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## Part A - Risk And Return Characteristics

The goal of this research is to identify and understand the risk and return characteristics of five worldwide asset classes, as well as make suggestions on whether or not each asset class is viable for investment. The first section of the research examines five asset classes: Australia's stock market, Canada's stock market, Australian 10-year government bonds, oil, and gold. A few statistical measures such as the arithmetic mean, geometric mean, and standard deviation are used to value asset classes. The report's second section offers a detailed examination of the Capital Asset Pricing Model (CAPM) and the Single Index Model (SIM). The distinctions between the two-asset pricing models are clearly outlined, along with a summary of the CAPM model changes and an explanation of each update. The needed rate of return of Fortescue Metals group ltd, which is traded on the Australian Stock Exchange, is also calculated and compared to the actual returns of the S&P/ASX 200 index in the report. In the report's conclusion, a recommendation is made on the models' suitability for AlphaWell.

The arithmetic mean, geometric mean, and standard deviation are three approaches for analyzing the financial performance of a portfolio and the suitability of a portfolio strategy. Based on yearly returns generated from 2002 to 2021, the following table shows the arithmetic mean, geometric mean, and standard deviation of all five asset classes picked by AlphaWell management for the purpose of creating an investing strategy.:

An arithmetic average is a simple average of all yearly returns that provides an estimate of the average return produced by each asset type (Amihud 2018). According to the research, shares traded on the Canadian Stock Exchange have produced higher returns than those traded on the Australian Stock Exchange. Canadian stocks have an average annual return of 6.51 percent, while Australian stocks have an average annual return of 5.13 percent. An investment in a 10-year Australian Treasury bond yielded 3,88 percent on average, which is higher than the yield on a 10-year US Treasury bond yield for the same time period (Macroteends.net 2022). Oil is a vital economic commodity since it is the world's major source of energy and the most traded commodity (Chen et al 2020). Oil pricing and consumption patterns are sticky due to the commodity's ultra-slow production and supply. From 2002 through 2021, the commodity's historical average arithmetic return was 13.48 percent. Gold is typically purchased in today's world as a hedge against inflation and to protect against issues associated with economic instability (Alkhazali and Zoubi 2020). The primary mode of investment in gold has been in the form of gold bars, mutual funds, futures, mining companies and different type of jewellery. The average arithmetic return provided by the commodity in the past 20 years was equal to 10.98% which is the second highest investment return from all the five asset classes included.

## Part B - Capm And Single Index Model

The standard deviation of returns is a measure of risk and volatility, with a higher standard deviation indicating greater return volatility. This statistic can be reported using any of the following items: investment, symbol, asset type, investment goal, sector, investment type, or sub-portfolio. The shares listed in Australian stock exchange exhibits greater standard deviation of 16.30% compared to the standard deviation of 16.09% exhibited by shares listed on Canadian Stock Exchange. The 10-year Australian treasury bond experienced the lowest standard deviation amongst all asset classes due to the risk-free nature of the bond. Oil has displayed the most extreme movements in price as represented by the high standard deviation of 35.94%. Standard deviation exhibited by Gold has been the second lowest after treasury bonds with a value of 15.11%. The low standard deviation of gold can be attributed to stable prices witnessed by the asset in events of extreme market volatility.

In comparison to the arithmetic mean, the geometric mean is a superior estimate of asset class returns since it takes into account the effect of compounding that occurs year after year. According to the geometric means derived across all asset classes, gold was the best-performing asset, returning 9.91 percent, followed by oil, which returned 7.13 percent. The geometric mean difference between CAD and US shares is 1.49 percent, making shares listed on the Canadian Stock Exchange more investable and lucrative.

To further evaluate the comparative performance of the asset classes, performance measures like Sharpe ratio could be useful in forming the base of the recommendation.

