## Introduction

More and more economies have developed the tendency to rely on private capital flows to sustain themselves and therefore have also become more prone to risks that come with the volatility associated with such capital flows (Baumol 2007). Researches have been carried out to help establish a comprehensive framework that can be used to carry out analysis and thus help prevent large scale capital account crises that come with financial distress (Babbel 2002). A more recent approach that has been in use since the Asian crisis has been the employment of risk assessment to identify the risks associated with potentially unstable areas in balance sheets, of financial as well as those of the corporate and public segments. The development of effective approaches is indeed important in ensure that risks are detected before they cause a severe effect on a business and the economy by extension. Different risk indicators such as beta, CAPM and Standard Deviation have been employed to assess risks in different contexts (Ziliak 2004).

Risk indicators employed for different kinds of investments are usually used to indicate the financial risk that is associated with a given type of investment. The choice of a risk indicator lies solely with personal preference, though some indicators may be more informative than others (Whelan & Bowie 2002).

This paper seeks to offer a critical discussion on the uses of standard deviation as a risk indicator for investments.

## Financial definition of standard deviation

Standard deviation (SD) can be defined as a statistical measure of the distribution of probability (Rappaport 1996). The function of SD in the measurement of tightness or vitality can be applied widely to inform decision making in business. Its often applied when cases where a business is faced with price fluctuations of given assets that may be in form of stocks, properties or bonds or risk associated with portfolio assets such as index managed mutual funds or actively managed mutual funds (Borch 1997). SD’s application in business offers investors with a mathematical model that is critical in evaluating and deciding on investment choices.

## Calculation of the standard Deviation

In the process of calculating standard deviation, the mean of the data points is first determined. There are always a given number of data points that are required in order to obtain a standard deviation that is useful. In the next step, the determined mean is subtracted from every individual figure in the data group (Prakash 2002). This is followed by squaring of each of the difference. A calculation if the sum is, the figure is then divided by the number of data points minus one (Mugambi 2001). The square root of the end figure that is achieved after all the calculation is the standard deviation.

## Use of standard deviation as a risk indicator

Measurement of risk associated with funds or an investment is often critical. Different studies have shown that there is an important relationship between the level of risk and the likely returns over a given period of time (Buhlmann 1997).

A common finding is that when there is a high risk associated with a given investment then there is a greater chance that the price may move downwards. This can occur over a short or even in the medium term of the investment period ( Muyumi 2006).

Standard Deviation (SD) is especially used when the comparison between different investment options is to be made. When a risk is calculated singularly, it does not offer much help as far as decision making is concerned. SD offers a good measure for comparing a risk indicator as between investment options and this often provides the all important idea of the relative risk.

SD is also sometimes used in technical analysis for specific functions such as cost projections. It has been applied in building of Bollinger bands that identify the upper and lower bands for the analysis (Howitt 2000). The bands are spread away from the middle point moving averagely depending on the given SD level. In cases when the volatility is low, a “of the Bollinger bands occurs alongside the diminishing of the range of prices during a certain period being used for data points” (Krugman 1999, p. 5). Similarly, in case the volatility increases in association with the security, then the lines for the standard deviation are seen to widen.

This technique, referred to as the Bollinger technique was put forward to identify “potential reversal points and the future price predictions” (Sutter 2007, p. 67). When using this technique, it’s recommended that one should use lines that are at least two SDs away from the identified moving average. SD can however be used to identify the variability of any data set, for instance the identification of sales over a given period, or on quarterly or monthly Price/Earnings values for a particular security (Daly 2006). If the data points identified are normally distributed then this implies that the data points that will fall within a particular range of the present mean (Davis 2006).

## Example of SD Use as a risk indicator and analysis

The example shown below, shows how standard deviation is used to indicate the relationship between risk and the investment returns (Frees 2006).

### Risk and Return of funds (1 July 2004- 30 June 2009)

As shown in the figure above, the fund risk indicator was most high for Fund A that is identified as the Asian Equity Fund. This was followed by Fund B, indicated as the mixed asset fund. The third was Fund C, the bond fund and finally D which is the conservative (Gowdy 1999).

