reliable statistical estimates and the use of recent data which has relevance to the period over which the beta estimate is to be applied”(Brailsford, (1997). ● The Choice of Market Index
In terms of CAPM model, the estimation of beta needs the market portfolio which contains all shares that are available to investor (Frino, (2009)). Practically, market indices are used as a proxy for the market portfolio as there is no single index can fully included all risky assets in existence. The market portfolio indicated the general rule for choosing the indices that “the indices that include more securities should provide better estimates than that include less, and the indices are value-weighted should yield better estimates than that is not” (Damodaran, (1999)). The most popular Australian share market index is the All Ordinaries Index (AOI), which measured the changes in the price of shares on the Australia Securities Exchange (ASX). However, the AOI did not fully reflect the change in the wealth of shareholders as it did not take the dividends paid to share holders into account (Frino, (2009)). “Hence, the accumulation indices are preferred than price index because a more accurate measure of total return” (Brailsford, (1997)). The S&P/ASX 200 covers the first 200 securities listed on the ASX and represents 80% of ASX market capitalization. It has become the benchmark accumulation index since the advent (Frino, (2009)).Based on the consideration above, S&P/ASX 200 Accumulation Index (Value-weighted) is chosen in this paper to calculate beta as AXA and CTX are on the top 200 companies listed on the ASX. ● The Choice of risk free asset
Ten-year bonds are chosen to be the risk free assets here. It was theoretically considered to be the risk free as the government guarantee the rate of the return to the investors who hold them to maturity. Actually, in practice the government bonds were only free of default risk but did subject to the inflation risk and interest rate risk. It is high likely that the 10-year bonds cover one or more interest rate changes due to its long-term holding maturity (Frino, (2009)).
3. Calculations ● 3.1 Mean Variance Approach ● The Calculation of individual stock expected return
The stocks expected returns are using the average return of all 60 monthly returns, in this case, the monthly expected returns for AXA and CTX are 1.42% and 0.29%, respectively. ● The Calculation of standard deviation of each stock
Under assumptions of random process that generated returns both in the past and the future, and the representation of an observed set of historical returns is a random draw from an underlying distribution of returns (Frino, (2009)). The standard deviation is calculated from the 60 monthly returns, for AXA it is 9.4648789% and for CTX it is 10.7818112%. ● The Calculation of portfolio return/risk combination
“The key principle of the mean-variance model is to use the expected return of a portfolio as the investment return and to use the variance of returns of the portfolio as the investment risk .Portfolio selection is concerned with the problem of allocating one’s wealth among alternative securities such that the investment goal can be achieved”(Zhang,(2007)).In order to obtain the portfolio return, the covariance of the monthly return of the two stocks should be calculated firstly(detail of calculation in appendix 2) ● The Graph of the portfolio combination
[pic]
Figure 1
As can be seen form the graph, the efficient portfolios which possess the minimum variance and maximize return at each level of risk are the curve above the global minimum portfolios which possesses the lowest risk (denoted with ) (Frino, (2009)). Figure 1 reveals the levels of risk and returns are various owing to the different proportions of AXA and CTX in portfolios. And the figure 1 also indicates that there are some portfolios of which risk are lower than the risk of either investing AXA or CTX separately. It benefits from the diversification of portfolios; the risk can be reduced through the combination of investing in two stocks (P.G.Cédric, M.Victoria-Fese, (2004)). ● 3.2 CAPM model. ● The Calculation of Beta for each stock
According to the CAPM, the quantity of market risk is measured by beta which is defined by the covariance of the asset’s return with the market return divided by the variance of the market return. In this report, the excess return which is equal to the raw return less the return on risk free asset was used to match the scenario of the CPAM. The beta estimates from the excess return should be same as the one from the raw return if the rate of the risk free asset is constant, and this would not give an apparent advantage in estimating the beta unless the volatility of the rate of risk free asset is great (Brailsford, (1997)). Referred to the appendix (3), the beta of AXA is 1.138425255 which means the risk of investment in AXA is slightly aggressive than the market risk whilst the beta of CTX is 0.916153928 which indicates a slightly passive response to the movement of the market. ● The Calculation of individual stock returns.
The CAPM illustrates that the expected return of one asset is equal to the return of the risk free asset plus the risk premium. The risk premium can be explained by the product of the quantity of risk which known as beta and the market risk premium (Frino, (2009)). According to the Appendix (3) ,The return of risk free asset was calculated by using the average of the monthly 10-year bonds yield (0.004633551) from March 2005 to March 2010 as it gives the a more stable insight over the past to apply in future. The risk premium was calculated by the average of 5 years monthly excess index return (0.002911401). With the application of the formula E(Ri) = Rf +β*E(Rm-Rf), the expected return with respect to AXA and CTX are 0.007947964 and 0.007300843. Nevertheless, the prediction would be valid only if the historical data is relevant and provide the better forecast of the future performance. ● The Calculation of portfolio return/risk combination
A series of portfolios of AXA and CTX by varying the weights of each at 2.5% intervals were constructed to reveal the relationship between the expected return and the beta. The Expected return and beta of each constructed portfolio was determined by the weight of those of the two stocks that make up the portfolio (The details are showed in Appendix 4). As shown in graph of the portfolio combinations, the Expected returns of the portfolios is positive related to the market risk and fluctuate within the range of merely investing in either of the stock that make up the portfolio (from 0.007300843 to 0.007947964) as the holding proportion of the two different stocks changes. ● Graph of the portfolio combinations
[pic]
Figure 2
4. Analysis of the two models ● Mean-Variance Approach:
In order to apply the mean-variance approach to select portfolio effectively, the assumptions of this approach should be recognized precisely. ● The Assumptions of Mean-Variance Approach:
1. The fundamental assumption refers to this approach is that the selection of stocks portfolio by investors only depend on the expected return and standard deviation of returns on shares, which amounts to no other factors should be taken into account in deciding which portfolio of stocks can be held(Frino, (2009)).
2. The M-V criterion relies on the normal distribution assumption of return, thereby expressing the future return outcome of assets only depend on the mean return and standard deviation (Levy, (2010)).
3. The establishment of optimum portfolio through this approach is based on the assumption which is the investors desire to obtain the maximum of their returns for any level of risk that can be accepted (Frino, (2009)).
4. This approach should satisfy the condition that all investors have a one period time horizon, which means this theory is based on one single period analysis (Lackman (1996)). ●The Criticisms of the Mean-Variance Approach
1. Firstly, the one drawback is that the approach depends on normal distribution assumption. But, in terms of almost all cases in share market, the normal distribution of the rates of return is invalid which is proved by the null hypothesis (Levy, (2010)). Owing to this reason, the application of Mean-Variance approach for choosing the best portfolio in stock market is inaccurate.
2. Secondly, the calculation of standard deviation in this model depends on the assumption which is the random processes are the same in terms of generating returns in the past and in the future(Frino, (2009)),which amounts the past return indicate the future return. But in fact, this assumption is not valid in the real stock market because the there is systematic risk in the share market. For example, the global financial crisis in the period of 2008 is a special systematic risk in which the data of stock return could not be as an indicator to the future return. ● CAPM Approach: ● The Assumptions of CAPM Approach:
1. CAPM indicated that a rational investor will only face the systematic risk as the unsystematic risk can be diversified by holding portfolio, and the return can only be acquired in facing the systematic risk.
2. This model should meet the requirement of maximizing the expected return with a quadratic preference and satisfy the condition of normal distribution of return and risk aversion (Levy, (2010)).
3. In order to guarantee equilibrium, the relationship between share and Beta must be positive and the share return is only affected by the Beta (Frino, (2009)).
4. The investors can borrow or lend capital at riskless rate (Lackman (1996)).
5. All investments in the market are infinitely divisible, which amounts to the investors can possess any part of one security in portfolio (Lackman (1996)).
6. There is no tax and transaction fee in the process of investment (Lackman (1996)).
7. Homogeneous expectations, that is, all investors have the same expectation of the level of risk and the expected return of the portfolios of stocks (Lackman (1996)).
8. All investors are rational; thereby seeking the efficient frontier and or the information which is related to the market and have influence on the investments are available to every investors in order to assure the capital market is in equilibrium (Lackman (1996)). ● The Criticisms of the CAPM Approach
1. The model relies on the assumption of normal distribution of the return, but in the real stock market the returns of the assets are not normally distributed. Some return distributions of assets are skewness and large swings ().
2. In the mean-variance efficient set, it is observed that some of the investment weights of the tangency portfolios of stocks are negative (Levy, (2010)).This phenomenon cannot satisfy the CAPM assumption since all the investment weights of the tangency portfolios must all be positive (Levy, (2010)).
3. This model indicates that the Beta is the only element to evaluate the risk of one assets and explain their returns, but in some case Beta cannot possess the adequate power to give the explanation of the variation in mean return, namely Beta cannot measure the risk completely(Levy, (2010)).
4. In fact, every investor could not share the whole information in the stock market and the extent to which they accept the expected return and risk of all assets varies from person to person, which objects the homogeneous expectations assumption.
5. In the real stock market, the investors should pay for the transaction fee and tax which are the compulsory payment, which has a conflict with the CAPM assumption.
6. This model suffers form some empirical problems because it is difficult to test this model in real stock market; meanwhile these empirical problems reflect the theoretical failings. For instance, the CAPM illustrates that the risk of a stock should be measured relative to a comprehensive market portfolio which consists of not just traded financial assets, but also consumer durables, real estate and human capital (Fama and French, (2004)). And in fact, some other asserts are very difficult to measure precisely, such as human capital.

