Quantitative Methods
Holding period return
Holding period return is the total returns received from holding a particular investment portfolio of assets. The holding period return rate usually calculated as the total sum of all income and capital gains of the investments divided by the investment value at the beginning of the trading period being measured (Hallerbach, 2003). It is a very basic way used to measure the rate of return obtained from a particular investment. Therefore, its calculation is based on a unit-value-invested rather than on a time basis. This, however, makes it difficult to provide a comparison of returns on different investments with also different time frames. Table 1 below shows the holding period return of Better Value Ltd and Gamma investments for a five-year period from 2005-2009.
In the year 2005, Better Value Ltd had a negative holding period return on investment of -5.63% while during the similar period (2005); Gamma Investments had a holding period return rate of 3.98%. However, during the subsequent years 2006, 2007, 2008 and 2009 the holding period return for Better Value Ltd was 10.02%, 6.27%, 9.54% and 7.97% respectively. In all the four subsequent years beginning from 2006 to 2009, Better Value Ltd had greater holding period returns compared to Gamma Investment, which recorded holding period returns of 4.30% in 2006, 5.00% in 2007, 4.10% in 2008 and 5.98% in 2009.
Graph 1 below illustrates and compares the holding period returns for Better Value Ltd and Gamma Investments for the five-year period (2005-2009).
Graph 1
Sharpe Ratio
The Sharpe ratio determines whether an investment portfolio's profit can be attributed to high risk or correct thinking. Typically, the higher the Sharpe ratio, the better the investment portfolio has performed after adjustment for risk (Maringer, 2008). While a certain portfolio may generate great profit, the profit may be the result of high and potentially dangerous risk. To obtain the Sharpe ratio subtract the rate of the risk-free investment from the investment portfolio expected return, divided by the investment portfolio's standard deviation. As illustrated in graph 2, the Sharpe ratio for Better Value Ltd is 0.08 while Gamma Investment fund has a Sharpe ratio of - 0.52. Comparing the Sharpe ratios of the two investment portfolios, we can conclude that Better Value Ltd is the better investment portfolio, since; it has a higher Sharpe ratio.
Graph 2
Arithmetic mean and median of the total returns and the average annual growth of dividends of Better Value Ltd
Arithmetic mean
The mean also referred to as the arithmetic mean, is the sum of all the numbers in a particular set divided by the numbers in the set (Conover, 2005). Thus, the arithmetic mean of the total returns from Better Value Ltd over the past five years is given by the sum of the dividends earned in the respective years (₤0.89) divided by the number of years (5). Thus, the arithmetic mean for the total returns for Better Value Ltd investment portfolio is ₤0.18.
Median
The median of a particular number set is its middle point, where half of the numbers in the set are above the median while the other half are below the median. In the set of the dividend earned from Better Value Ltd investment portfolio, which are ₤0.14, ₤0.17, ₤0.17, ₤0.19 and ₤0.22, the median of the data set is ₤0.17.
Average annual growth of dividends of Better Value Ltd
The average annual growth of dividends of Better Value Ltd is derived by obtaining the sum of the annual growth of dividends in the respective years divided by the number of years in the period of concern (Maringer, 2008), In the year 2005, the annual dividend growth was negative -₤0.01, while, in 2006, the annual dividend growth for Better Value Ltd was ₤0.03. However, in the year 2007, there was no annual growth of the dividend. In the year 2008 and 2009, the annual growth of dividend was ₤0.02 and ₤0.03 respectively. Thus, the average annual growth of dividend is given by the sum of the annual growth in dividend in the respective years (0.07) divided by 5 years. This gives an average annual growth of dividend of ₤0.014 over the five-year period. The mean absolute deviation (MAD), which is also referred to as the average absolute deviation, is the arithmetic mean of the absolute deviations of a particular data set about its mean. For the Gamma Investments fund, the mean absolute deviation (MAD) is 0.73.
Range and mean absolute deviation (MAD)
The range of an investment in the Gamma Investment fund between the year 2004 and 2009 is given by the difference between the highest and least return rate. This equals to 5.98(highest) minus 3.02(lowest) which gives the range of 2.96.
Compound interest rate of investment at Better Value Ltd
The future value of an investment is usually given by;
Fv=P(1+r100)n
In the formula, P is the principal amount invested while r is the interest rate on the investment per the accounting period and n is the duration period of the investment. The principal amount at year-end 2004 is ₤28.45 while the future value at year-end 2009 is ₤37.25. Hence, the average compound interest rate per Annum is the interest rate at which the principal amount of ₤28.45 in year-end 2004 yields the future value of the investment of ₤37.25 in the year-end 2009 which is a five-year period. Thus, the average compound annual return rate on an investment at Better Value Ltd is 5.54% per Annum.
Coefficient of variation
The coefficient of variation (CV) is usually derived from the ratio of the standard deviation of a particular data set to the non-zero mean of the same data set (Hallerbach, 2003). Typically, the absolute value is normally taken for the mean of the data set to ensure that the coefficient of variation obtained is always positive. The mean of the total returns on the investment portfolio in Better Value Ltd between the year 2005 and 2009 is 5.64. The standard deviation of the annual returns of the investment portfolio Better Value Ltd is 6.47. Therefore, the coefficient of variation (CV) for the total returns on investment between the year 2005 and 2009 for Better Value Ltd is given by 6.47/5.64 which is 1.15.
References List
Conover, W.J., 2005. Practical Nonparametric Statistics, New York: Wiley & Sons.
Hallerbach, G.W., 2003. Holding Period Return-Risk Modeling: Ambiguity in Estimation.
Maringer, D., 2008. Statistical and Computational Methods for Data Analysis, University of Basel, HS.