 Particulars US SHARES BOND CAD SHARES OIL GOLD Sharpe ratio -0.01 0.00 0.08 0.09 0.40

Sharpe ratio was calculated using the excess return of each asset classes over and above the 10-year treasury bond yield and dividing it by the standard deviation. Sharpe ratio based on the arithmetic average return of Gold was equal to 0.47 which was the highest amongst all asset classes. The shares listed in the Canadian stock exchange has a positive Sharpe ratio of 0.08 compared to the Sharpe ratio of -0.01 of the shares listed in Australian stock markets.

Based on the arithmetic mean, geometric mean and standard deviation, AlphaWell should invest 50 percent of the total investment corpus in the commodity asset class, 40 percent in equity ETFs and the remaining 10% in Bond. Due to recent political and regional instability and rising demand of oil from Asian countries, the prices of oil are expected to move up significantly (eia.gov 2022). Hence, it is recommended to invest 30 percent of the total capital into Oil ETFs. In these turbulent economic times, if investors take a flight to safety, gold would be the most beneficial asset, hence 20% of the total asset should be invested in gold making the total asset allocation to commodities equal to 50%.

The shares of Canada have outperformed the shares listed on Australian stock exchange return wise, with a better Sharpe ratio, hence 30% of the total assets should be invested in Canadian stocks with a 10% investment in Australian stocks.

To reduce the exposure to riskier asset classes like equity and commodity, some allocation needs to be made in bond, hence it is recommended to invest 10% of the total capital into Australian 10-year treasury bonds. The following table summarizes the asset allocation:

 Assets Weights Australian Shares 10% Australian 10-year bond 10% Canadian shares 30% Oil 30% Gold 20%

CAPM

Capital Asset Pricing Model is a financial model which helps evaluate the relationship between the systematic risk of the company and expected returns of the assets. It is the most used financial model in the industry to evaluate the value/price of a risky asset taking into consideration the riskiness of the assets (Sattar 2017).

The formula for calculating expected return of a security under CAPM is given below:

It is assumed that the primary requirement for an investor is to be paid for time value of money. The risk-free rate component of the formula accounts for the time value of money aspect and the remaining parts of the formula depends on the level of additional risk taken by the individual investor (Michalkova and Kramarova 2017). The beta of the stock represents the volatility of the stock in comparison to the movement in the price of the index. The following section contains an example of CAPM return calculation of Fortescue Metals Group Ltd, a stock listed on the ASX.

The 10-year Australian Treasury Bond yield was taken as the proxy for risk free rate of interest and the average 10-year return on the S&P/ASX 200 index represents the market return of the stock. The CAPM expected rate of return was equal to 7.47% compared to the actual realized return of index equal to 5.13%.

The Single index model is a financial model similar to the CAPM model which is used to price assets based on the risk characteristics. The model defines that the expected return on a security are linearly correlated with any sort of economic variable that is associated with the particular security. The market is the single factor that has a linear correlation with the return of the security according to this model. The model can be defined using the following formula:

The alpha represents the unique part of the expected return or the abnormal return, B (Rm -Rf) represents the movement of the market which is capture by the beta of the stock, ei  represents the factors that underlines the firm-specific risks called the unsystematic risk.

CAPM is an equilibrium model which is defined by certain microeconomic factors like concave utilities, diversification without costs and it predicts the actual expected return of the stock. On the other hand, single index model finds out the correlation between (Ri-Rf) and (Rm-Rf) and represents the expected return of a stock based on it. Single index model, is a lot less descriptive than CAPM as it explains far less about the magnitude of the CAPM model

The original CAPM model is suitable for estimating cost of equity in developed countries with established capital markets and it requires the information which is available on market data basis. Historically, it has been found that the model’s estimation of cost of equity is not always accurate as it fails to incorporate multiple factors essential for a true picture of a cost of equity. Emerging market returns, with issues of low liquidity and lower level of capitalization cannot be accurately estimated using the traditional CAPM model (Semenyuk 2016). The information obtained from emerging markets regarding the liquidity and capitalization may not be reliable due to inefficiency in financial performance reporting. Hence, various updates to the traditional CAPM model has been made to incorporate the essential factors and present a fair and accurate picture of the market. The two of such factors included in the original CAPM model are the size of the company and country risk.