Fund A, described as the Asian Equity fund showed the highest fluctuation, indicating that it has the highest risk indicator. However, as seen from the table, the same fund had the highest return out of the four funds compared. The returns were associated with high volatility going up by 13.65% in one of the months and as low as 20.84% in another month (Niles 2010). In the five year period under review, there were up to 11 months where the price of the Asian equity (Fund A) went down by more than 5 percentile points.

On the other hand, Fund D, presented the lowest risk indicator, and in correspondence with that, it yielded the lowest returns at a lowly 1.62% per annum. As expected, the fluctuations between monthly incomes were minimal. The highest was at 0.37% and the worst month at 0% (Nordhaus 2002). This particular fund did not have instances where the price fluctuated by more 5 percentile points.

In the table, it’s also clearly visible that two funds, B and C, were neither high nor low in all measurements. Fund B, had the second most risky indicator, yielded the second highest returns, showed the second highest range of fluctuation and had a total of six months where the price of the fund dropped by more than 5% (Krugman 1999).

The illustration showed above provides a good example to indicate how standard deviation is used to determine the relationship between the risks of an investment in relation to its performance under prevailing market conditions. It’s clear that investments that are associated with a high risk are likely to produce better returns in the long term. This is however associated with some instances of losses, some of which may be high. The relationship that is made available through the use of standard deviation has formed a rationale for decision making (Mugambi 2001). For instance, such data that indicates higher long-term returns for the reason as to why most financial advisors recommend that younger investors should always try to invest in higher risk funds (Prakash 2002). In this case, an investor (young) has a time to do away with the volatility that comes in the short term and later rip the benefits of the better long term benefits.

The standard deviation risk indicator is one of the best ways through which rationale investments decisions are based. The use of standard deviation is as a risk indicator is often recommended by financial advisors due to its ability to lend itself to the computation of other measures; its ability to give the average of all deviations that take place around the mean; and the easiness to describe it (Ziliak 2004). Certain other factors such as an individual’s circumstances, finances, availability and other costs are also relevant in decision making (Babbel 2002).

The use of standard deviation as a measure of volatility may not be available for use by several investors due to different reasons.

First, the calculation of standard deviation is a process that many investors are not conversant with. The method employs use of formulas that may prove to be challenging for different categories of investors. In such cases, some investors may opt to get professionals to do the analysis but again it won’t be of much help as they will need something that they understand (Frees 2005).

Standard deviation also uses data that has been collected over a period of time in order to determine the variance and the risk associated with a certain kind of investment. The method cannot be used as a risk indicator in cases where the investment concept is completely new.

Another major disadvantage of using standard deviation as a risk indicator lies in its ability to be influenced by extreme scores. Investments may perform differently due to market conditions. In some cases, the market conditions are influenced by one time factors, or factors that may be considered to be special in the sense that they cannot be influenced by investors. Such factors may include drought or natural calamities and will have a major impact on a business. Standard deviation measures fluctuate the same way as the extreme scores that might represent business performance due to above mentioned factors. In that case, the analysis may not give a true picture of the risk associated with the business in question (Howitt 2000).

This challenge may however be addressed if standard deviation measure as a risk indicator is used in conjunction with other factors to give a more precise picture. This may include the use of other risk indicators such as beta and CAPM to address other inherent challenges that may come with the use of standard deviation alone (Niles 2010).

## Conclusion

This paper sought to critically discuss the use of standard deviation as an investment risk indicator. It has been identified that standard deviation gives the precise volatility measure associated with different investment options and thus helps an investor make an informed decision regarding a business option. The measures given by standard deviation are relatively easy to interpret making it to be preferred over other risk indicators. However, some challenges have been identified to influence the use of standard deviation as a risk indicator. The most important disadvantage is its ability to be influenced by extreme scores. It may also give a false picture if some other coherent factors are not considered and thus must always be used in conjunction with other risk indicators. All in all, standard deviation is a good risk indicator which, if well used, can guide in the selection of proper investment options.

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