Analysis of Sharpe Ratio, Beta, Treynor Ratios, and Standard Deviation of Funds

FUNDS, INVESTMENT AND PORTFOLIO MANAGEMENT TO FINANCE
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Table of Contents Introduction. 4 Fund Selection and Comparison According to Betas and Standard Deviation. 4 Ranking the Funds in the Same Order 6 Comparing Five Funds with Betas Greater than or Equal to 1.50. 7 Three Funds that Appear on both lists of the Highest 1-year and 3-year Returns. 8 The Standard Deviation of the Funds. 8 The Sharpe Ratio of the Funds. 9 The Treynor Ratio of the Funds. 10 The Standard and Best-Fit Indices. 12 Standard Index and the Best-fit Index to calculate beta and alpha coefficients.    13 Management Section Report Analysis. 14 Recommendation Fund Selection. 15 Conclusion. 16 References. 17 Appendix. 18   Funds, Investment and Portfolio Management to Finance Introduction             Investment selection require thorough analysis by the investor or investment analysis to ensure that maximum return is obtained while risk is minimized. Risk measurement is based on the fund’s standard deviation and beta. In this analytical paper, two section are undertaken whereby section 1 requires selection of five mutual funds. The volatility of the funds in analyzed by selecting different degrees of betas. In the second section, three fund are selected based on the highest return achieved in 1-year and 3-year period. The analysis of the Sharpe ratio, beta, Treynor ratios and standard deviation for each of the three funds is done. The data for analysis is obtained through Fidelity and Morningstar website. An investment choice from the funds is considered based on the analysis undertaken. Fund Selection and Comparison According to Betas and Standard Deviation             The five funds selected, and the results are shown in Table 1. When measuring the risk of the fund, various parameters are used. However, volatility is the most applied metric in measuring fund risk. In measuring volatility, fund manager and analysts use standard deviation and beta. The beta of an investment is used to measure the systematic risk associated with the fund. Systematic risk is the risk that is inherent to the entire market and cannot be predicted or controlled by firm specific measures (Jagric, T., Podobnik, B., Strasek, S. and Jagric, V., 2015). Beta is therefore used in measuring the fund’s risk against a market index or the return volatility of the fund relative to the entire market. A higher beta (β > 1) implies that the fund’s returns are more volatility that the market while a low beat (β < 1) indicates that the return of the funds are less volatility than the market. On the other hand, a beta of one (β = 1) shows that the return of the fund varies in the same way as the market, i.e., the fund is as volatile as the market.              Based on the betas as a measure of fund investment risk as presented in Table 1, Fidelity Balanced Fund has the highest beta of 0.75 followed by American Funds Growth and Income Portfolio with a beta of 0.73. MFS Conservative Allocation Fund comes third with a beta of 0.50 while American Funds Tax-Aware Conservative Growth and Income Portfolio and Eventide Multi-Asset Income Fund closes the list with betas of 0.44 and 0.40 respectively. From the results, it is evident that Fidelity Balanced Fund is more volatility to the market than all the other funds and hence the returns are much more affected by the changes in the market than other funds. Volatility of an investment fund can also be measured using the fund’s standard deviation. In investment, standard deviation is used to measure the risk that the investment return will differ from the expected return is a given period (Choudhary, V., & Chawla, P. S., 2014). The higher the standard deviation, the more likely is actual return fluctuates from the expected return. On the other hand, the lower the standard deviation, the less likely expected return fluctuates from the actual returns. Risk averse investors prefer an investment with low standard deviation while risk loving investor prefer investments with higher risk though they require higher returns as a compensation for the high risk.             