Standard Deviation

Contents
Time Value of Money
Annuities
Perpetuities
Kinds of Interest Rates
Future Value of an Uneven Cash flow
Probability Distribution
Standard Deviation
CAPM
Security Market Line
Bond Valuation
Stock Valuation
Cost of Capital
The Balance Sheet
Financial Terms
Scientific Terms
Disclaimer

Standard Deviation

We can measure risk by using standard deviation. Higher standard deviation means higher risk.

Here is the example from the probability distribution page

Probability Distribution - In Business

Economic Outcome	Probability	Return on Investment
Great	20%	25%
Good	40%	15%
So-So	30%	5%
Really Bad	10%	0%

Economic Outcome	Return on Investment	minus	ERR - the Expected Rate of Return	equals	answer	squared	times	Probability of the Economic Outcome	equals	Answer
Great	25%	-	12.5%	=	12.5	156.25	X	20%	=	31.25
Good	15%	-	12.5%	=	2.5	6.25	X	40%	=	2.5
So-So	5%	-	12.5%	=	7.5	56.25	X	30%	=	16.875
Really Bad	0%	-	12.5%	=	12.5	156.25	X	10%	=	15.625
								Total	=	66.25

So the total is 66.25. This is called the Variance.
The square root of 66.25 = 8.139
So the Standard Deviation is 8.139

Detailed Explanation

Interpreting Standard Deviation - The interpretation of standard deviation in finance is fairly straightforward. A high standard deviation indicates that the data points are spread out over a larger range, which means that there is a greater level of risk associated with the investment. On the other hand, a low standard deviation indicates that the data points are clustered closely around the mean, which means that there is a lower level of risk associated with the investment.

To understand the interpretation of standard deviation in more detail, let us consider an example. Suppose we have two investments, A and B, and we want to assess the level of risk associated with each investment. Investment A has an average return of 8% and a standard deviation of 10%, while investment B has an average return of 8% and a standard deviation of 2%.

The standard deviation of investment A is higher than that of investment B, which means that investment A is riskier than investment B. This is because the data points for investment A are spread out over a larger range, indicating that there is a greater level of uncertainty and volatility associated with this investment. On the other hand, investment B has a lower standard deviation, which means that the data points are clustered more closely around the mean, indicating that there is less uncertainty and volatility associated with this investment.

It is important to note that while standard deviation is a useful measure of risk, it is not the only measure that should be considered. Other factors, such as the expected return, the correlation with other investments in the portfolio, and the investor's risk tolerance, should also be taken into account when assessing the risk associated with an investment.

Standard Deviation and Risk

In finance, standard deviation is a key measure of risk. It is used to assess the level of risk associated with an investment and to develop strategies to mitigate that risk. The relationship between standard deviation and risk is straightforward: investments with higher standard deviation are riskier, while investments with lower standard deviation are less risky.

To understand the relationship between standard deviation and risk in more detail, let us consider another example. Suppose we have two investments, C and D, with the following characteristics:

Investment C has an average return of 8% and a standard deviation of 10%. Investment D has an average return of 6% and a standard deviation of 5%. Investment C has a higher standard deviation than investment D, which means that it is riskier than investment D. This is because investment C has a greater level of uncertainty and volatility associated with it, which means that the returns of investment C are more likely to deviate from the mean. On the other hand, investment D has a lower standard deviation, which means that it is less risky than investment C.

When assessing the risk associated with an investment, it is important to consider both the expected return and the standard deviation. Higher risk investments may have higher expected returns, but they may also have a higher chance of losing money. Lower risk investments may have lower expected returns, but they may also have a lower chance of losing money.

Standard Deviation and Diversification

One of the key benefits of diversification in finance is the reduction of risk. By diversifying a portfolio with investments that have different risk levels, investors can reduce the overall risk of the portfolio. Standard deviation is a useful measure in portfolio management, as it is used to assess the risk associated with individual investments and the portfolio as a whole.

Standard deviation is a key measure of risk and is used to assess the level of risk associated with an investment. By calculating the standard deviation of an investment, finance professionals can identify the level of risk associated with the investment and develop strategies to mitigate that risk.

Generally, investments with higher standard deviation have higher expected returns, as they are riskier. On the other hand, investments with lower standard deviation have lower expected returns, as they are less risky.

Historical Analysis - Historical analysis is important in finance for several reasons. First, it provides a useful tool for understanding the risk associated with an investment. By analyzing an investment's historical returns, investors can gain insight into the level of volatility associated with the investment, and make more informed decisions about future investment. Second, historical analysis can help to identify trends and patterns in an investment's performance. By analyzing an investment's historical returns, investors can identify trends in the investment's performance, such as whether the investment tends to perform well in certain market conditions or at certain times of the year. This information can be useful in making investment decisions, such as when to buy or sell an investment. Third, historical analysis can help to identify anomalies in an investment's performance. Anomalies can indicate a potential opportunity or risk in the investment, and can provide valuable insight into the investment's performance. For example, an investment may have a period of unusually high returns, which could indicate a good opportunity to invest in the asset.

How to Conduct Historical Analysis

To conduct historical analysis of standard deviation, investors typically gather data on an investment's historical returns and use statistical software to calculate the standard deviation of those returns. Historical data can be obtained from a variety of sources, such as financial statements, market data, and investment research reports.

Once the data has been gathered, investors can use statistical software to calculate the standard deviation of the investment's historical returns. This involves calculating the mean return of the investment over the historical period, and then calculating the variance of the returns from the mean. The square root of the variance is then calculated to give the standard deviation.

Once the standard deviation has been calculated, investors can use it to assess the level of risk associated with the investment. A higher standard deviation indicates a greater level of risk, while a lower standard deviation indicates a lower level of risk.

Limitations of Historical Analysis

While historical analysis of standard deviation is a valuable tool in finance, it is important to be aware of its limitations. One limitation is that historical data may not be a good indicator of future performance. Past performance does not necessarily guarantee future results, and economic and market conditions can change, making it difficult to predict future investment performance.

Another limitation of historical analysis is that it may not take into account changes in an investment's structure or management. For example, a company may undergo a significant change in management or ownership that could impact its future performance. Historical data may not reflect these changes, making it difficult to predict future performance based solely on past performance.

Bibliography

Bodie, Z., Kane, A., & Marcus, A. J. (2019). Investments. McGraw-Hill Education.

Damodaran, A. (2012). Investment valuation: Tools and techniques for determining the value of any asset. John Wiley & Sons.

Elton, E. J., Gruber, M. J., Brown, S. J., & Goetzmann, W. N. (2014). Modern portfolio theory and investment analysis. John Wiley & Sons.

Fabozzi, F. J., & Markowitz, H. M. (2011). The theory and practice of investment management. John Wiley & Sons.

Hull, J. C. (2017). Options, futures, and other derivatives. Pearson.

Jorion, P. (2011). Value at risk: The new benchmark for managing financial risk. McGraw-Hill.

Sharpe, W. F., Alexander, G. J., & Bailey, J. V. (1999). Investments. Prentice Hall.

Van Horne, J. C., & Wachowicz Jr, J. M. (2014). Fundamentals of financial management. Pearson.

Verbeek, M. (2017). A guide to modern econometrics. John Wiley & Sons.

West, K. D. (2006). Time series econometrics. Princeton University Press.

About the author

Author: Mark McCracken is a corporate trainer and author living in Higashi Osaka, Japan. He is the author of thousands of online articles as well as the Business English textbook, "25 Business Skills in English".