5. Recommendation
It can be seen form the above that there are some differences between Mean-variance approach and CAPM model in terms of evaluating the risk and expected return of one assets and both the two models have limitations. The main difference between the two models is that Mean-variance approach only focus on the performance of company itself while CAPM illustrates the relationship between the performance of one company and the whole market.

In terms of CAPM model, Beta represents the risk of investing in one share or in portfolio and it has a positive relationship with the expected return of one share or portfolio.
In other words, the higher return matches the higher Beta. Therefore, under the CAPM approach, there is no best recommendation which can help investors to gain the best selection of the portfolio of the stocks. In respect of the portfolios in which AXA shares and CTX shares occupied with different proportions, the range of Beta is from 0.916153928 to 1.138425255 which matches the scope of the expected return from 0.7301% to 0.7948%.The selection of optimum portfolio for each investor is diverse, it depends on the extent to which the level of risk and expected return are accepted by every investor. For example, if an investor who desire the highest returns and does not care about the risk from the portfolio of the two stocks, the portfolio in which AXA occupies 100% and CTX accounts for 0% should be chose because it possesses the highest
return.

In terms of Mean-variance approach, if the investors wish to minimize the risk of investment, the portfolio which possesses the lowest standard deviation should be selected. For the portfolios which are analyzed in this report, the portfolio in which AXA occupies 57.5% and CTX accounts for 42.5% should be recommended to the investors because its standard deviation is 0.072294206 which is lowest one of the whole portfolios. Additionally, its expected return is 0.94% which is not the lowest one of the whole portfolios.

Comparing the two models, the Mean-variance approach should prior to be recommended to investors in terms of evaluating the future performance of shares because on the basis of the definition of efficient portfolios, the higher return could not be matched to the higher risk, which amounts to the investors can obtain higher return with lower risk. In contrast, for CAPM model, the higher return matches the higher risk, which makes no material recommendation to investor. And one of the assumptions of CAPM which is no transaction fee and tax fee could not occur in any stock market.

The investors also can combine the two models to decide the investment in AXA and CTX. Specifically, using Mean-variance approach to obtain the set of efficient portfolio firstly; then calculate the Beta of the portfolios in the efficient frontier, each portfolio possesses the different proportion of the two stocks and the diverse Beta. The portfolio in the efficient frontier which has the lower beta can be chose because it has the lowest systematic risk and the unsystematic risk is also reduced through investing portfolios, meanwhile it has the maximum expected return in the level of risk.

References:
A. Damodaran,1999, “Estimating risk parameters.” Stern School of Business.

Cédric Perret-Gentila , Maria-Pia Victoria-Feserb,2004, Robust Mean-Variance Portfolio Selection

Wei-Guo Zhang , Ying-Luo Wang , Zhi-Ping Chen , Zan-Kan Nie; Positivistic mean–variance models and efficient frontiers for portfolio selection problem; Information Sciences 177 (2007) 2787–2801

Marc C.
Steinbach, 2001, Markowitz Revisited: Mean-Variance Models in Financial Portfolio Analysis, SIAM Review, Vol.43 no.1, pp31-85

Alex Frino, Amelia Hill, Zhian Chen, 2009, Introduction to Corporate Finance, 4th edition, Pearson Education Australia
Haim Levy, 2010, The CAPM is Alive and Well: A Review and Synthesis, European Financial Management, Vol. 16 no. 1, 2010, pp 43-71

Conway L. Lackman, 1996, Exchange Risk: A Capital Asset Pricing Model Frame- work, Journal of Financial and Strategic Decisions Vol.9 no.1

Timothy J. Brailsford, Robert W. Faff, Barry Oliver, 1997, Research Design Issues in the Estimation of Beta, Vol.1

Fama, EF, and French KR,1992, The Cross-Section of Expected Stock Returns.” Journal of Finance, Vol 47,pp427-465.

Fama, EF, French KR, 2004, The Capital Asset Pricing Model: Theory and Evidence, Journal of Economic Perspectives, Vol 18 no 3, pp
25-46