From Table 1, it is evident that the American Funds Growth and Income Portfolio has highest standard deviation of 13.94% followed by Fidelity Balanced Fund and  Eventide Multi-Asset Income  with 13.97% and 10.03% respectively. On the other hand, MFS Conservative Allocation Fund and American Funds Tax-Aware Conservative Growth and Income Portfolio have the lowest standard deviation of 8.41% and 8.78% respectively. Therefore, based on the measure of standard deviation, American Funds Growth and Income Portfolio is more riskers than all other four funds since its actual return is 13.94% more likely to differ from the expected return. Hence, investors selecting this fund will demand higher compensation though high return the additional risk associated with the fund. On the flip side, MFS Conservative Allocation Fund has the lowest possibility that the actual return will differ from the expected return. The riskiness of the other funds lies within this extreme ends. Ranking the Funds in the Same Order             Using the five funds selected, the ranking list based on both beta and standard deviation is as follows in Table 2. From the table, only three funds (Fidelity Balanced Fund , American Funds Growth and Income Portfolio  and American Funds Tax-Aware Conservative Growth and Income Portfolio) maintained their ranks when ranking based on beta and standard deviation simultaneously. The other two funds, Eventide Multi-Asset Income Fund and MFS Conservative Allocation changed their rankings. The difference in the ranking can be explained by the fact that based on the variability of the fund, MFS Conservative Allocation varies more than Eventide Multi-Asset Income Fund. On the other hand, Eventide Multi-Asset Income Fund is more affected by changes in the market than MFS Conservative Allocation Fund thereby ranking higher in the list. Another reason for the difference in the ranking is that the ranking using standard deviation is based on an individual investment while beta is based on the portfolio of assets (Jakšić, M., Leković, M. and Milanović, M., 2015). Hence, the impact in the changes in variability differs between the two funds based on individual investment variability and market variability.             The funds that retained their ranking shows that the effects of the changes due to individual investment and market conditions affects the return in almost the same manner. For instance, Fidelity Balanced Fund ranks position 1 in both cases. Similarly, from Table 1, the fund has highest beta and standard deviation. Hence, the fund may be well diversified in the market thereby any changes in the individual funds or market affects the fund in the same manner. Unlike Eventide Multi-Asset Income Fund and MFS Conservative Allocation where changes in individual funds and market causes a different effect to their return. The reasoning is the same for other funds that maintained their ranks. Comparing Five Funds with Betas Greater than or Equal to 1.50             For mutual funds with a beta equal or greater than 1.50, the following funds are selected for comparison purposes. Table 3 presents the selected mutual funds. Comparing based on beta, the American Beacon AHL Managed Futures Strategy Fund  From has a highest beta of 3.44 among the five funds as shown in Table 3. Cohen & Steers Low Duration Pref & Inc and JPMorgan Research Market Neutral Fund follows with 2.61 and 2.14 respectively. Rydex Energy Fund and Fidelity® Select Energy Portfolio has the lowest betas of 1.99 and 1.79 respectively. Using standard deviation to compare the funds, Rydex Energy Fund has the highest standard deviation of 46.09% followed by Fidelity® Select Energy Portfolio with a standard deviation of 42.03 while JPMorgan Research Market Neutral Fund has the least standard deviation of 5.19%.             The ranking of the funds using both beta and standard deviation concurrently is as shown in Table 4. Evidently, the ranking is differing when using beta and standard deviation for mutual funds with higher betas (Christoffersen, S.E. and Simutin, M., 2017). The difference in the ranking is attributed to the investor’s strategy of beating the market if the fund prices rise or are expected to rise in the future. Hence, a fund with higher beta, for instance, American Beacon AHL Managed Futures Strategy Fund imply that their actual returns are less likely to have a large variability from the expected return and hence low standard deviation making the fund to be ranked among the bottom based on standard deviation. On the other hand, investors consider funds with low beta when prices are expected to fall in future. On the other hand, investors select funds with low betas when prices are expected to fall in the future. Hence, when prices of the mutual funds start falling, investors rush to sell of the funds which results in decrease in return and hence higher standard deviation. Therefore, ranking of funds with high beta versus the standard deviation is difficult due to the varying reactions within the stock when prices changes. Three Funds that Appear on both lists of the Highest 1-year and 3-year Returns The selected funds are shown in Table 5. The Standard Deviation of the Funds             The standard deviation of the three funds is given in Table 6. The values were obtained from Morningstar.com website under the ratings and risk section. The standard deviation is used to measure the variability of the fund’s returns. A higher standard deviation implies that the fund’s returns fluctuate more during the period and hence the