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 employed over times to measure the risks associated with investment portfolios.

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Standard deviation is a popular basis for risk measurement used for investment purposes (Today Forward, 2010). Standard deviation hence helps to tell a story behind a data and the concept the normal distribution of data (Niles, 2010). This though has been a scary and sometimes complicated topic to people, students and practitioners as well (Niles, 2010; Williamson, 2010). Standard deviation was first discovered and used by a renaissance scientist in Victoria London, Karl Pearson in 1897 in his quest to help his friend Weldon to use the measure of variation to understand the evolution process and to use empirical evidence of natural selection to find out how new species emerged (Magnello, 2005).

Standard deviation is defined as a measure of dispersion of a set of data from its mean (Investopedia, 2010). It is calculated as the square root of variance. The more spread apart the data, the higher the deviation. It is also seen as a measure of variability among the values of a frequency distribution (Taylor & Francis, 2009). Standard deviation, also known as historical volatility is also seen as the “mean of the mean” (Niles, 2010). 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 ÃÆ’ = Standard deviation; Ã¢Ë†â€˜ = 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 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 returns (CFP, 2005). In risk measurement, standard deviation is seen as important in modern portfolio theory and tin risk quantification by way of price volatility for asset classes and securities. In the measure of spread, standard deviation is very useful in that if the mean and standard deviation of a normal distribution are known, the percentile rank linked with any given score can be computed and it is also mathematically traceable (Hyperstat online contents, 2010). However, standard deviation also has its defects. It is believed to be difficult to calculate and interpret. It is also a mathematical construction which may be difficult to explain intuitively (Social Studies 201, 2006). More weight is however given to extreme values and less weight to those near the mean. (Sharma, 2007). Ibrahim et al, 2006, believes that standard deviation is influenced by extreme scores. Arguably, while some critics believe that standard deviation offers a valuable tool for comparing one type of risk and is found useful in getting a general idea of available risks, others believe that it fails to reflect the true position of what happens in the capital markets in terms of how returns are distributed around the mean (JP, 2006). Standard deviation is also flawed in that in the calculation, it assumes a normal distribution and this normal distribution seems to work well in physics and general statistic and not risk. This is because it fails analysing the tendency of investment return to suffer “fat tail distribution” which constantly hunts the investment world. This simply means that less than normal events can and do happen once in a while and the basic concept of standard deviation does not cover this (JP, 2006; Glogger, 2008; JP Morgan, 2008/09). JP, 2006 also believes that standard deviation should neither be neglected nor used exclusively in risk measurement as the real world imperfections demand that a collection of flawed risk measures can be put together to outline the overall risk available. Carther, 2007 also points out the importance of standard deviation in reporting a fund’s volatility. It indicates a tendency of funds to drastically rise and fall in a short period of time. She however sees the calculation as intimidating though useful. There has been a contention however on the reliance of standard deviation as a measure of portfolio risk. This is because it is seen as being inconsistent. It is also said to assume symmetric distributions as it treats desirable upside movements as if they were as undesirable as downside movements (JP Morgan, 2008/09). This has called for alternatives in measure of risk.

