## Introduction

Investors are faced with two main options in their effort to maximize the value of their investment. Feibel (2003, p.184) asserts that investors can either invest in real assets or financial assets. There are a wide range of investment vehicles that investors can select from the financial market. Some of the core investment vehicles that investors can consider investing in include stocks, mutual funds, options and futures, certificate of deposits, annuities, collectibles and exchange-traded funds (ETFs) (Frush, 2007, p. 34). To maximize their returns, it is critical for investors to develop an optimal investment portfolio.

When making investment decision, investors must take into consideration two main elements. These include the risk and return related to the investment. Ellis (2002, p.34) asserts that risk is a core element that should be taken into consideration when undertaking investment analysis. According to Jorion (2006, p.539), the degree of volatility with regard to investments varies across markets. As a result, some markets are more volatile compared to others.

The importance of analyzing risk arises from the fact that it affects both the rate of return and the price of a particular investment (Kapil, 2008, p.34). According to Elton (2010, p.248), most investors are risk averse in their investment decisions which makes them to avoid risk.

In order to generate high returns, investors must develop an optimal investment portfolio. One of the ways through which they can achieve this is by having a comprehensive understanding of the risk associated with an investment. According to Casterline and Yetman (2010, p.316), there are various indicators that investors can take into consideration when analyzing risk.One of these entails determining the standard deviation associated with a particular investment. This paper entails an analysis of how investors use standard deviation as risk indicator for their investment purposes.

## Standard deviation and its advantages in evaluating risk

Standard deviation refers to a statistical measure that is used to determine the degree of deviation of an investment’s returns from the expected return. According to Solin (2004, p.65), standard deviation is considered to be an absolute measure of investment risk. In making their investment decisions, investors usually use standard deviation to measure the degree of risk or volatility associated with a particular security (Zask, 2000, p.54). This is due to the fact that it gives insight on the variation of an investment’s return. As a result, investors can be able to project an investment’s future returns. Kiplinger’s (2007, p.3) is of the opinion that the higher an investment’s return varies from its mean, the higher the degree of risk involved. Additionally Solin (2004, p.65) is of the opinion that the returns of an investments which have a low standard deviation tend to be close to the investment’s historical mean. On the other hand, the returns of an investment which have a high standard deviation tend to more dispersed from its historical mean (Alphanose & Satchell, 2001, p. 135). In summary, the lower the standard deviation of a security, the less volatile it is which means that it is less risky.

By evaluating the volatility of stocks using standard deviation, an investor can be able to develop an optimal investment portfolio (Feibel & Vincent, 2011, p.119). Using standard deviation as a measure of risk is also advantageous in that it enables an investor to develop a comprehensive understanding of a particular security. This arises from the fact that every stock responds differently to changes in the broad market. Fiebel and Vincent (2011, p. 119) asserts that a stock market index may not effectively reflect the response of a particular security to market changes.

According to Hirt, Block & Basu (2006, p.45), standard deviation can give investors an insight on an investment’s historical variation in its return. If the standard deviation of a stock or a portfolio of stock is high, it means that the stock’s return has been varying with a large margin. On the other hand, if the standard deviation is low, it means that the rate of variation is minimal. The variation can either be positive or negative.

Two investors, Investor A and Investor B have a stock portfolio of $1,000. However, they have invested in different stocks whose rate of return varies. Investor A’s monthly rate of return ranges between -1.5% and 3%. On the other hand, investor B’s monthly rate of return during the same period ranges between -9% and 12%. At the end of the six month investment period, the two investment portfolios have a similar return of $1,058. However, the standard deviation of the two investment portfolio differs. Portfolio A has a standard deviation of 1.52 while that of portfolio B is 7.24. This shows that despite stock B having a high expected rate of return, it is more risky compared to stock A.