Appendices
Appendix 1-- Calculation of the expected return and standard deviation under Mean Variance Approach
AXA:
|Month end(t) |Share Price of |Dividend paid per share of AXA |Monthly Return of |
| |AXA (p) |(d) |AXA |
|03/2005 |4.2 |0.065 | |
|04/2005 |4.29 | |0.021428571 |
|05/2005 |4.64 | |0.081585082 |
|06/2005 |4.38 | |-0.056034483 |
|07/2005 |4.47 | |0.020547945 |
|08/2005 |4.93 | |0.102908277 |
|09/2005 |4.86 |0.0625 |-0.001521298 |
|10/2005 |4.73 | |-0.026748971 |
|11/2005 |5.08 | |0.073995772 |
|12/2005 |5.08 | |0 |
|01/2006 |5.45 | |0.072834646 |
|02/2006 |5.85 | |0.073394495 |
|03/2006 |5.8 |0.0775 |0.004700855 |
|04/2006 |6.3 | |0.086206897 |
|05/2006 |5.96 | |-0.053968254 |
|06/2006 |6.27 | |0.052013423 |
|07/2006 |6.35 | |0.012759171 |
|08/2006 |6.55 |0.075 |0.043307087 |
|09/2006 |6.5 | |-0.007633588 |
|10/2006 |6.66 | |0.024615385 |
|11/2006 |6.56 | |-0.015015015 |
|12/2006 |7.29 | |0.111280488 |
|01/2007 |7.22 | |-0.009602195 |
|02/2007 |7.45 | |0.031855956 |
|03/2007 |7.22 |0.1125 |-0.015771812 |
|04/2007 |7.39 | |0.023545706 |
|05/2007 |7.7 | |0.041948579 |
|06/2007 |7.43 | |-0.035064935 |
|07/2007 |7.35 | |-0.01076716 |
|08/2007 |7.54 |0.0925 |0.038435374 |
|09/2007 |7.8 | |0.034482759 |
|10/2007 |8.16 | |0.046153846 |
|11/2007 |7.99 | |-0.020833333 |
|12/2007 |7.38 | |-0.076345432 |
|01/2008 |5.93 | |-0.196476965 |
|02/2008 |5.8 | |-0.021922428 |
|03/2008 |5.5 |0.13 |-0.029310345 |
|04/2008 |5.94 | |0.08 |
|05/2008 |5.28 | |-0.111111111 |
|06/2008 |4.68 | |-0.113636364 |
|07/2008 |4.5 | |-0.038461538 |
|08/2008 |5.19 |0.0925 |0.173888889 |
|09/2008 |5.03 | |-0.030828516 |
|10/2008 |4.4 | |-0.125248509 |
|11/2008 |4.5 | |0.022727273 |
|12/2008 |4.94 | |0.097777778 |
|01/2009 |4.73 | |-0.042510121 |
|02/2009 |3.08 | |-0.348837209 |
|03/2009 |3.4 |0.0925 |0.133928571 |
|04/2009 |3.9 | |0.147058824 |
|05/2009 |3.8 | |-0.025641026 |
|06/2009 |3.89 | |0.023684211 |
|07/2009 |4.25 | |0.092544987 |
|08/2009 |4.3 |0.0925 |0.033529412 |
|09/2009 |4.37 | |0.01627907 |
|10/2009 |4.24 | |-0.029748284 |
|11/2009 |5.8 | |0.367924528 |
|12/2009 |6.56 | |0.131034483 |
|01/2010 |6.57 | |0.00152439 |
|02/2010 |6.45 | |-0.01826484 |
|03/2010 |6.32 |0.0925 |-0.005813953 |

CTX:
|Month end(t) |Share Price of |Dividend paid per share of CTX |Monthly Return of |
| |CTX (p) |(d) |CTX |
|03/2005 |15.5 |0.25 | |
|04/2005 |14 | |-0.096774194 |
|05/2005 |15.1 | |0.078571429 |
|06/2005 |15.85 | |0.049668874 |
|07/2005 |17.62 | |0.111671924 |
|08/2005 |17.3 | |-0.01816118 |
|09/2005 |20.52 |0.15 |0.194797688 |
|10/2005 |20.32 | |-0.009746589 |
|11/2005 |21.2 | |0.043307087 |
|12/2005 |19.38 | |-0.085849057 |
|01/2006 |19.35 | |-0.001547988 |
|02/2006 |17.2 | |-0.111111111 |
|03/2006 |19.2 |0.31 |0.134302326 |
|04/2006 |20.15 | |0.049479167 |
|05/2006 |19.15 | |-0.049627792 |
|06/2006 |23.6 | |0.232375979 |
|07/2006 |24.39 | |0.033474576 |
|08/2006 |22.89 | |-0.061500615 |
|09/2006 |23.9 |0.32 |0.058103976 |
|10/2006 |22.15 | |-0.073221757 |
|11/2006 |22.15 | |0 |
|12/2006 |23 | |0.038374718 |
|01/2007 |21.75 | |-0.054347826 |
|02/2007 |22.33 | |0.026666667 |
|03/2007 |23.86 |0.48 |0.090013435 |
|04/2007 |24.24 | |0.015926236 |
|05/2007 |25.6 | |0.056105611 |
|06/2007 |23.67 | |-0.075390625 |
|07/2007 |24.98 | |0.055344318 |
|08/2007 |24.2 | |-0.03122498 |
|09/2007 |23.54 |0.47 |-0.00785124 |
|10/2007 |21.38 | |-0.091758709 |
|11/2007 |22.1 | |0.033676333 |
|12/2007 |19.37 | |-0.123529412 |
|01/2008 |15.79 | |-0.18482189 |
|02/2008 |14.8 | |-0.06269791 |
|03/2008 |13.01 |0.33 |-0.098648649 |
|04/2008 |12.02 | |-0.076095311 |
|05/2008 |14.95 | |0.243760399 |
|06/2008 |13.06 | |-0.126421405 |
|07/2008 |11.9 | |-0.088820827 |
|08/2008 |12.55 | |0.054621849 |
|09/2008 |12.35 |0.36 |0.012749004 |
|10/2008 |9.39 | |-0.239676113 |
|11/2008 |7.4 | |-0.211927583 |
|12/2008 |7.19 | |-0.028378378 |
|01/2009 |8.77 | |0.219749652 |
|02/2009 |9.4 | |0.071835804 |
|03/2009 |8.91 | |-0.05212766 |
|04/2009 |9.9 | |0.111111111 |
|05/2009 |11.97 | |0.209090909 |
|06/2009 |13.85 | |0.157059315 |
|07/2009 |13.03 | |-0.059205776 |
|08/2009 |12.37 | |-0.050652341 |
|09/2009 |12.11 | |-0.021018593 |
|10/2009 |10.26 | |-0.152766309 |
|11/2009 |9.72 | |-0.052631579 |
|12/2009 |9.3 | |-0.043209877 |
|01/2010 |8.99 | |-0.033333333 |
|02/2010 |10.5 | |0.167964405 |
|03/2010 |11.31 |0.25 |0.100952381 |

|Expected return |Standard deviation |Expected return |Standard deviation |
|of AXA |of AXA |of CTX |of CTX |
|0.014213084 |0.094648789 |0.002944643 |0.107818112 |

Formula:

Monthly rate of return [pic] (1)
Expected return:[pic] (2)
Standard deviation of returns [pic] (3)
Where: [pic] = the price of the stock at the end of period t; [pic]= the return on stock during interval t; [pic]= the dividend paid during period t; n= the number of available observations

Appendix 2—calculation of expected return and standard deviation of portfolios with various weights under Mean Variance Approach