JP Morgan, (2008/09), sees Conditional Value at Risk (“CVaR95”) as it defines the average real portfolio loss (gain) in relative to the starting portfolio in the worst five percent of scenarios which is based on 10,000 simulations. Unlike standard deviation which sees risk as being only a one standard deviation event and fails to capture the “fat” left tail effects, CVaR95 is seen to have overcome this drawback as it captures both the asymmetric risk preferences of investors which is the fear of loss being greater than the gain and the incidence of “fat” left tails which is prompted by skewed return distributions (JP Morgan, 2009/09). The absolute mean deviation is regarded as the most direct alternative for standard deviation. This is the average of the absolute differences between each score and the overall mean. In a realistic situation where some of the measurements are in error, the mean deviation is seen to be more efficient than standard deviation. Though the standard deviation and mean deviation are not used for same measurement, standard deviation is always greater than the mean deviation, and there is more than one possible mean deviation to standard deviation and vice versa, the mean deviation is seen to be simpler to compute than the standard deviation (Gorard, 2004). Sharpe ratio derived in 1966 by William Sharpe has been popular in risk/return measures in finance. It is given by the formula; Source: https://www.investopedia.com/terms/s/sharperatio.asp Gaurav and Kat (2002) point that one outstanding quality of Sharpe ratio is its simplicity in performance evaluation. This is done by calculating the highest expected return for a given standard deviation that is attainable which is the sum of interest rate and the product on the Sharpe ratio of market portfolio and standard deviation in question. An unlimited number of normally distributed funds can therefore be evaluated using this (Gaurav and Kat, 2002). Sharpe ratio also shows if a portfolio return are due to result of excess risk of good investment decision, as the higher the Sharpe ratio, the higher the risk adjusted performance and vice versa (Vishwanath and Krishnamurti, 2009). Arguably, in as much as Sharpe ratio is simple, popular and easy to calculate, the drawback is that it is a restricted measure in the mean-variance frame work and it does not give a full picture of the fund performance (Jiang and Zhu, 2009.) It also assumes that the risk free rate is constant and this is not true. In addition, it can be problematic when it uses standard deviation to calculate the ratio of asymmetric return as standard deviation is most appropriately used to measure strategies that has approximate symmetric return distribution. In addition the Sharpe ratio is based on historical data and historical data are not reliable because past performance is not always an indicator for future results (Quantshare, 2010). Jensen’s Alpha is also an alternative measure of risk to standard deviation. It however, measures the degree to which a stock’s average return exceeds the expected return, given the firm’s beta. Source: https://www.investopedia.com/terms/j/jensensmeasure.asp The outstanding quality of Jensen’s alpha is its ability to do a hypothesis test rather than comparison of the results (Beck et al, 2007). Similarly, the Treynor ratio looks like the Sharpe ratio, the difference being that the Treynor ratio uses Beta as a measurement of volatility. Treynor relies on Beta and this simply implies an assumption that non-systemic risk can be mitigated by diversification. As a result, the ratio has a limited utility in evaluating non-diversified portfolios. Treynor’s ratio is calculated as (Average Return ofÂ the Portfolio – Average Return of theÂ Risk-Free Rate)Â /Â Beta of the PortfolioÂ Source: https://www.investopedia.com/terms/t/treynorratio.asp Comparatively, these measures are not suitable in all scenarios. Jensen’s and Treynor’s ratio are not suitable for evaluation of hedgefunds as it gives no opportunity for the investment to be repriced and this, as a result can make investments appear less risky than they are. In addition, the rewards to risk ratios will most likely run for this portfolio in the premium collection cycle until a leveraged loss is sustained (Zigler, 2007).