In order to use standard deviation to analyze investment risk, investors must calculate the variance (Choudhry, 2006, p. 9). According to Fabozzi (2009, p.90), variance refers to a measure of dispersion of the actual outcome from the mean. With regard to investments, variance refers to the degree of dispersion of an investment’s rate of return from the expected return. Standard deviation is calculated by obtaining the square root of the variance which is represented by the symbol σ^{2 }. Therefore, standard deviation is calculated using the following formula.

SD = (σ)^{1/2 }.

An investor is faced with a decision to select from two securities to include in his investment portfolio. Stock A has an expected rate of return of 12.5%. On the other hand, Stock B has an expected rate of return of 20%. Additionally, the two stocks differ with regard to their respective variance. Stock A has a variance of 0.00236 while stock B has a variance of 0.04200.

Based on the expected rate of return, stock B appears to be more appealing to the investor compared to stock A. However, it is important for the investor to evaluate the degree of risk associated with each stock so as to determine the best stock to select. To achieve this, the investor should determine the standard deviation of each stock.

Standard deviation for stock A= (0.00236)^{1/2 }=0.0513=5.13%.

Standard deviation for stock B= (0.04200)^{1/2 }=0.2049=20.49%.

From the above illustration, it is evident that Stock B has a high standard deviation compared to Stock A. This means that Stock B is more risky compared to stock A despite having a high expected rate of return.

## Limitations of standard deviation in evaluating risk

Despite the fact that standard deviation is a good indicator in evaluating investment risk thus contributing to an investor’s ability to construct an optimal investment portfolio, there are some limitations associated with this indicator. According to Solin (2004, p.66), standard deviation mainly relies on historical data. This means that it cannot help an investor to determine an investment’s future performance. an investment’s past performance that it will or will not occur in the future. Additionally, the credibility of the historical data used in determining degree of an investment’s volatility is low. This arises from the fact that historical data can be easily manipulated (Alphanose & Satchell, 2001, p.57).

Considering the fact that standard deviation measures the volatility of a stock’s return on the basis of a certain period for example days, months, weeks or years, there is a probability of the actual standard deviation being shrouded over a long period for example 10 years. This means that by considering a long duration such as 10 years, a particular stock may portray a low standard deviation. Upon evaluating the same stock using a short period for example the last six months, the same stock may depict a high standard deviation.

One of the factors that may cause this difference is the prevailing market conditions during the period under consideration. Fitch (2010, para. 7) is of the opinion that when determining the period to consider in the evaluation of an investment’s standard deviation, investors should first determine the degree of accuracy that the measurement should have. During volatile economic periods, investors should consider adopting a long period in determining standard deviation. For example, investors can consider a number of years. This will ensure that the standard deviation calculated is a true reflection of the stocks volatility. Therefore, investors should be conversant with the parameters that they are using in determining the standard deviation.

According to Maginn (2007, p.43), using standard deviation to evaluate the degree of risk associated with a particular investment may result into unreliable conclusion. This means that an investor may not be able to avoid risk which is his or her core objective (Kaye, 2008, p.128). Another limitation of standard deviation as an indicator of investment risk is that it assumes that the distribution of an investment’s return is symmetrical. This means that investors consider unexpected gains (profit) to be risky similar to unexpected losses. However, in real life situations investors do not consider unexpected profits as a risk but as benefits (Sumnicht, 2009, p. 2). Additionally, standard deviation assumes that investors have a similar perception of risk. This is not true because investors have a varying perception of risk depending on the prevailing scenarios. Additionally, the distribution of an investment’s return is not symmetrical but is skewed either positively or negatively. According to Sumnicht (2008, p.9), the reliability of standard deviation in making investment decision is hindered by the fact that it is not effectively aligned with the concept of risk.