|Portfolio Number |Portfolio in |Standard Deviation |Expected Return |
| |AXA |CTX | | |
|1 |1 |0 |0.094648789 |0.014213084 |
|2 |0.975 |0.025 |0.092410942 |0.013931373 |
|3 |0.95 |0.05 |0.090255509 |0.013649662 |
|4 |0.925 |0.075 |0.088188532 |0.013367951 |
|5 |0.9 |0.1 |0.086216374 |0.01308624 |
|6 |0.875 |0.125 |0.084345685 |0.012804529 |
|7 |0.85 |0.15 |0.082583363 |0.012522818 |
|8 |0.825 |0.175 |0.080936485 |0.012241107 |
|9 |0.8 |0.2 |0.079412235 |0.011959396 |
|10 |0.775 |0.225 |0.0780178 |0.011677685 |
|11 |0.75 |0.25 |0.076760255 |0.011395974 |
|12 |0.725 |0.275 |0.075646428 |0.011114263 |
|13 |0.7 |0.3 |0.074682749 |0.010832552 |
|14 |0.675 |0.325 |0.073875095 |0.010550841 |
|15 |0.65 |0.35 |0.073228627 |0.01026913 |
|16 |0.625 |0.375 |0.072747644 |0.009987419 |
|17 |0.6 |0.4 |0.072435441 |0.009705708 |
|18 |0.575 |0.425 |0.072294206 |0.009423996 |
|19 |0.55 |0.45 |0.07232494 |0.009142285 |
|20 |0.525 |0.475 |0.072527425 |0.008860574 |
|21 |0.5 |0.5 |0.072900228 |0.008578863 |
|22 |0.475 |0.525 |0.073440758 |0.008297152 |
|23 |0.45 |0.55 |0.074145345 |0.008015441 |
|24 |0.425 |0.575 |0.075009366 |0.00773373 |
|25 |0.4 |0.6 |0.076027387 |0.007452019 |
|26 |0.375 |0.625 |0.077193314 |0.007170308 |
|27 |0.35 |0.65 |0.078500557 |0.006888597 |
|28 |0.325 |0.675 |0.079942184 |0.006606886 |
|29 |0.3 |0.7 |0.081511066 |0.006325175 |
|30 |0.275 |0.725 |0.083200003 |0.006043464 |
|31 |0.25 |0.75 |0.08500184 |0.005761753 |
|32 |0.225 |0.775 |0.086909555 |0.005480042 |
|33 |0.2 |0.8 |0.088916333 |0.005198331 |
|34 |0.175 |0.825 |0.091015622 |0.00491662 |
|35 |0.15 |0.85 |0.093201171 |0.004634909 |
|36 |0.125 |0.875 |0.095467055 |0.004353198 |
|37 |0.1 |0.9 |0.097807692 |0.004071487 |
|38 |0.075 |0.925 |0.100217845 |0.003789776 |
|39 |0.05 |0.95 |0.102692618 |0.003508065 |
|40 |0.025 |0.975 |0.105227452 |0.003226354 |
|41 |0 |1 |0.107818112 |0.002944643 |

|Covariance |
|0.000337317 |

Formula:
Covariance: [pic] (1)

Expected returns of each portfolio [pic] (2)

Variance of returns on a two-security portfolio: [pic] (3)
Where: [pic], [pic]= proportion of the portfolio invested in ATX and CTX ; [pic]= expected return on ATX and CTX [pic]= the standard deviation of ATX and CTX; [pic]= the covariance of ATX and CTX

Appendix 3—Calculation of Beta of ATX and CTX

AXA:
|Month end(t) |Share Price of |S&P/ASX 200 |10-year bond yield (%) |Dividend paid per |
| |AXA (p) |Accumulation Index | |share of AXA (d) |
|03/2005 |4.2 |23373 |5.65 |0.065 |
|04/2005 |4.29 |22664 |5.47 | |
|05/2005 |4.64 |23413 |5.29 | |
|06/2005 |4.38 |24534 |5.14 | |
|07/2005 |4.47 |25173 |5.19 | |
|08/2005 |4.93 |25678 |5.22 | |
|09/2005 |4.86 |26982 |5.19 |0.0625 |
|10/2005 |4.73 |25943 |5.40 | |
|11/2005 |5.08 |27108 |5.44 | |
|12/2005 |5.08 |27943 |5.35 | |
|01/2006 |5.45 |28918 |5.20 | |
|02/2006 |5.85 |29087 |5.27 | |
|03/2006 |5.8 |30467 |5.34 |0.0775 |
|04/2006 |6.3 |31246 |5.58 | |
|05/2006 |5.96 |29776 |5.75 | |
|06/2006 |6.27 |30405 |5.74 | |
|07/2006 |6.35 |29882 |5.83 | |
|08/2006 |6.55 |30878 |5.77 |0.075 |
|09/2006 |6.5 |31288 |5.60 | |
|10/2006 |6.66 |32719 |5.67 | |
|11/2006 |6.56 |33476 |5.60 | |
|12/2006 |7.29 |34711 |5.70 | |
|01/2007 |7.22 |35345 |5.88 | |
|02/2007 |7.45 |35921 |5.81 | |
|03/2007 |7.22 |37104 |5.74 |0.1125 |
|04/2007 |7.39 |38177 |5.91 | |
|05/2007 |7.7 |39185 |5.92 | |
|06/2007 |7.43 |39119 |6.20 | |
|07/2007 |7.35 |38304 |6.15 | |
|08/2007 |7.54 |39241 |5.93 |0.0925 |
|09/2007 |7.8 |41424 |5.99 | |
|10/2007 |8.16 |42624 |6.17 | |
|11/2007 |7.99 |41417 |6.03 | |
|12/2007 |7.38 |40291 |6.21 | |
|01/2008 |5.93 |35920 |6.08 | |
|02/2008 |5.8 |35674 |6.29 | |
|03/2008 |5.5 |34492 |6.09 |0.13 |
|04/2008 |5.94 |36055 |6.17 | |
|05/2008 |5.28 |36605 |6.36 | |
|06/2008 |4.68 |33875 |6.59 | |
|07/2008 |4.5 |32330 |6.37 | |
|08/2008 |5.19 |33652 |5.86 |0.0925 |
|09/2008 |5.03 |30339 |5.65 | |
|10/2008 |4.4 |26515 |5.22 | |
|11/2008 |4.5 |24870 |4.94 | |
|12/2008 |4.94 |24801 |4.22 | |
|01/2009 |4.73 |23592 |4.09 | |
|02/2009 |3.08 |22513 |4.25 | |
|03/2009 |3.4 |24310 |4.33 |0.0925 |
|04/2009 |3.9 |25664 |4.51 | |
|05/2009 |3.8 |26012 |5.00 | |
|06/2009 |3.89 |27054 |5.56 | |
|07/2009 |4.25 |29032 |5.49 | |
|08/2009 |4.3 |30940 |5.53 |0.0925 |
|09/2009 |4.37 |32870 |5.32 | |
|10/2009 |4.24 |32186 |5.45 | |
|11/2009 |5.8 |32760 |5.47 | |
|12/2009 |6.56 |33986 |5.47 | |
|01/2010 |6.57 |31886 |5.56 | |
|02/2010 |6.45 |32576 |5.48 | |
|03/2010 |6.32 |34449 |5.62 |0.0925 |

