Most organizations today collect and store large volumes of data, which include both financial and operational information. Decisions in these organizations rely on a careful analysis of this data. The analysis entails the application of statistical tools. Statistical tools are crucial to managers in the business environment as they assist them in making sound decisions and in running of their businesses based on scientific research. An understanding of statistical analysis tools allows managers to explore the condition of the organizations, measure its current value, predict its future value, and evaluate the desired bond or stock for investment purposes. In fund management, basic tools of statistics are employed to analyze the historical performance and to predict future returns of a given portfolio by fund managers . Mutual funds are professionally managed investment fund s that pool money from many investors to invest in securities such as equities, bonds, commercial papers, money market instruments among other assets (Fink, 2011). These investors may be individual retail or institutional in nature.
Statistical analysis is based on the available data regarding the performance of the portfolio for the past years. The most commonly data used is the market values of the different portfolios and weighting of the different asset classes ( Wong, Filbeck & Baker, 2015). Analysis helps managers in making informed choices during uncertain circumstances regarding the type of investments to undertake. Two analysis techniques are employed to do this, which include descriptive analytics and predictive analytics ( Evans & Lindner, 2012) . Descriptive analytics considers what has happened in the historical years under review and helps explain the underlying economic conditions underpinning the performance (Wong, Filbeck & Baker, 2015). Managers can analyze past successes and failures by applying descriptive analytics. The technique also enables managers to understand whether their portfolios are making positive returns or losses. Predictive analysis, however, uses a variety of modelling statistical techniques to predict future probabilities and trends based on historical data (Wong, Filbeck & Baker, 2015). The technique generates best estimates of the expected future returns.
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The individual investor's expectations and the desired return level define a good return for most mutual funds (Fink, 2011). A comparable return to the overall market return like the NASDAQ or FTSE 100 satisfies most investors. A good return equals to or exceeds the average market return.
Three common statistical return ratios can be used to compute return or performance of a given portfolio. They include the annual return (also referred to as year to date), the annualized rate of return and the expected return ( Slee, 2011) . Investors regularly use the annual return calculation due to the technique’s easiness concerning calculations compared to the annualized return and expected return (Wong, Filbeck & Baker, 2015). The required variable to compute the annual return and annualized return include the initial price value of the investment at the beginning of the holding period, usually the first day of January of that year, and the price value of the investment at the end of the one-year period, usually 31 of December (Slee, 2011). Variables required to calculate the expected return include the rates of return for each asset class, which can be equity, bonds or money markets and their corresponding weights based on the size and type of the asset (Fink, 2011). The total portfolio comprises 100% and the individual asset investments form a fraction of this. It is important to differentiate between annual return and annualized return. Annual return focuses on the gain or loss of the initial investment over a one year period while the annualized return focuses on the average rate of return over multiple year time frames. The annualized return can also be referred to as the Compounded Annual Growth Rate (CAGR) (Slee, 2011).
When analyzing mutual fund returns and the performance of other investment securities other important measures considered include the return on investment and the return of the investment. Return on investment ( ROI ) means the actual return realized by the investor, which can be described as the extra value earned on top of what was initially invested (Fink, 2011). Return of the investment means the return of the investment itself without any additional value or loss on top. The process of computing the above ratios is demonstrated below.
Annual Return
The first thing to do is to determine the initial starting value and the final value of a portfolio to calculate the annual return. The initial price is then subtracted from the end price to determine the investment's change in price over time. The result is divided by the initial price and multiplied by 100% to give it a percentage figure.
As an example, the table below gives initial and closing values of a portfolio for company X for a period of 3 years:
| Year | Price Value as at January 1 (USD mn) | Value as at December 31 (USD mn) |
| 2011 | 20 | 25 |
| 2012 | 25 | 30 |
| 2013 | 30 | 34 |
From the table and using the formula,
Annual Return = ((Value at End of Year-Value at Start of Year)/Value at Start of Year) ×100%
Annual Return for 2011 = ((25-20)/20) ×100% = (5/20)×100%
= 25%
Annual Return for 2012 = ((30-25)/25) ×100% = (5/25) ×100%
= 20%
Annual Return for 2013 = ((34-30)/30) ×100 = (4/30) ×100%
= 13.3%
Annualized Return
Annualized return, on the other hand, is used in different ways to evaluate performance over time such as several years. The first step when calculating the annualized rate of return involves determining the beginning period and end period values and the period under review.
The annualized return from this can be determined by putting in the corresponding values into the following equation:
Annualized Return = (End Value for Y / Start Value X) ^ (1/N) -1
From our table example above:
Annualized Return = (End Value for 2013 / Start Value 2011) ^ (1/N) -1
Where N is the total number of years under review = 3.
From our example above, to calculate the annualized return for 2011 to 2013 will be as follows:
Annualized return = (34/20) ^ (1/3)-1
= 0.193 (multiplied by 100%) = 19.3%
Expected Return
Expected return measures the mean, or expected value, of the probability distribution of investment returns for the future. The variables required include the returns by asset class and their corresponding asset weights. The expected return of a portfolio is calculated by multiplying the weight of each asset by its return and adding the values for each investment.
The table below shows an example of a portfolio with three investments :
| Asset Class | Asset Weight (%) | Expected Return (%) |
| Asset A | 30 | 6 |
| Asset B | 25 | 8 |
| Asset C | 45 | 10 |
Getting the Expected Return of the Portfolio involves the following computations
Expected Return of the Portfolio = (Weight of Asset A× Expected Return of Asset A) × (Weight of Asset Expected Return of Asset B) × (Weight of Asset Expected Return of Asset C)
Expected Return of the Portfolio = ((30×6) + (25×8) + (45×10))/100%
Expected Return of the Portfolio = (180+200+250)/100% = 830/100%
Expected Return of the Portfolio = 8.3%
These three rates of return as shown in the above examples form the basis of comparison among portfolios invested in various asset classes. The bigger the return, the more attractive the investment, which translates to good returns to the investor.
In conclusion, statistical analysis tools are vital because fund managers use them as standard measures that allow them to compare the performance/returns of different portfolios at glance to make good investments decisions with the funds under their control to achieve high and positive returns for their trustees and their investors.
Mutual funds provide diversification, low transaction costs, economies of scale and easy access to a broader choice of assets because they are pooled funds. Additionally, professional management offered by fund managers to the individual investors who do not fully understand the art of investment in funds are factors that have propelled their popularity in the past few years going into the future. It is vital for managers to fully understand the calculation and the underlying assumptions used at arriving at these statistical ratios. The higher the risk an investor exposes themselves to, the higher a return they will seek to gain. The meaning of this is that most savvy investors are likely to evaluate the returns offered by the mutual funds in the past and compare these returns with those of other assets before making an investment decision regarding the choice of a particular fund manager and the asset class.
References
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Evans, J. R., & Lindner, C. H. (2012). Business Analytics: The next Frontier for Decision Sciences. Decision Line , 43 (2), 4-6.
Fink, M. P. (2011). The Rise of Mutual Funds: an Insider's View . OUP USA
Slee, R. T. (2011). Private Capital Markets: Valuation, Capitalization, and Transfer of Private Business Interests . Hoboken, N.J: Wiley.
Wong, K. P., Filbeck, G., & Baker, H. K. (2015). Options. Investment Risk Management . Oxford University Press.
