Investment Plan Four Firms

Table of Contents

Contents

Table of Contents 1

Executive Summary 1

1. Introduction 1

2. Asset classes 1

2.1. Australian Shares (AUD) S&P/ASX 200 1

2.2. Australian Bonds (AUD) 2

2.3. US Shares S&P500 2

2.4. US Federal Funds Rate 2

2.5. Brent Oil (USD) 2

4. Efficient portfolios 3

5. Modern portfolio theory 4

6. Conclusion and Recommendation 5

References 5

Appendix 6

Appendix 1: Arithmetic & Geometric Mean, Standard Deviation & Variance 6

Appendix 2 Correlation Matrix 6

Appendix 3: Covariance Matrix 6

Appendix 4: Bordered Covariance Matrix 7

Appendix 5: Efficient Portfolio 7

Executive Summary

Multiple methods of establishing stock market volatility and performance exist with the majority of the methods founded on the Markowitz’s 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. Markowitz’s 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(Šir??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

The S&P/ASX 200 index represents a float-adjusted stock market and market-capitalization-weighted index of the 200 largest stocks listed on the Australian Securities Exchange (ASX). The index is maintained by Standard & 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 a float-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 US federal funds rate entails 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 investment’s expected future returns. The geometric mean is the time-weighted average return of an investment. The geometric mean enables compounding of the return over the historical period. The greater discrepancy between the arithmetic mean and the geometric mean implies greater volatility in the rates of return. Overall, the geometric mean for the assets under evaluation is lower than the arithmetic mean. The Brent Oil stock has the highest discrepancy between the geometric mean (2.94%) and arithmetic mean (10%) implying that it’s the stock with the highest volatility, hence the highest risk, but also, it’s the stock with the highest return. The US Fed Funds Rates are the least volatile stocks in the above portfolio demonstrated by the least difference between the arithmetic mean and geometric mean, but the stock has the least average return on investment.

Variance and standard deviation, which are measures of dispersion, are the predominant statistical methods of measuring investment risk. Standard deviation and variance measure the return volatility with large variance implying higher variability, indicating the riskiness of an asset. Consistent with the arithmetic mean and geometric mean, Brent Oil the highest standard deviation of 37.4% and a variance of 14%. However, the Australian Bond has the least variance and standard deviation implying it’s the least risky asset (See Appendix 1).

4. Efficient portfolios

The Markowitz Portfolio Optimization Model informs the determination of the most efficient portfolio by evaluating multipole possible portfolios of a given stock. An efficient portfolio is informed by an analysis of the assets expected returns and the covariance matrix. The Minimum-variance frontier that indicates the lowest possible variance associated with an expected return of a given portfolio, inform the optimal risk-return combinations. The efficient frontier of risk assets which is the optimal portfolio contains the combination of assets that lie on and above the global minimum- variance portfolio. In combination with the efficient frontier, capital allocation is informed by the Capital Allocation Line which is derived from the Sharpe ratio. The Sharpe Ratio is the difference between the portfolio’s risk premium and the risk-free rate as a ratio of the standard deviation. A higher Sharpe ration reflecting a higher expected return commensurate to volatility level. The steepest of the capital allocation line (CAL) plotted using the Sharpe ratio demonstrates the best risky portfolio. Independently the Sharpe ration can inform the optimal investment with no consideration of the minimum variance frontier. An optimal portfolio mix is determined by the tangent of the CAL and the efficient frontier

Maximizing the Sharpe ration demonstrates that the Australian Bonds and the US S&P500 and the Federal Fund Rate stocks as the optimal stock portfolio that yields the maximum returns with minimal risk. A combination of 57% Australian Bonds, 3% US S&P500 shares, and 39% Federal Fund Rate stocks yields an expected return of 3.1% with a risk of 1.53%. This implies that the optimal portfolio would only include three assets (Appendix 5).

Figure 1: Sharpe Ratio and Capital Allocation Line (CAL)

5. Modern portfolio theory

The Modern Portfolio Theory (MPT) posits the variance computed from the expected portfolio risk and expected portfolio return as the core variable in determining the optimal portfolio asset allocation. The theory provided the rationale for diversification of investments across assets portfolio. The MPT argues that risk-averse investors with low-risk tolerance desire to maximize returns and minimize portfolio risk, hence the diversification decision can’t be determined by maximizing expected portfolio return. The MPT is premised on the assumptions that an investor only seeks to avoid risk and maximize returns, variance as measures the risk, the expected returns and returns can be accurately established ex-ante, the investor's utility function is quadratic, normal distribution of the expected returns and investors utility is maximized over a single investment period.

Moreover, the MPT doesn’t 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 hypothesis 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 doesn’t 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.