expected returns largely vary from the actual return (Pangestuti, I.R.D., Wahyudi, S. and Robiyanto, R., 2017). Using the three-year period, the standard deviations of the three selected funds are 39.87%, 36.37% and 39.86% for Rydex Monthly Rebalance, ProFunds Semiconductor UltraSector Fund and Direxion Monthly respectively. From the results of the standard deviation, the return for the Rydex Monthly Rebalance Fund is expected to range between 39.87 standard deviations from the average returns for the three-year period. In essence, use the three-year total return of 65.82%, an investor expects the return of the Rydex Monthly Rebalance fund to be between 25.95% and 104.82% 68% of the time, i.e., one standard deviation of the average return. Hence, a one-standard deviation change of the returns of the fund will result in a 39.87% deviation from the actual return. A significant deviation from the average return, say 3 standard deviations would result into huge losses or very high returns since the standard deviation is significantly high.             Similarly, 68% of the returns of ProFunds Semiconductor UltraSector Fund are expected to lie between 29.42% and 102.16% for the 3-year total return. The total return therefore is expected to vary greatly when there is significant change in expected returns of the fund. The same argument holds for Direxion Monthly NASDAQ -100 Bull 2X Fund since the high standard deviation of 39.86% implies that the three-year total return of the fund will range between 25.19% and 104.91% 68% of the time for the three-year period under study.              From Table 6 therefore one can conclude that funds that lie higher in 1-year and 3-year return have their corresponding standard deviations (variability from the average return) also high. This is expected since funds that have high returns tend to highly risky as indicated by the high standard deviations. Hence, if the market conditions act to the benefit of the investors, they will earn significantly high returns even with a small positive change of the funds’ returns. On the downside, a small negative change of the returns of the funds will result in huge losses to the investor. The standard deviation thus provides the investors with the measurement of how the actual return of the funds will deviate/vary from the expected returns over the given period. Both funds show high variability from the expected returns and the high risk is compensated with the high returns which investors receive for 1-year and 3-year period. The Sharpe Ratio of the Funds             The Sharpe ratio of the three funds was also obtained from Morningstar’s rating and risk section. Sharpe ratio is used in measuring the risk adjusted return of the funds using the standard deviations of the funds. A higher Sharpe ratio of the funds is preferred since it indicates that the fund’s return is better relative to the investment risk taken by the fund to achieve the return (Choudhary, V. and Chawla, P.S., 2014). The Sharpe ratio for the selected three funds is shown Table 7.             From the table, it is evident that ProFunds Semiconductor UltraSector Fund has higher Sharper ratio of 1.57 as compared to Direxion Monthly NASDAQ -100 Bull 2X and Rydex Monthly Rebalance NASDAQ-100 ® 2x Strategy Fund with Sharpe ratios of 1.47 and 1.46 respectively. The implication here is that the risk taken by ProFunds Semiconductor UltraSector Fund to achieve a 3-Yr. return is less compared to other two funds. Although all the three funds have Sharpe ratio of greater than 1 (which is considered good and attractive), the fund with a higher Sharpe is considered better than others. Hence, ProFunds Semiconductor UltraSector Fund is better than other funds since it requires less risk to achieve the required returns.             However, it is important to note that funds with higher Sharpe ratio tend to have higher standard which in essence result in higher returns. This can be observed from Table 7 and Table 6. However, the Sharpe ratio only provides a measure of the risk-adjusted return of the funds over the period and does not imply that volatility has decreased. There may be other factors such as the market dynamics that impact the funds resulting to high variability in the returns and hence higher standard deviation which causes the Sharpe ratio to be high. Based on the three selected funds, the funds ratios are relatively close to each other as well as the standard deviation and hence high returns are shown in Table 5.            The Treynor Ratio of the Funds             The Treynor ratio is also used to measure the risk-adjusted return of the fund similar to Sharpe ratio whereby it uses the market risk (beta) instead of the fund’s total risk given by the standard deviation which is used in Sharpe ratio. The higher the fund’s Treynor ratio the better the performance efficiency of the fund and hence...