Portfolio Analysis
The study derived the efficient frontier of risky assets for a portfolio consisting of seven companies. It used historical data for monthly stock prices from January 1st, 2012 to December 1st, 2017. All the stock prices were for the first date of every month throughout the period. The study also assumed that the risk-free rate of interest in the market was 2.4 percent annually or 0.20 percent monthly. Besides, the yearly expected return for the market was 9 percent which translated to 0.75 percent monthly according to the forecast for the market consensus. The data helped in generating portfolio for the seven stocks and compare the investment return on the collection according to the expectations.
Initial Estimation of Portfolio Return
The initial estimation of the portfolio return used equally weighted stocks for all the seven companies. The weight of each of the stock was 14.29%. The study established that an investment in the portfolio would lead to a monthly profit of 1.15 percent translating to 13.8 annually using the monthly returns for each of the seven stocks. The standard ratio for the portfolio was 3.3445 while its Sharpe ratio was 0.2843. According to the study results, investment in seven companies equally will result in a monthly return of 1.15 percent. The venture will be highly profitable as it beats the market projection of 0.75 percent per month.
Optimization of the Portfolio
Optimization of the portfolio produced an expected return of 1.48 percent per month with a standard deviation of 3.580. The Sharpe ratio for the optimal portfolio of seven stocks was 0.3584 representing 35 percent return against 28 percent risk-free profit from the previous collection (Kristoufek, 2013). The optimization, however, found that the investors can only realize monthly returns of 1.48 percent upon investment in five of the seven companies. The investor would, therefore, have zero investments in WOW and WPL. However, AGL should have a weight of 44.88 percent among all the stocks.
Limitations of the Markowitz Model
Since the model uses the past prices to predict the future returns, there is a lot of bias since there is no guarantee that the market will continuously behave over the years (Moskowitz " Grinblatt, 1999). In other words, the past stock behavior in the market may not necessarily predict the future prices. On the other hand, increased purchase for a particular stock will lead to increased costs while the reduced demand for another will contribute to price falls. Thus, the ratios used in the Markowitz model may not apply. It is also difficult to have all investors in the market having similar ideas. The diversification of the market intelligence by various players in the stock market is essential in the portfolio returns. Further, the Markowitz model provides the portfolio weights infractions against the market trend where investors purchase the shares in whole numbers (Chopra " Ziemba, 2013). Finally, there are no mathematical calculations of the association between the risks and returns and the past share prices limiting the viability of the projection by the model (Kolm, Tütüncü, " Fabozzi, 2014).
Momentum Strategy
The study used the past equity prices for 30 firms from the US to calculate the momentum strategy. It used the 6/6 approach to identify six companies for the research. Among the six organizations, three were winners while the other 3 were losers based on the six-six strategy. Since it was difficult to establish the firms that had provided a similar return trend for six months. However, each of the three companies including Beer, Clothes, and Construction had each endured consecutive loss while Games, Chemistry, and Textiles had also received six months of constant gained.
Portfolio of Three Stocks
The portfolio of three stocks consisting of Beer, Clothes, and Construction realized a return of 1.034 percent with a standard deviation of 5.07. All the three stocks had equal weights of 0.33. The study used a risk-free rate of 0.02 percent per month or 2.4 percent annually. The study further assumed the beta function of 0.90. The calculations resulted in a Sharpe ratio of 0.1645 representing 16.54 percent risk-free returns. The Jensen’s alpha for the portfolio was 0.95 indicating a positive performance.
Comparison of Gainers and Losers
The risk-free rate used in the estimation of the returns for the three gaining companies including Games, Chemistry, and Textiles was also 0.20 percent monthly translating to an annual yield of 2.4. Similarly, the study maintained the beta value at 0.90. Upon the calculation, the expected return for the portfolio consisting of the three gainers from the market was 1.0313 percent per month with a standard deviation of 5.9945. The Sharpe ratio for the collection was 0.1387 percent showing 13.87 percent return. The Jensen’s alpha for the portfolio was 0.9482. Thus, there was no significant difference between the gainers and losers in the stock market investment among the two groups.
