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# Disertation Essay

2911 words - 12 pages

Product Risk And Uses Of Standard Deviation Finance Essay
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Product Risk And Uses Of Standard Deviation Finance Essay
Risks and returns are the two most important concepts in the investing world. The concept of return, which is the profit on investment, is a very clear subject to many investors but the risk is often vague. Several approaches had been ...view middle of the document...

However, in finance, standard deviation is applied to annual rate of return of an investment. This enables investors to measure and estimate the expected volatility of an investment over a period under consideration (Investopedia, 2010). The standard deviation is therefore given by the formula:
where σ = Standard deviation; ∑ = the sum of; and = means 'the mean' (mathsrevision.net, 2010).
Standard deviation assesses the degree of how the values are dispersed around the mean. It estimates the mean by assessing the error to which the mean of the sample is subject. In addition, it finds probability of events occurring in a given period (Manager-Net, 2008). In finance, the most common use of standard deviation is to the measure risk of holding a portfolio or security. It however, represents risk associated with a given security such as stocks, bonds, etc. Risk is an important factor used to determine how to efficiently manage a portfolio of investments as it determines the variation in return on the asset or portfolio and gives the investors a mathematical basis for investment decisions (Hedge funds Index, 2010).
Standard deviation shows how close various values are clustered around the mean. When the standard deviation is small, the values are therefore tightly close together and the bell-shaped curve is steep. On the other hand, the bell curve is relatively flat when you have relatively high standard deviation. This is expressed graphically below (Niles, 2010).
The red area on the above graph represents one standard deviation from the mean and this account for about 68% of the people in this group. Two standard deviations from the mean are represented with green and accounts for about 95% of the people while three standard deviations from the mean are represented with blue and accounts for 99% of the people (Niles, 2010).
STANDARD DEVIATION AS A RISK INDICATOR
Standard deviation is also seen to have some outstanding qualities. Fitzgerald (1999) points out that standard deviation is used to estimate how accurate the sample mean is as an estimate of the population mean. In addition, it can also be used to convert scores which are calculated on different scales to scores on standard scale known as standard scores and this in turn gives an accurate idea of its relative importance or size. This, he said has several advantages for the decision maker. In statistical analysis, standard deviation is the most widely used measure of variation. Not only that, it is regarded as an excellent means of summarizing the extent of concentration of dispersion of values and it is relatively easy to use (Social Studies 201, 2006; Sharma, 2007). It also plays a very important role in comparing skewness and correlation (Sharma, 2007). Standard deviation also provides additional understanding of the future volatility of a fund’s performance, comparable to volatility of other funds in the sector or benchmark for the fund. The higher the volatility, the higher the average...

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