Size of the factor – The size of a firm plays an important role in determining the profitability from an investment made into it based upon factors of scalability and expertise. The CAPM model has been modified by including a factor that measures the size of the corporation. The factor is included in the process of equity estimation and are essential for valuing stocks belonging to the developed as well as emerging markets (Fard and Falah 2015).

Country risk premium – This factor is added to the traditional CAPM model and it takes into account the risk accepted by an investor by investing into emerging market equities. The premium is based upon the riskiness of the country for which an investor needs to be compensated for (Petrovi? 2017).

The financial reporting procedure are robust and effective in developed countries like Australia and Canada which assures an investor about good quality of the capital market information received. The accounting and financial oversight institution present in both countries are efficient in exercising prudence over corporate financial reporting matters. Taking into consideration the above factors, a traditional CAPM model can be used by AlphaWell to estimate the cost of equity. To enhance the accuracy of the model, the size of the corporation factor can be included in the model which might explain the risk and returns characteristics of the equity more efficiently.

Conclusion

The first part of the report was focused towards analyzing and discussing the risk and reward characteristics of five asset classes that AlphaWell, an investment firm in Australia, chose to form an investment strategy. Returns for the past 20 years of each asset class has been assessed based on three appraisal techniques; arithmetic mean, geometric mean and Standard deviation. Shares listed in Canadian Stock Exchange were found to be more profitable compared to shares listed in Australia. In commodity, oil outperformed gold based on the return performance of the past twenty years. An asset allocation recommendation based upon the recent economic developments were provided with a major chunk of capital being invested in oil followed by Canadian stocks. The second part of the report focused on discussing the CAPM model and the single index model and identifying the major differences between them. The report went on to discuss the updates to the traditional CAPM where two additional factors; size of corporation and country risk, were added. The concluding part of the report provides a recommendation on the appropriateness of the cost of equity model best suited for AlphaWell.

References

10 Year Treasury Rate - 54 Year Historical Chart (2022). Available at: https://www.macrotrends.net/2016/10-year-treasury-bond-rate-yield-chart (Accessed: 25 March 2022).

Alkhazali, O.M. and Zoubi, T.A., 2020. Gold and portfolio diversification: A stochastic dominance analysis of the Dow Jones Islamic indices. Pacific-Basin Finance Journal, 60, p.101264.

Amihud, Y., 2018. Illiquidity and stock returns: A revisit. Critical Finance Review, Forthcoming.

Chen, X., Li, Y., Xiao, J. and Wen, F., 2020. Oil shocks, competition, and corporate investment: evidence from China. Energy Economics, 89, p.104819.

Crude oil prices rise above \$100 per barrel after Russia’s further invasion into Ukraine (2022). Available at: https://www.eia.gov/todayinenergy/detail.php?id=51498 (Accessed: 26 March 2022).

Fard, H.V. and Falah, A.B., 2015. A New Modified CAPM Model: The Two Beta CAPM. Jurnal UMP Social Sciences and Technology Management, 3(1).

Michalkova, L. and Kramarova, K., 2017. CAPM model, Beta and relationship with credit rating. In Advances in Applied Economic Research (pp. 645-652). Springer, Cham.

Petrovi?, D., 2017. Contemporary challenges in applying of the modified model CAPM with country risk premium in emerging economies. Škola biznisa, (1), pp.51-69.

Sattar, M., 2017. CAPM Vs Fama-French three-factor model: an evaluation of effectiveness in explaining excess return in Dhaka stock exchange. International journal of Business and Management, 12(5), p.119.

Semenyuk, V., 2016. Pragmatics of using a modified CAPM model for estimating cost of equity on emerging markets. Baltic Journal of Economic Studies, 2(2), pp.135-142.

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