Executive Summary

Multiple methods of establishing stock market volatility and performance exist with the majority of the methods founded on the Markowitzs Modern Portfolio Theory (MPT). In this analysis, and application of the MPT concept on five stocks is undertaken to establish an efficient investment portfolio. The analysis identifies the Brent Oil and the Australian S&P/ASX 200 shares as high risky assets, despite having the highest returns implying that the optimal portfolio would consist of the Australian Bond, US S&P 500 shares, and the US Federal Funds). Divergent literature highlights extensive critique of the founding model on portfolio optimization, MPT, which entails the mean-variance model. The theory is critiqued for its failure to resonate with the financial markets. Consequently, alternative asset allocations models departing from the original mean-variance model have been established and posit the need for use of alternative risk measures in addition to variance.

1. Introduction

Investments are characterized by uncertainty in returns, hence, applying the appropriate model in determining the asset allocation is key for realizing portfolio optimization. Markowitzs Modern Portfolio Theory (MPT) is recognized as the predominant model that enables the determination of efficient investment portfolios with the highest expected returns and low volatility(ir??ek & K?en, 2015). Investment risk, a measure of the probability of dispersion of investment returns from the desirable return, determines an investment portfolio (Bodie et al., 2018). Higher investment risks are associated with greater returns, implying that investment returns of a riskier asset are relatively higher. Investments are characterized by two distinct risks: idiosyncratic risk and systematic risk. According to Bodie et al., (2018) systematic risk arises from the uncertainty of prediction of macroeconomic factors such as changes in the business cycle, interest rates, inflation, and exchange rates. The idiosyncratic risk arises from firm-specific factors that affect an individual firm without necessarily affecting the entire economy. A diversification strategy is inherent in spreading the risk exposure of an investment portfolio. A diversified portfolio entails the highest excepted return sand lower risks reflected by the standard deviations. According to McKay et al. (2018), Asset price movement is characterized by imperfect correlations that enable minimizes risk through diversification of the asset portfolio. McKay et al. (2018) cautions that over-diversification as an inherent tradeoff which demands an increase in forecast accuracy

2. Asset classes

2.1. Australian Shares (AUD) S&P/ASX 200

TheS&P/ASX 200index represents a float-adjustedstock market and market-capitalization-weighted indexof the 200 largest stocks listed on theAustralian Securities Exchange (ASX). The index is maintained byStandard & Poor's (S&P)and is considered the benchmark for Australian equity performance as it tracks the stock performance of the largest 200 stocks listed in ASX. Historical analysis of the S&P/ASX 200 highlights annualized total return averaging 8.7%.

2.2. Australian Bonds (AUD)

The Reserve Bank of Australia (RBA) cash rate represents an interest rate of chargeable unsecured overnight loans between banks. The Australian Bonds are characterized by no risk of investment, hence offers an attractive return in an investment portfolio. Given that investing in the Australian Bonds has no risk, investors are able to form a minimum risk portfolio that could effectively perform in the face of a volatile capital market.

2.3. US Shares S&P500

The S&P 500 index entails a stock market index that measures and tracks the share performance of 500 of 505 stocks issued by 500 largest companies listed on stock exchanges in the United States. The index is weighted by afloat-adjusted market cap. The 505 stocks account for approximately 80% of the US stock market capitalization. Given that the index weighted market capitalization, large companies have a greater impact on the index, hence the index is employed by investors as a barometer of the US stock market performance. Investment vehicles for the S&P 500 index include exchange-traded fund (ETF) and mutual fund designed to passively track the index. Investing in S&P/ASX 200 and S&P 500 implies diversification of risk since the portfolio return is not entirely dependent on the performance of a single listed company. Investing in the S&P 500 index fund has been identified as attracting investment portfolios with an annualized total d 9%-10%.

2.4. US Federal Funds Rate

The USfederal funds rateentails the interest rate charged by depository institutions, credit unions, and banks, for overnight and uncollateralized lending of reserve balances to other depository institutions. The federal fund's effective rate is computed as a weighted average of lending rate across all such overnight transactions. The federal fund rate is volatile which has a significant impact on short-term rates charged on credit cards, consumer loans, and consequently on stock prices.

2.5. Brent Oil (USD)

The Brent Oil (USD) per barrel % return is predominantly high but equivocally with a high risk of investments. The brent crude oil price and the US dollar exchange rate display a volatile and inverse relationship with the rising price of Brent oil causing a depreciation of the US dollar. Using adequate stocks for hedging in the Brent oil stock would enable the maximization of an investment portfolio.

3. Portfolio Construction

Arithmetic mean enables assessment and inference of holding period returns using historical data. The arithmetic mean estimates the expected return, E(r), and provides an unbiased estimate of the...…investors utility is maximized over a single investment period.

Moreover, the MPT doesnt incorporate transaction costs such as taxes despite that the investors could maximize their returns by rebalancing the portfolio to earn capital gain taxes. Empirical evidence demonstrates a positive skewness of the asset returns centrally to the normal distribution hypotesis by the MPT Moreover, the assumption of increasing investor risk aversion is inconsistent with common investor behavior. Such differences have necessitated the identification of other parameters that determine optimal asset allocation. Such parameters include the mean and variance of expected returns, the correlation between returns, value at risk (VAR), lower partial moments (LPM), semi-variance, and conditional value at risk (CVAR) (Santacruz, 2016).

An alternative model has been put across to address the limitation of the MPT. The multi-period asset allocation models address the limitation of the static risk-reward criterion assumption of the MPT hence enabling strategic asset allocation. Acknowledging that investors entail multiple time horizons at any particle time, the model posits a rebalancing of the portfolio to appropriately respond to the changes in the value of stock in the market. Consequently, a portfolio entails an aggregate of multiple sub-portfolios with varied time horizons. The MPT is the Non-Quadratic Utility Function Models posit to address the MPT assumption of the quadratic utility function. The model proposes the use of full-scale optimization to establish a utility-maximizing portfolio as it generates disproportionately higher investor utility. Contrary to the expected utility theory assertion that investors are risk-averse, the prospect theory posits that investors are averse to losses as opposed to risks.

The challenge of asymmetry in stocks pauses a risk of failure of portfolio diversification. According to Page & Panariello (2018), risk-on factors such as the size of a stock and currency carry pauses the risk of failing to diversify stock when needed. The analysis identifies a stock-size differential in beta exposures during stock market drawdowns with the small-cap having relatively by higher equity betas. Page & Panariello (2018) identifies that diversification in equity regions, sizes, styles, sectors, alternative assets, credit, and risk factors that embed short positions doesnt yield a diversification of risk compared to average correlations, hence there is a need for investors to rely on average correlation as a methodology to optimize their portfolio. Page & Panariello (2018) propose dynamic risk-based strategies, risk factors, and tail risk hedging strategies as more effective in stabilizing the volatility of the portfolio, exposing the portfolio to fewer losses without a compromise of the returns.

6. Conclusion and Recommendation

The analysis above reveals the optimal risky portfolio informed by…