Applied Portfolio Management

Question 1

Equally Weighted Portfolio

Solver Optimal Portfolio

Limitations of Markowitz Model

1. Impact of Size and Market to Book Ratio

Different models have been embraced over the years in developing an investment strategy in firms. However, the three-factor Fama-French model was used to advance this indicator. Being an asset pricing model, the model included market capitalization and the market to book value to the CAPM model. Operating profitability and investments are significant factors that determine the extent to which firms are willing to go regarding investments in a specific venture. Therefore, the size and value will always affect returns on investments bearing in mind the different stocks. Considering Hagstrom’s (2001) initial research and portfolio management was pegged on stock pricing and the ability to determine its costs, the assumptions have changed enormously. Currently, stocks with low market capitalization have a relatively high return compared to the high capitalization in markets bearing in the same results is acquired with the high market to book ratio and the low market to book ratio. According to Markowitz (1991), Inefficiencies in portfolios can be determined by the ability to increase the expected return, whereas the risk factor is considerably low. Factors such as liquidity have played a role in the differences witnessed.

Additionally, the behaviours of the prospective investors and the costs attributed to the different transactions have also contributed to the difference experienced. In most cases, investors demand a premium for sales since the shares of small-capitalization stocks rarely acquire demand from them. Furthermore, growth firms are mostly considered when it comes to prospective investors since there are perceptions of increased opportunities compared to the value companies, therefore, leading to the high performance of the market to book ratio.

2. Seasonal Anomaly

Expounding on the seasonal anomaly will entail the clarification of the unexplained variations experienced in stocks return, which more often than not tends to contract the standard price-return of assets, which is caused by the changes in seasons. Seasonality, which generally entails different periods, is brought by the changes in the calendar. These abnormal returns are attributed to different factors and operations that occur on different days, weeks, or even months in a calendar year. According to Sharma (2014), low returns usually are experienced on Mondays due to the work settings and busy schedules experienced in other industries, thus limited concentration, whereas high returns are posted on Fridays. Furthermore, during the festive seasons, most notably in December, returns of stocks are lower compared to months like January, where high returns are posted. Different strategies by investors are considered in different periods where high and low returns are experienced. Considering year-end closures, investors will most likely sell their stocks to actualize their losses. This measure ensures that the tax declared will be low considering the outcome of the returns hence a tax minimization strategy by the investors. Weekly or monthly anomalies can be attributed to different market behaviours, which are a result of various regulations by the government or approaches that were experienced in the non-trading days.

Question 2

Momentum Strategy

The behaviour of investors in the market will always affect the pricing model of stocks in the market. Momentum strategy seeks to expound on the reaction of investors towards both positive and negative news, which is related to stocks. The theory inclines the assumption that future increases or decreases in stock returns will be attributed to the past increases or decreases, respectively. This approach is considered relevant for a specific period where the pattern of returns will most probably look the same. Worth noting is the quest for maximization of returns on investment that will always push investors to develop different strategies to ensure their goal is attained. Hence through the momentum strategy, investors select stocks in pursuit of abnormal returns. According to Jagadeesh and Titman (1993), data mining has been adopted as one of the significant approaches in developing a market strategy to ascertain future returns. The available data can be used to generate past information about the stock, which is relevant to develop the pattern of returns. In ascertaining the correct stock, momentum strategy obtains long positions for the past victors and short selling stocks, which are related to the past losers. As earlier mentioned, the quest for abnormal returns will push investors to perform a selection of stocks. Thereby, the abnormal return in momentum strategy will be accredited to the delays caused by the investor’s reaction time, which will translate to market efficiencies in the long term. Ensuring no time difference between the variable that is leading and the one that is lagging will enhance the lag effect and further enable minimization or prevention of the difference in portfolio formation and the time frame concerning the withholding of the portfolio. This approach will predominantly use the 12/12 strategy, which elaborates on the portfolio formation, which is attributed to average performance for the last twelve months. After that, the selected stock will be held for an additional period of not less than the twelve months, which is after the period of formation. The two periods will be 2012 and 2013, with the formation period being assumed as 2012 while the holding period is considered to be 2013. According to the analysis and findings, the three best performers were between P10, P2, and P11. On the other side, the losers were P8, P4, and P1, considering their performance. The fact that the same stocks were to be used in the corresponding year, future performance reflected the current trend. Though the numerical findings vary, there is always a correlation between the returns, thus paving the way for investors’ decisions. Be it small versus large stocks or the long versus the short side of business trading, and the findings will always depict a correlation; hence investors ascertainment of returns. The findings above were correlated with the previous empirical studies, which emphasizes the principle of going long for previous price increases will result in extraordinary profits.