|Month end(t) |Stock Return of |Index return (Rm,t) |Monthly bond return (Rf,t)|
| |AXA (Ri,t) | | |
|03/2005 | | | |
|04/2005 |0.021428571 |-0.030334146 |0.00456 |
|05/2005 |0.081585082 |0.033048006 |0.004406439 |
|06/2005 |-0.056034483 |0.047879383 |0.00428373 |
|07/2005 |0.020547945 |0.026045488 |0.004325198 |
|08/2005 |0.102908277 |0.020061177 |0.004348913 |
|09/2005 |-0.001521298 |0.050782771 |0.00432197 |
|10/2005 |-0.026748971 |-0.038507153 |0.004500198 |
|11/2005 |0.073995772 |0.04490614 |0.004529356 |
|12/2005 |0 |0.030802715 |0.004455417 |
|01/2006 |0.072834646 |0.03489246 |0.00433625 |
|02/2006 |0.073394495 |0.005844111 |0.004393333 |
|03/2006 |0.004700855 |0.047443875 |0.004451087 |
|04/2006 |0.086206897 |0.025568648 |0.004649755 |
|05/2006 |-0.053968254 |-0.047046022 |0.004791667 |
|06/2006 |0.052013423 |0.021124395 |0.004781548 |
|07/2006 |0.012759171 |-0.017201118 |0.004861706 |
|08/2006 |0.043307087 |0.033331102 |0.004811051 |
|09/2006 |-0.007633588 |0.013278062 |0.004668056 |
|10/2006 |0.024615385 |0.045736385 |0.004720833 |
|11/2006 |-0.015015015 |0.023136404 |0.004666288 |
|12/2006 |0.111280488 |0.036892102 |0.004747149 |
|01/2007 |-0.009602195 |0.018265103 |0.004898016 |
|02/2007 |0.031855956 |0.016296506 |0.004841042 |
|03/2007 |-0.015771812 |0.032933382 |0.004780682 |
|04/2007 |0.023545706 |0.028918715 |0.004924769 |
|05/2007 |0.041948579 |0.026403332 |0.004934058 |
|06/2007 |-0.035064935 |-0.001684318 |0.005170625 |
|07/2007 |-0.01076716 |-0.020833866 |0.005124811 |
|08/2007 |0.038435374 |0.024462197 |0.004938258 |
|09/2007 |0.034482759 |0.05563059 |0.004993421 |
|10/2007 |0.046153846 |0.028968714 |0.00514529 |
|11/2007 |-0.020833333 |-0.02831738 |0.005021212 |
|12/2007 |-0.076345432 |-0.027186904 |0.005173026 |
|01/2008 |-0.196476965 |-0.108485766 |0.00506369 |
|02/2008 |-0.021922428 |-0.006848552 |0.005245437 |
|03/2008 |-0.029310345 |-0.033133374 |0.005071272 |
|04/2008 |0.08 |0.045314856 |0.005142063 |
|05/2008 |-0.111111111 |0.015254472 |0.005295833 |
|06/2008 |-0.113636364 |-0.074579975 |0.005488958 |
|07/2008 |-0.038461538 |-0.045608856 |0.005305435 |
|08/2008 |0.173888889 |0.040890813 |0.004885417 |
|09/2008 |-0.030828516 |-0.098448829 |0.004704924 |
|10/2008 |-0.125248509 |-0.126042388 |0.004346023 |
|11/2008 |0.022727273 |-0.062040355 |0.004117292 |
|12/2008 |0.097777778 |-0.002774427 |0.003513095 |
|01/2009 |-0.042510121 |-0.048748034 |0.003404792 |
|02/2009 |-0.348837209 |-0.045735843 |0.003544167 |
|03/2009 |0.133928571 |0.079820548 |0.003606439 |
|04/2009 |0.147058824 |0.055697244 |0.00376 |
|05/2009 |-0.025641026 |0.01355985 |0.004170238 |
|06/2009 |0.023684211 |0.040058435 |0.004630556 |
|07/2009 |0.092544987 |0.073113033 |0.004573188 |
|08/2009 |0.033529412 |0.065720584 |0.004611042 |
|09/2009 |0.01627907 |0.062378798 |0.004436364 |
|10/2009 |-0.029748284 |-0.020809249 |0.004541865 |
|11/2009 |0.367924528 |0.017833841 |0.004555556 |
|12/2009 |0.131034483 |0.037423687 |0.004560913 |
|01/2010 |0.00152439 |-0.061790149 |0.004633333 |
|02/2010 |-0.01826484 |0.021639591 |0.004566667 |
|03/2010 |-0.005813953 |0.057496316 |0.004683333 |

|Month end(t) |Excess stock return(Y) |Excess index return(X) |Y-Y ' |X-X ' |(Y-Y ')*(X-X ') |
|03/2005 | | | | | |
|04/2005 |0.016868571 |-0.034894146 |0.00728904 |-0.0378055 |-0.0002756 |
|05/2005 |0.077178642 |0.028641566 |0.06759911 |0.02573016 |0.00173934 |
|06/2005 |-0.060318213 |0.043595653 |-0.0698977 |0.04068425 |-0.0028437 |
|07/2005 |0.016222747 |0.021720289 |0.00664321 |0.01880889 |0.00012495 |
|08/2005 |0.098559364 |0.015712264 |0.08897983 |0.01280086 |0.00113902 |
|09/2005 |-0.005843268 |0.046460802 |-0.0154228 |0.0435494 |-0.0006717 |
|10/2005 |-0.03124917 |-0.043007351 |-0.0408287 |-0.0459188 |0.0018748 |
|11/2005 |0.069466416 |0.040376784 |0.05988688 |0.03746538 |0.00224368 |
|12/2005 |-0.004455417 |0.026347298 |-0.0140349 |0.0234359 |-0.0003289 |
|01/2006 |0.068498396 |0.03055621 |0.05891886 |0.02764481 |0.0016288 |
|02/2006 |0.069001162 |0.001450778 |0.05942163 |-0.0014606 |-8.679E-05 |
|03/2006 |0.000249768 |0.042992788 |-0.0093298 |0.04008139 |-0.0003739 |
|04/2006 |0.081557142 |0.020918893 |0.07197761 |0.01800749 |0.00129614 |
|05/2006 |-0.058759921 |-0.051837689 |-0.0683395 |-0.0547491 |0.00374152 |
|06/2006 |0.047231875 |0.016342848 |0.03765234 |0.01343145 |0.00050573 |
|07/2006 |0.007897464 |-0.022062825 |-0.0016821 |-0.0249742 |4.2008E-05 |
|08/2006 |0.038496036 |0.028520052 |0.0289165 |0.02560865 |0.00074051 |
|09/2006 |-0.012301643 |0.008610006 |-0.0218812 |0.00569861 |-0.0001247 |
|10/2006 |0.019894551 |0.041015551 |0.01031502 |0.03810415 |0.00039304 |
|11/2006 |-0.019681303 |0.018470116 |-0.0292608 |0.01555871 |-0.0004553 |
|12/2006 |0.106533339 |0.032144953 |0.09695381 |0.02923355 |0.0028343 |
|01/2007 |-0.014500211 |0.013367087 |-0.0240797 |0.01045569 |-0.0002518 |
|02/2007 |0.027014914 |0.011455464 |0.01743538 |0.00854406 |0.00014897 |
|03/2007 |-0.020552494 |0.0281527 |-0.030132 |0.0252413 |-0.0007606 |
|04/2007 |0.018620938 |0.023993946 |0.0090414 |0.02108255 |0.00019062 |
|05/2007 |0.037014521 |0.021469274 |0.02743499 |0.01855787 |0.00050914 |
|06/2007 |-0.04023556 |-0.006854943 |-0.0498151 |-0.0097663 |0.00048651 |
|07/2007 |-0.015891971 |-0.025958677 |-0.0254715 |-0.0288701 |0.00073536 |
|08/2007 |0.033497117 |0.01952394 |0.02391758 |0.01661254 |0.00039733 |
|09/2007 |0.029489338 |0.050637169 |0.0199098 |0.04772577 |0.00095021 |
|10/2007 |0.041008556 |0.023823424 |0.03142902 |0.02091202 |0.00065724 |
|11/2007 |-0.025854545 |-0.033338592 |-0.0354341 |-0.03625 |0.00128449 |
|12/2007 |-0.081518458 |-0.03235993 |-0.091098 |-0.0352713 |0.00321315 |
|01/2008 |-0.201540655 |-0.113549457 |-0.2111202 |-0.1164609 |0.02458724 |
|02/2008 |-0.027167865 |-0.012093989 |-0.0367474 |-0.0150054 |0.00055141 |
|03/2008 |-0.034381617 |-0.038204646 |-0.0439612 |-0.041116 |0.00180751 |
|04/2008 |0.074857937 |0.040172792 |0.0652784 |0.03726139 |0.00243236 |
|05/2008 |-0.116406944 |0.009958639 |-0.1259865 |0.00704724 |-0.0008879 |
|06/2008 |-0.119125322 |-0.080068934 |-0.1287049 |-0.0829803 |0.01067997 |
|07/2008 |-0.043766973 |-0.050914291 |-0.0533465 |-0.0538257 |0.00287141 |
|08/2008 |0.169003472 |0.036005397 |0.15942394 |0.033094 |0.00527598 |
|09/2008 |-0.035533441 |-0.103153753 |-0.045113 |-0.1060652 |0.00478491 |
|10/2008 |-0.129594532 |-0.13038841 |-0.1391741 |-0.1332998 |0.01855188 |
|11/2008 |0.018609981 |-0.066157646 |0.00903045 |-0.069069 |-0.0006237 |
|12/2008 |0.094264683 |-0.006287522 |0.08468515 |-0.0091989 |-0.000779 |
|01/2009 |-0.045914913 |-0.052152826 |-0.0554944 |-0.0550642 |0.00305576 |
|02/2009 |-0.352381376 |-0.049280009 |-0.3619609 |-0.0521914 |0.01889125 |
|03/2009 |0.130322132 |0.076214109 |0.1207426 |0.07330271 |0.00885076 |
|04/2009 |0.143298824 |0.051937244 |0.13371929 |0.04902584 |0.0065557 |
|05/2009 |-0.029811264 |0.009389612 |-0.0393908 |0.00647821 |-0.0002552 |
|06/2009 |0.019053655 |0.035427879 |0.00947412 |0.03251648 |0.00030807 |
|07/2009 |0.087971799 |0.068539845 |0.07839227 |0.06562844 |0.00514476 |
|08/2009 |0.02891837 |0.061109543 |0.01933884 |0.05819814 |0.00112548 |
|09/2009 |0.011842706 |0.057942434 |0.00226317 |0.05503103 |0.00012454 |
|10/2009 |-0.034290149 |-0.025351114 |-0.0438697 |-0.0282625 |0.00123987 |
|11/2009 |0.363368973 |0.013278285 |0.35378944 |0.01036688 |0.00366769 |
|12/2009 |0.12647357 |0.032862775 |0.11689404 |0.02995137 |0.00350114 |
|01/2010 |-0.003108943 |-0.066423482 |-0.0126885 |-0.0693349 |0.00087975 |
|02/2010 |-0.022831507 |0.017072924 |-0.032411 |0.01416152 |-0.000459 |
|03/2010 |-0.010497287 |0.052812983 |-0.0200768 |0.04990158 |-0.0010019 |