Discussion on Momentum Investment Strategies Theories
According to the momentum strategy, the companies that make consecutive losses for six consecutive months are less profitable, and the investors should avoid them. Similarly, the theories argue that the firms that gain consecutively six times in the market are likely to produce positive returns (Jegadeesh "Titman, 1993). However, the study proved that there was no significant difference between the two portfolios. First, the collection consisting of three assets that had experienced six consecutive gains realized similar volumes of returns to those that registered six successive losses. Hence, the study proved that both the magnitude and direction of the momentum premium did not affect the future returns of a stock. It established that short-term market movements did not necessarily influence the long-term profit for the companies. It challenged the theories that had significantly claimed that the investors should avoid loss-making companies (Jegadeesh " Titman, 2001).
Seasonal Anomalies
A month of the year effect analysis of the provided data for the monthly returns of both TOTMKAU and TOTMKUS established a lack of effect on the companies. The markets registered both gains and losses randomly in each month. A close analysis of the markets found that it was quite tricky for the two exchanges to incur losses in a particular month for subsequent years as it occurs in the theory of the month of the year effect (Schwert, 003). The markets just had a fair distribution of both the gains and losses. For example, there were negative returns for both TOTMKAU and TOTMKUS in both in August 1986, but the subsequent August had a positive performance. Thus, there was no month of the year effect on the monthly stock returns provided in the data.
Day of the Week Effect
The study also analyzed on the day of the week effect on the stock prices to establish the bad or good days of the two markets. It had similar reports to the month of the year analysis as it registered no significant trend on the same. It was rare to find each of the TOTMKAU and TOTMKUS having negative returns on the same day. However, if the scenario occurred, it would rarely reappear on the subsequent day of the week. The result proved that the day of the week effect failed to happen in the two markets of TOTMKAU and TOTMKUS as opposed to theory.
Discussion on Seasonal Anomalies
Seasonal anomalies might be common in some markets where the investors know specific days of the week or months of the year with poor or good stock performance in the market (Cross, 1973). Such knowledge is essential in ensuring that the investors purchase the stocks on the days when they trade at reduced prices and sell them on the days with huge gains. Thus, study, however, proved that the investors would rarely benefit from the seasonal anomalies as they were uncommon in the specified markets. The study further showed that the investors rely on the annual anomalies and such practice has made the market behave strangely. For example, the stock prices will heavily shoot on a specific day if the same day experienced negative returns in the previous week (Rozeff " Kinney, 1976; Rozeff, " Kinney, 1976). It means that the investors may approach the market with a different attitude of failing to sell their stocks only to influence a high demand for the shares leading to high prices. The same occurrence appeared for days with previous high stock prices as the investors would experience losses on the subsequent days. Thus, the seasonal anomalies belief is the cause of losses in the market since they influence the purchase or sale behavior of the investors.
References
Jegadeesh, N. and Titman, S. (1993). Returns to buying winners and selling losers: implications for stock market efficiency. The Journal of Finance, 48:65–91.
Jegadeesh, N. and Titman, S. (2001). Profitability of momentum strategies: an evaluation of alternative explanations. The Journal of Finance, 56:699–720.
Moskowitz, Tobias and Grinblatt, Mark (1999) Do Industries Explain Momentum? The Journal of Finance, 54, 1249-1290.
Schwert, G. William, 2003. "Anomalies and market efficiency," Handbook of the Economics of Finance, in: G.M. Constantinides " M. Harris " R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 15, pages 939-974 Elsevier.
Cross, F. (1973). The behavior of stock prices on Fridays and Mondays. FinancialAnalysts Journal, 29(6), 67–69.
Rozeff, M. S., " Kinney, W. R. (1976). Capital market seasonality: The case of stockreturns. Journal of Financial Economics, 3(4), 379–402.
Seif M, Docherty P, Shamsuddin A. (2017). Seasonal anomalies in advanced emerging stock markets', Quarterly Review of Economics and Finance, 66 169-181.
Chopra, V. K., " Ziemba, W. T. (2013). The effect of errors in means, variances, and covariances on optimal portfolio choice. In HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING: Part I (pp. 365-373).
Kolm, P. N., Tütüncü, R., " Fabozzi, F. J. (2014). 60 Years of portfolio optimization: Practical challenges and current trends. European Journal of Operational Research, 234(2), 356-371.
Kristoufek, L. (2013). Can Google Trends search queries contribute to risk diversification?. Scientific reports, 3, 2713.