Question 3

Seasonal Anomalies

1. Day of the Week Effect

High and low returns are witnessed on different days of the week, depending on various factors. Various uncertainties ranging from the Monday effect or even the weekend effects will affect the stock prices in security exchange. According to Linn and Lockwood (1988), the US stock returns will most definitely record a negative mean return on Mondays compared to relatively high mean returns on Fridays. An assumption that was shared with Gibbon & Hess (1981) with the approach that the stock returns are exceptionally high on Fridays and low on Mondays. This approach was further expounded to create a positive Friday and a negative Monday correlation. Stocks in Australia tend to exhibit meagre returns on Tuesdays as compared to low Mondays for the US stocks.

Additionally, according to Marrett and Andrew (2009), there is usually a higher return on the Australian stock on Thursdays. Srinivasan and Kalaivani (2013) did similar research on the Asian market with specifications to India’s NSE-Nifty and BSE-SENSEX. The findings showed positive Mondays and Wednesdays with significant mean return high on Mondays compared to Wednesdays during the week. Investors’ approach in the different continents is likely to be inclined on the specific days that register positive outcomes compared to the negatives.

A look at the analysis, it is clear that in the USA, the returns were very low on Mondays compared to other days of the week. In Australia, the highest negative returns were realized on Fridays, considering Tuesdays were also low. For the positive returns, it is evident that Thursdays had the highest positive returns in Australia, while the highest positive returns for the US were on Tuesdays.

2. The month of the Year Effect

Just like the days’ effect, this seasonal anomaly emphasizes on the months of a year concerning stocks and their returns. Various aspects of the trade, such as tax hypothesis, have played a significant role in determining the highs and lows of stocks. In most cases, January seems to be a relatively positive month compared to the others, whereas December factors in as one of the lowest or negative months. This hypothesis considers December as the month where investors are likely to declare their losses to reduce the tax payable at the moment. In contrast, January is approached with the acquisition mentality. Investors will be seeking to purchase the stocks sold in December hence a positive return experience.

Looking at both the US and Australian stock markets, there is a relative similarity in January and December. In both stock markets, there is a considerable high return in January compared to December hence attributing the results to investors’ behaviours when it comes to closing the year. Although February, March, June, July, and November also record low returns on stocks, the correlation between December and January explains investors trends.

References

Gibbons, Michael & Hess, Patrick. (1981). Day of the Week Effects and Asset Returns.

The Journal of Business. 54. 579-96. 10.1086/296147.

Hagstrom, R. G. Jr. (2001). The Essential Buffett: Timeless Principles for the New

Economy. John Wiley & Sons, New York.

Jagadeesh, Narasimhan: and Sheridan Titman, 1993, Returns to buying winners and

selling losers: Implications for stock market efficiency, Journal of Filzance 48,65-91.

Linn, S. and L. Lockwood, “Short Term Stock Price Patterns: NYSE, AMEX, OTC,”

Journal of Portfolio Management (Winter 1988), pp. 30-34

Markowitz H. M. (1991). Foundations of Portfolio Theory. The Journal of Finance. Vol.

46, No. 2, pp. 469-477.

Marrett, George & Worthington, Andrew. (2009). The day-of-the-week Effect in the

Australian Stock Market: An Empirical Note on the Market, Industry and Small

Cap Effects. International Journal of Business and Management. 3. 10.5539/ijbm.

v3n1p3.

Sharma, Arun. (2014). Stock Market Anomalies: A Challenge to Efficient Market

Hypothesis. International Journal of Trends in Finance. Volume 3. 222-230.

Srinivasan. P, and Kalaivani. M (2013). “Day-of-the-Week Effects in the Indian stock

market,” MPRA Paper 46805, University Library of Munich, Germany.