|mean return of ten-years bond |Y ' |X ' |
|0.004633551 |0.00958 |0.002911401 |

|Covariance(X,Y) |Variance(X) |β(AXA) |Expected return of AXA |
|0.002399742 |0.002107949 |1.138425255 |0.007947964 |

CTX
|Month end(t) |Share Price of |S&P/ASX 200 |10-year bond |Dividend paid per share of |
| |AXA (p) |Accumulation Index |yield (%) |CTX (d) |
|03/2005 |15.5 |23373 |5.65 |0.25 |
|04/2005 |14 |22664 |5.47 | |
|05/2005 |15.1 |23413 |5.29 | |
|06/2005 |15.85 |24534 |5.14 | |
|07/2005 |17.62 |25173 |5.19 | |
|08/2005 |17.3 |25678 |5.22 | |
|09/2005 |20.52 |26982 |5.19 |0.15 |
|10/2005 |20.32 |25943 |5.40 | |
|11/2005 |21.2 |27108 |5.44 | |
|12/2005 |19.38 |27943 |5.35 | |
|01/2006 |19.35 |28918 |5.20 | |
|02/2006 |17.2 |29087 |5.27 | |
|03/2006 |19.2 |30467 |5.34 |0.31 |
|04/2006 |20.15 |31246 |5.58 | |
|05/2006 |19.15 |29776 |5.75 | |
|06/2006 |23.6 |30405 |5.74 | |
|07/2006 |24.39 |29882 |5.83 | |
|08/2006 |22.89 |30878 |5.77 | |
|09/2006 |23.9 |31288 |5.60 |0.32 |
|10/2006 |22.15 |32719 |5.67 | |
|11/2006 |22.15 |33476 |5.60 | |
|12/2006 |23 |34711 |5.70 | |
|01/2007 |21.75 |35345 |5.88 | |
|02/2007 |22.33 |35921 |5.81 | |
|03/2007 |23.86 |37104 |5.74 |0.48 |
|04/2007 |24.24 |38177 |5.91 | |
|05/2007 |25.6 |39185 |5.92 | |
|06/2007 |23.67 |39119 |6.20 | |
|07/2007 |24.98 |38304 |6.15 | |
|08/2007 |24.2 |39241 |5.93 | |
|09/2007 |23.54 |41424 |5.99 |0.47 |
|10/2007 |21.38 |42624 |6.17 | |
|11/2007 |22.1 |41417 |6.03 | |
|12/2007 |19.37 |40291 |6.21 | |
|01/2008 |15.79 |35920 |6.08 | |
|02/2008 |14.8 |35674 |6.29 | |
|03/2008 |13.01 |34492 |6.09 |0.33 |
|04/2008 |12.02 |36055 |6.17 | |
|05/2008 |14.95 |36605 |6.36 | |
|06/2008 |13.06 |33875 |6.59 | |
|07/2008 |11.9 |32330 |6.37 | |
|08/2008 |12.55 |33652 |5.86 | |
|09/2008 |12.35 |30339 |5.65 |0.36 |
|10/2008 |9.39 |26515 |5.22 | |
|11/2008 |7.4 |24870 |4.94 | |
|12/2008 |7.19 |24801 |4.22 | |
|01/2009 |8.77 |23592 |4.09 | |
|02/2009 |9.4 |22513 |4.25 | |
|03/2009 |8.91 |24310 |4.33 | |
|04/2009 |9.9 |25664 |4.51 | |
|05/2009 |11.97 |26012 |5.00 | |
|06/2009 |13.85 |27054 |5.56 | |
|07/2009 |13.03 |29032 |5.49 | |
|08/2009 |12.37 |30940 |5.53 | |
|09/2009 |12.11 |32870 |5.32 | |
|10/2009 |10.26 |32186 |5.45 | |
|11/2009 |9.72 |32760 |5.47 | |
|12/2009 |9.3 |33986 |5.47 | |
|01/2010 |8.99 |31886 |5.56 | |
|02/2010 |10.5 |32576 |5.48 | |
|03/2010 |11.31 |34449 |5.62 |0.25 |