## Conclusion

Considering the fact that investors’ objective is to maximize their investment returns, it is critical that they make effective investment decisions. There are two main elements that investors should take into consideration when making investment decision. These include the risk and return associated with a particular investment. In most cases, investors consider stocks that have a high rate of return to be optimal investment vehicles. However, there is a high probability of investors losing their money by basing their decision on the expected returns as illustrated above. Therefore, investors should consider conducting a comprehensive analysis of a particular investment prior to committing their money. This makes an analysis of the investment’s risk to be paramount. The objective of determining the degree of an investment’s volatility is that risk affects an investment’s return. Therefore, it is paramount for investors to conduct a comprehensive analysis of risk.

One of the indicators that investors can consider integrating in evaluating investment’s risk is standard deviation. Standard deviation illustrates how volatile an investment such as stock is. If a particular investment has a high standard deviation, it means that it is more volatile and hence has a high degree of risk. On the other, an investment that has a low standard deviation is less risky.

Standard deviation is an important indicator that investors should consider when evaluating risk. This arises from the fact that it takes into account a security’s historical data. The resultant effect is that an investor is able to understand the performance of a particular security. The ultimate result is that it enhances an investor’s ability to construct an optimal investment portfolio.

Despite the widespread utilization of standard deviation by investors as a measure of investment risk, there are a number of limitations associated with this indicator. By using historical data to determine an investment’s standard deviation, an investor cannot be able to project the future performance of the investment. Additionally, it is not certain that historical events will occur in the future. The period considered when calculating the standard deviation may result into varying results depending on the prevailing economic conditions. For example, if the historical data used belongs to a period characterized by high economic volatility, there is a high probability that the standard deviation calculated will be high. This means that the standard deviation calculated may result into investors making a poor decision.

## Reference List

Alphanose, F., & Satchell, S., 2001. *Managing downside risk in financial markets: **theory practice and implementation*. Oxford: Butterworth-Heinemann.

Casterline, S., & Yetman, R., 2010. *Investors passports to hedge fund profits**: Unique investment strategies for today’s global capital market*. Hoboken, N.J: Wiley.

Choudhry, M., 2006. *An introduction to value at risk*. Chichester: John Wiley.

Ellis, C., 2002. *Winning the loser’s game*. New York: McGraw-Hill Professionals.

Elton, E., 2010. *Modern portfolio theory and investment analysis*. Hoboken, N.J: Wiley& Sons.

Fabozzi, F., 2009. *Institutional investment management: Equity and bond portfolio **strategies and applications*. Hoboken, N.J: Wiley.

Feibel, B., 2003. *Investment performance measurement. * Hoboken, N.J: John Wiley.

Feibel, B., & Vincent, K., 2011. *Complying with the global investment **performance standards*. Hoboken, N.J: John Wiley.

Fitch, C., *Understanding standard deviation and its importance and limitations **when assessing risk. Web.*

Frush, S., 2007. *Understanding hedge funds*. New York: McGraw-Hill.

Hirt, G., Block, S., & Basu, S., 2006. *Investment planning for financial **professionals*. New York: McGraw- Hill.

Jorion, P., 2006. *Value at risk: The new benchmark for managing financial risk*. New York: McGraw-Hill.

Kapil, S., 2008. *Financial management*. New Delhi: Pearson.

Kaye, M., 2008. *The Standard & Poor’s guide to the perfect portfolio: Five steps **to allocate your assets and ensure a lifetime of wealth*. New York: McGraw-Hill.

Kiplingers. 2007. *Kiplinger’s personal finance*. London: Kiplinger Washington Editors Incorporation.

Maginn, J., 2007. *Managing investment portfolio: A dynamic process*. Hoboken: John Wiley & Sons.

Sumnicht, V., 2008. *Practical applications of post modern portfolio theory*. Web.

Sumnicht, V., 2009. *Standard deviation as a measure of risk: Risk and the real-life investor. *Web.

Solin, D., 2004. *Does your broker owe you money? If you have lost money in **the market and it’s your broker’s fault , you can get it back*. New York: NY Penguin Group.

Zask, E., 2000. *Global investment, risk management*. New York: McGrawHill.