Conclusively, in the investment world, risk is very important and cannot be separated from return and performance. Every investment, however involves some form of risk which can either low or high. Risk is therefore quantifiable both in relative and absolute terms and a good understanding of risk will help an investor or financial services make better financial decisions (Lamb, 2008). Beck, K and Niendorf, B. 2007. Good to Great, or Great Data Mining. (Online). Available from: https://69.175.2.130/~finman/Orlando/Papers/GreatDataMining.pdf. (Accessed 25th October, 2010). Carther, S. 2010. Understanding volatility measurements. (Online). Available from: https://www.investopedia.com/articles/mutualfund/03/072303.asp (Accessed 15 October, 2010). Certificate in Financial Planning (CFP), 2005. CF2: Investment and Risk. London. BPP Professional Education. Gaurav, A and Kat, H M. 2002. Generalization of the Sharpe Ratio and the Arbitrage-Free Pricing of Higher Moments. ISMA Discussion Papers in Finance 2002-15. (Online). Available from: https://www.icmacentre.ac.uk/pdf/discussion/DP2002-15.pdf. (Accessed 21 October, 2010). Glogger, M. 2008. Risk and Return. (Online). Available from: https://university.akelius.de/library/pdf/risk_and_return_martin_glogger.pdf (Accessed 12 October, 2010). Gorard, S. 2004. Revisiting a 90-year-old debate: the advantages of the mean deviation. Online. Available from: https://www.leeds.ac.uk/educol/documents/00003759.htm. (Accessed 20th October, 2010). Graeme, P. 2010 Standard Deviation. (Online). Available from: https://moneyterms.co.uk/standard-deviation/. (Accessed 08 October, 2010). Fitzerald, J. (1999). The Uses of Variation. (Online). Available from: https://www.actualanalysis.com/vary.htm (Accessed 10 October, 2010) Hedge fund Consistency Index, 2010. Standard Deviation (Online). Available from https://www.hedgefund-index.com/d_standarddev.asp. (Accessed 10th October, 2010). Hypersat Online Contents, 2010. Standard Deviation and Variance. (Online). Available from: https://davidmlane.com/hyperstat/A16252.html. (Accessed 20th October, 2010). Ibrahim, A.S and Mikhail N.N.H. 2006. Measure of Dispersion (Variability). Online. Available from: https://www.seci.info/amalsamy/Epi%202.1.pdf. (Accessed 10th October, 2010). Investopedia, 2010. Standard Deviation. (Online), Available from: https://www.investopedia.com/terms/s/standarddeviation.asp. (Accessed 05th October, 2010.) Jiang, G J and Zhu, K X. 2009. Generalized Sharpe Ratios: Performance Measures Focusing on Downside Risk. International Research Journal of Finance and Economics. ISSN 1450-2887 Issue 30.pp. 134-136. (Online). Available from: https://www.eurojournals.com/irjfe_30_10.pdf. (Accessed 15 October, 2010). JP, 2006. In Praise of Volatility. The Capital Spectator; Investing, Asset allocation, Economics & the search for the Bottom line. 12.10.2006 (Online). Available from: https://www.capitalspectator.com/archives/2006/10/in_praise_of_vo.html. (Accessed 15 October, 2010). JP Morgan, 2008/09. Alternatives to Normality; Some lessons from the credit crisis. LV-JPM3044. PP 4. (Online). Available from: https://www.jpmorganassetmanagement.co.uk/Institutional/_documents/JPM3044%20Alternatives%20to%20normality%20paper%20indd%20125.pdf. (Accessed 25th October, 2010). Lamb, K. 2008. Measuring and Managing Investment Risk. (Online). Available from: https://www.investopedia.com/articles/08/risk.asp. (Accessed 20 October, 2010). Magnello, M.E, 2005. Karl Pearson and the Origin of Modern Statistics: An Elastician becomes a Statistician. The Rutherford Journal; The New Zealand Journal for the history and Philosophy of Science and Technology. Vol 1.(Online). Available from: https://www.rutherfordjournal.org/article010107.html (Accessed, 05th October, 2010). Managers-net, 2008. Standard Deviation and Variance. (Online). Available from: https://managers-net.org/stddev.html (Accessed 05 October, 2010). Mathsrevision.net, 2010. Standard Deviation. (Online). Available from: https://www.mathsrevision.net/gcse/pages.php?page=42 (Accessed 10 October, 2010). Niles, D. 2010. Standard Deviation. (Online). Available from https://www.robertniles.com/stats/stdev.shtml. (Accessed 05th October,2010). Quantshare Trading Software, 2010. Sharp Ratio- Part 2. (Online). Available from: https://www.quantshare.com/sa-90-sharpe-ratio-part-2. (Accessed 25th October, 2010). Sharma, J.K. (2007). Business Statistics. India: Dorlin Kindersely PVT. Ltd. (Online). Available from: https://books.google.co.uk/books?id=tVkYRf0ydE8C&pg=PA147&lpg=PA147&dq=disadvantages+of+standard+deviation&source=bl&ots=RE9brmrb4s&sig=NUe_zuXTriNB65PYkpQ-xsiVMCE&hl=en&ei=OXfDTMuOB5HQjAfwx526BQ&sa=X&oi=book_result&ct=result&resnum=4&ved=0CCcQ6AEwAzgU#v=onepage&q=disadvantages%20of%20standard%20deviation&f=false. (Accessed 12th October, 2010). Social Studies 201. (2006). Standard deviation and variance for percentage distributions. Journal of Social Studies. Section 5.10, pp 259-264. (Online). Available from: https://uregina.ca/~gingrich/o2306.pdf (Accessed 12th October, 2010). Taylor & Francis, 2009. Standard Deviation from the Dictionary of British Education. (Online). Available from: https://www.bookrags.com/tandf/standard-deviation-5-tf/. (Accessed 05th October, 2010). TodayFoward; The Simple Way to Plan, Manage, and Organize Your Money, 2010. Understanding Standard Deviation as a Measure of Risk. (Online). Available from: https://todayforward.typepad.com/todayforward/2010/04/understanding-standard-deviation-aka-risk.html. (Accessed: 07th October, 2010). Vishwanath, R and Krishnamurti, C (2009). Investment Management: A Modern Guide to Security Analysis and Stock Selection. Heilderberg, Library of Congress. (Online). Available from: https://books.google.co.uk/books?id=oowq_PkME3UC&printsec=frontcover#v=onepage&q&f=false Accessed: (20 October, 2010). Williamson, D. 2010. Accounting Business Spreadsheeting. (Online). Available from: https://www.duncanwil.co.uk/stdev.html (Accessed 05th October, 2010). Zigler, B. 2004. No Pain, No Gain: Risk-adjusted returns in action. (Online). Available from https://registeredrep.com/advisorland/career/no_pain_no/. (Accessed 21 October, 2010).

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