|Month end(t) |Stock Return of |Index return (Rm,t) |Monthly bond return (Rf,t) |
| |CTX (Ri,t) | | |
|03/2005 | | | |
|04/2005 |-0.096774194 |-0.030334146 |0.00456 |
|05/2005 |0.078571429 |0.033048006 |0.004406439 |
|06/2005 |0.049668874 |0.047879383 |0.00428373 |
|07/2005 |0.111671924 |0.026045488 |0.004325198 |
|08/2005 |-0.01816118 |0.020061177 |0.004348913 |
|09/2005 |0.194797688 |0.050782771 |0.00432197 |
|10/2005 |-0.009746589 |-0.038507153 |0.004500198 |
|11/2005 |0.043307087 |0.04490614 |0.004529356 |
|12/2005 |-0.085849057 |0.030802715 |0.004455417 |
|01/2006 |-0.001547988 |0.03489246 |0.00433625 |
|02/2006 |-0.111111111 |0.005844111 |0.004393333 |
|03/2006 |0.134302326 |0.047443875 |0.004451087 |
|04/2006 |0.049479167 |0.025568648 |0.004649755 |
|05/2006 |-0.049627792 |-0.047046022 |0.004791667 |
|06/2006 |0.232375979 |0.021124395 |0.004781548 |
|07/2006 |0.033474576 |-0.017201118 |0.004861706 |
|08/2006 |-0.061500615 |0.033331102 |0.004811051 |
|09/2006 |0.058103976 |0.013278062 |0.004668056 |
|10/2006 |-0.073221757 |0.045736385 |0.004720833 |
|11/2006 |0 |0.023136404 |0.004666288 |
|12/2006 |0.038374718 |0.036892102 |0.004747149 |
|01/2007 |-0.054347826 |0.018265103 |0.004898016 |
|02/2007 |0.026666667 |0.016296506 |0.004841042 |
|03/2007 |0.090013435 |0.032933382 |0.004780682 |
|04/2007 |0.015926236 |0.028918715 |0.004924769 |
|05/2007 |0.056105611 |0.026403332 |0.004934058 |
|06/2007 |-0.075390625 |-0.001684318 |0.005170625 |
|07/2007 |0.055344318 |-0.020833866 |0.005124811 |
|08/2007 |-0.03122498 |0.024462197 |0.004938258 |
|09/2007 |-0.00785124 |0.05563059 |0.004993421 |
|10/2007 |-0.091758709 |0.028968714 |0.00514529 |
|11/2007 |0.033676333 |-0.02831738 |0.005021212 |
|12/2007 |-0.123529412 |-0.027186904 |0.005173026 |
|01/2008 |-0.18482189 |-0.108485766 |0.00506369 |
|02/2008 |-0.06269791 |-0.006848552 |0.005245437 |
|03/2008 |-0.098648649 |-0.033133374 |0.005071272 |
|04/2008 |-0.076095311 |0.045314856 |0.005142063 |
|05/2008 |0.243760399 |0.015254472 |0.005295833 |
|06/2008 |-0.126421405 |-0.074579975 |0.005488958 |
|07/2008 |-0.088820827 |-0.045608856 |0.005305435 |
|08/2008 |0.054621849 |0.040890813 |0.004885417 |
|09/2008 |0.012749004 |-0.098448829 |0.004704924 |
|10/2008 |-0.239676113 |-0.126042388 |0.004346023 |
|11/2008 |-0.211927583 |-0.062040355 |0.004117292 |
|12/2008 |-0.028378378 |-0.002774427 |0.003513095 |
|01/2009 |0.219749652 |-0.048748034 |0.003404792 |
|02/2009 |0.071835804 |-0.045735843 |0.003544167 |
|03/2009 |-0.05212766 |0.079820548 |0.003606439 |
|04/2009 |0.111111111 |0.055697244 |0.00376 |
|05/2009 |0.209090909 |0.01355985 |0.004170238 |
|06/2009 |0.157059315 |0.040058435 |0.004630556 |
|07/2009 |-0.059205776 |0.073113033 |0.004573188 |
|08/2009 |-0.050652341 |0.065720584 |0.004611042 |
|09/2009 |-0.021018593 |0.062378798 |0.004436364 |
|10/2009 |-0.152766309 |-0.020809249 |0.004541865 |
|11/2009 |-0.052631579 |0.017833841 |0.004555556 |
|12/2009 |-0.043209877 |0.037423687 |0.004560913 |
|01/2010 |-0.033333333 |-0.061790149 |0.004633333 |
|02/2010 |0.167964405 |0.021639591 |0.004566667 |
|03/2010 |0.100952381 |0.057496316 |0.004683333 |

|Month end(t) |Excess stock |Excess index |Y-Y ' |X-X ' |(Y-Y ')*(X-X ') |
| |return(Y) |return(X) | | | |
|03/2005 | | | | | |
|04/2005 |-0.101334194 |-0.034894146 |-0.099645286 |-0.037805548 |0.003767145 |
|05/2005 |0.074164989 |0.028641566 |0.075853897 |0.025730165 |0.001951733 |
|06/2005 |0.045385144 |0.043595653 |0.047074052 |0.040684252 |0.001915173 |
|07/2005 |0.107346726 |0.021720289 |0.109035634 |0.018808888 |0.002050839 |
|08/2005 |-0.022510094 |0.015712264 |-0.020821186 |0.012800862 |-0.000266529 |
|09/2005 |0.190475718 |0.046460802 |0.192164626 |0.0435494 |0.008368654 |
|10/2005 |-0.014246787 |-0.043007351 |-0.012557879 |-0.045918753 |0.000576642 |
|11/2005 |0.038777731 |0.040376784 |0.040466639 |0.037465383 |0.001516098 |
|12/2005 |-0.090304473 |0.026347298 |-0.088615565 |0.023435897 |-0.002076785 |
|01/2006 |-0.005884238 |0.03055621 |-0.00419533 |0.027644808 |-0.000115979 |
|02/2006 |-0.115504444 |0.001450778 |-0.113815536 |-0.001460624 |0.000166242 |
|03/2006 |0.129851239 |0.042992788 |0.131540147 |0.040081387 |0.005272312 |
|04/2006 |0.044829412 |0.020918893 |0.04651832 |0.018007492 |0.000837678 |
|05/2006 |-0.054419458 |-0.051837689 |-0.05273055 |-0.05474909 |0.00288695 |
|06/2006 |0.227594431 |0.016342848 |0.229283339 |0.013431446 |0.003079607 |
|07/2006 |0.02861287 |-0.022062825 |0.030301778 |-0.024974226 |-0.000756763 |
|08/2006 |-0.066311666 |0.028520052 |-0.064622758 |0.02560865 |-0.001654902 |
|09/2006 |0.05343592 |0.008610006 |0.055124828 |0.005698605 |0.000314135 |
|10/2006 |-0.077942591 |0.041015551 |-0.076253683 |0.03810415 |-0.002905582 |
|11/2006 |-0.004666288 |0.018470116 |-0.00297738 |0.015558715 |-4.63242E-05 |
|12/2006 |0.033627569 |0.032144953 |0.035316477 |0.029233551 |0.001032426 |
|01/2007 |-0.059245842 |0.013367087 |-0.057556934 |0.010455686 |-0.000601797 |
|02/2007 |0.021825625 |0.011455464 |0.023514533 |0.008544063 |0.00020091 |
|03/2007 |0.085232753 |0.0281527 |0.086921661 |0.025241298 |0.002194016 |
|04/2007 |0.011001468 |0.023993946 |0.012690376 |0.021082545 |0.000267545 |
|05/2007 |0.051171553 |0.021469274 |0.052860461 |0.018557872 |0.000980978 |
|06/2007 |-0.08056125 |-0.006854943 |-0.078872342 |-0.009766344 |0.000770294 |
|07/2007 |0.050219507 |-0.025958677 |0.051908415 |-0.028870078 |-0.0014986 |
|08/2007 |-0.036163238 |0.01952394 |-0.03447433 |0.016612538 |-0.000572706 |
|09/2007 |-0.012844661 |0.050637169 |-0.011155753 |0.047725768 |-0.000532417 |
|10/2007 |-0.096903998 |0.023823424 |-0.09521509 |0.020912023 |-0.00199114 |
|11/2007 |0.028655121 |-0.033338592 |0.030344029 |-0.036249993 |-0.001099971 |
|12/2007 |-0.128702438 |-0.03235993 |-0.12701353 |-0.035271332 |0.004479936 |
|01/2008 |-0.18988558 |-0.113549457 |-0.188196672 |-0.116460858 |0.021917546 |
|02/2008 |-0.067943347 |-0.012093989 |-0.066254439 |-0.01500539 |0.000994174 |
|03/2008 |-0.103719921 |-0.038204646 |-0.102031013 |-0.041116048 |0.004195112 |
|04/2008 |-0.081237375 |0.040172792 |-0.079548467 |0.037261391 |-0.002964087 |
|05/2008 |0.238464566 |0.009958639 |0.240153474 |0.007047238 |0.001692419 |
|06/2008 |-0.131910363 |-0.080068934 |-0.130221455 |-0.082980335 |0.01080582 |
|07/2008 |-0.094126262 |-0.050914291 |-0.092437354 |-0.053825692 |0.004975505 |
|08/2008 |0.049736432 |0.036005397 |0.05142534 |0.033093995 |0.00170187 |
|09/2008 |0.00804408 |-0.103153753 |0.009732988 |-0.106065155 |-0.001032331 |
|10/2008 |-0.244022136 |-0.13038841 |-0.242333228 |-0.133299812 |0.032302974 |
|11/2008 |-0.216044874 |-0.066157646 |-0.214355966 |-0.069069048 |0.014805362 |
|12/2008 |-0.031891474 |-0.006287522 |-0.030202566 |-0.009198924 |0.000277831 |
|01/2009 |0.216344861 |-0.052152826 |0.218033769 |-0.055064227 |-0.012005861 |
|02/2009 |0.068291637 |-0.049280009 |0.069980545 |-0.052191411 |-0.003652383 |
|03/2009 |-0.055734099 |0.076214109 |-0.054045191 |0.073302707 |-0.003961659 |
|04/2009 |0.107351111 |0.051937244 |0.109040019 |0.049025843 |0.005345779 |
|05/2009 |0.204920671 |0.009389612 |0.206609579 |0.006478211 |0.00133846 |
|06/2009 |0.152428759 |0.035427879 |0.154117667 |0.032516478 |0.005011364 |
|07/2009 |-0.063778965 |0.068539845 |-0.062090057 |0.065628443 |-0.004074874 |
|08/2009 |-0.055263382 |0.061109543 |-0.053574474 |0.058198141 |-0.003117935 |
|09/2009 |-0.025454957 |0.057942434 |-0.023766049 |0.055031033 |-0.00130787 |
|10/2009 |-0.157308174 |-0.025351114 |-0.155619266 |-0.028262515 |0.004398192 |
|11/2009 |-0.057187135 |0.013278285 |-0.055498227 |0.010366884 |-0.000575344 |
|12/2009 |-0.047770789 |0.032862775 |-0.046081881 |0.029951373 |-0.001380216 |
|01/2010 |-0.037966667 |-0.066423482 |-0.036277759 |-0.069334884 |0.002515314 |
|02/2010 |0.163397738 |0.017072924 |0.165086646 |0.014161523 |0.002337878 |
|03/2010 |0.096269048 |0.052812983 |0.097957956 |0.049901582 |0.004888257 |

|mean return of ten-years |Y ' |X ' |
|bond | | |
|0.004633551 |-0.001688908 |0.002911401 |

|Covariance(X,Y) |Variance(X) |β(CTX) |Expected return of CTX |
|0.001931205 |0.002107949 |0.916153928 |0.007300843 |

Formula:
[pic]
Where: Yt= (ri,t – rf,t) ri,t = the return on stock i during interval t Xt = (rm,t – rf,t) rf,t = the risk-free rate of return, during interval t rm,t = the market rate of return, during interval t
Expected return of individual stock
[pic][pic].

Appendix 4—calculation of expected return and Beta of portfolios with various weights under CAPM model

| |AXA |CTX |
|β |1.138425255 |0.916153928 |
|Expected Return |0.007947964 |0.007300843 |

|Portfolio Number |Portfolio in |β |Expected return of Portfolio |
| |AXA |CTX | | |
|1 |1 |0 |1.138425255 |0.007947964 |
|2 |0.975 |0.025 |1.132868472 |0.007931786 |
|3 |0.95 |0.05 |1.127311689 |0.007915608 |
|4 |0.925 |0.075 |1.121754905 |0.00789943 |
|5 |0.9 |0.1 |1.116198122 |0.007883252 |
|6 |0.875 |0.125 |1.110641339 |0.007867074 |
|7 |0.85 |0.15 |1.105084556 |0.007850896 |
|8 |0.825 |0.175 |1.099527773 |0.007834718 |
|9 |0.8 |0.2 |1.09397099 |0.00781854 |
|10 |0.775 |0.225 |1.088414206 |0.007802362 |
|11 |0.75 |0.25 |1.082857423 |0.007786184 |
|12 |0.725 |0.275 |1.07730064 |0.007770006 |
|13 |0.7 |0.3 |1.071743857 |0.007753828 |
|14 |0.675 |0.325 |1.066187074 |0.00773765 |
|15 |0.65 |0.35 |1.060630291 |0.007721472 |
|16 |0.625 |0.375 |1.055073507 |0.007705294 |
|17 |0.6 |0.4 |1.049516724 |0.007689116 |
|18 |0.575 |0.425 |1.043959941 |0.007672938 |
|19 |0.55 |0.45 |1.038403158 |0.00765676 |
|20 |0.525 |0.475 |1.032846375 |0.007640582 |
|21 |0.5 |0.5 |1.027289592 |0.007624404 |
|22 |0.475 |0.525 |1.021732808 |0.007608225 |
|23 |0.45 |0.55 |1.016176025 |0.007592047 |
|24 |0.425 |0.575 |1.010619242 |0.007575869 |
|25 |0.4 |0.6 |1.005062459 |0.007559691 |
|26 |0.375 |0.625 |0.999505676 |0.007543513 |
|27 |0.35 |0.65 |0.993948892 |0.007527335 |
|28 |0.325 |0.675 |0.988392109 |0.007511157 |
|29 |0.3 |0.7 |0.982835326 |0.007494979 |
|30 |0.275 |0.725 |0.977278543 |0.007478801 |
|31 |0.25 |0.75 |0.97172176 |0.007462623 |
|32 |0.225 |0.775 |0.966164977 |0.007446445 |
|33 |0.2 |0.8 |0.960608193 |0.007430267 |
|34 |0.175 |0.825 |0.95505141 |0.007414089 |
|35 |0.15 |0.85 |0.949494627 |0.007397911 |
|36 |0.125 |0.875 |0.943937844 |0.007381733 |
|37 |0.1 |0.9 |0.938381061 |0.007365555 |
|38 |0.075 |0.925 |0.932824278 |0.007349377 |
|39 |0.05 |0.95 |0.927267494 |0.007333199 |
|40 |0.025 |0.975 |0.921710711 |0.007317021 |
|41 |0 |1 |0.916153928 |0.007300843 |