Introduction
Standard deviation is a quintessential measure in the bond market. Fundamentally, standard deviation quantifies how much a series of numbers, for example, the returns and the funds vary around its average (Fernández, Schmitt-Grohé, & Uribe, 2017). Investors are fond of employing the standard deviation method since it provides them with an accurate measure of how varied the returns of a fund have been over a given time in the upside and the downside (Campos et al., 2017). The usefulness of standard deviation in investing goes on to providing historical volatility of a fund, which enables the investors to make proper, decisions while engaging in business. The use of standard deviation to measure the volatility of a fund quantifies the risks of an investment (Chen, Cui, He, & Milbradt, 2017). Typically, a fund or return with a high deviation from the average is more volatile and hence riskier than that which has a lower deviation from the average. Standard deviation is thus an essential calculation in the determination of the various aspects of risk.
Standard Deviation 5 Step Procedure
As it applies to the bond market, the standard deviation is procedurally calculated in several steps. The rate of return of an investment is calculated by considering the mean probability distribution for all the possible returns. The following is an example of calculating the expected rate of return.
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A model has a 10% chance at a 100% rate of return and a 90% chance at a 50% rate of return. What is the expected rate of return?
Expected rate of return= 0.1(1) + 0.9(0.5)
= 0.1 + 0.45
= 0.55 or 55%
Investors have to make sound decisions regarding the expected rates of return before they can engage in fields of business. With the application of standard deviation, the investors can determine the volatility of their investments. Therefore, the deduction of 15% from an expected rate of return is used to give a range of volatility to the investment so that it can favor the different investors (DeFusco et al., 2015). Market factors may also reduce the rate of return, which calls for the anticipation of the less expected rate of return.
Step 1: Finding the mean
The first step in finding the standard deviation of a given dataset is to find its average. The calculation of the average is the first most essential step that determines the success in calculating the standard deviation accurately. The following is an example of a dataset that can be used.
6,3,2,1.
Mean (µ) is given by:
µ = (6+3+2+1)/4
µ = 12/4
µ = 3
Step 2: Finding the square of the distance from the mean for each data point
The following is an illustration of how to get the square of the distance of each data point from the mean.
| Data Point (x) | Mean (µ) | Distance from the mean (ǀ x- µ ǀ) | Square of the distance from the mean (ǀ x- µ ǀ 2 ) |
| 6 | 3 | 3 | 9 |
| 3 | 3 | 0 | 0 |
| 2 | 3 | 1 | 1 |
| 1 | 3 | 2 | 4 |
Step 3: Summing the values from step 2
The next step in calculating the standard deviation is the determination of the summation of the squares of distance from the mean, which have been derived from step 2. The following is the calculation of the summation.
| Data Point (x) | Mean (µ) | Distance from the mean (ǀ x- µ ǀ) | Square of the distance from the mean (ǀ x- µ ǀ 2 ) |
| 6 | 3 | 3 | 9 |
| 3 | 3 | 0 | 0 |
| 2 | 3 | 1 | 1 |
| 1 | 3 | 2 | 4 |
| ∑ ǀ x- µ ǀ 2 | 14 |
Step 4: Dividing by the number of data points
The next step is the division of the summation acquired from step 3 above by the number of data points (N) initially provided. Therefore, the calculation is as follows.
(∑ǀ x- µ ǀ 2 ) /N
=14/4
= 3.5
Step 5: Taking the square root
Taking the square root of the value obtained in step 4 above is usually the last step in the calculation of the standard deviation as it applies in the bond market. The standard deviation is, therefore, calculated as follows.
√ (∑ǀ x- µ ǀ 2 ) /N
= √3.5
= 1.87
The standard deviation in the example provided above is, therefore, 1.87.
Assets and Conclusion
Risk diversification is a concept that investors have at their disposal when it comes to the determination of standard deviation, such as in the bond market. Mostly, the risks can be diversified based on the industry that an investor targets with his or her investments (Schmitt, Sun, Snyder, & Shen, 2015). It is also possible for investors to diversify their risks within an asset class. Most of the investors have held the popular belief that increasing the number of stocks in their business will reduce the risk (Schmitt, Sun, Snyder, & Shen, 2015). Contrary to their opinion, an increase in the number of shares does not reduce the risks involved in investments.
The standard deviation of a portfolio return determines how variable the expected rate of a return is. The value of the standard deviation of the return of a portfolio is based on three quintessential determinants. One of the determinants is the rate of return of every asset in the portfolio (He, Ma, & Pan, 2017). The other factor of the standard deviation of a portfolio return is the proportion of each asset in the portfolio. In the calculation of the standard deviation of a portfolio return, the investors have to use the standard deviation and expected rate of return values that pertain to the assets. The other factor that determines the standard deviation of the return of a portfolio is the covariance of returns among the pairs of assets in the portfolio (He, Ma, & Pan, 2017). Thus, the determination of the standard deviation of a portfolio returns largely depends on the returns of each of the assets in the portfolio.
Indeed, Standard deviation is an essential calculation in the determination of the various aspects of risk. Firstly, the measure applies to the calculation of volatility, which points to the risks involved in particular business investment. Secondly, the standard deviation is fundamental to the diversification of risks across a class of assets or even across one specific sector of business.
References
Campos, F., Frese, M., Goldstein, M., Iacovone, L., Johnson, H. C., McKenzie, D., & Mensmann, M. (2017). Teaching Personal Initiative Beats Traditional Training in Boosting Small Business in West Africa. Science , 357 (6357), 1287-1290.
Chen, H., Cui, R., He, Z., & Milbradt, K. (2017). Quantifying Liquidity and Default Risks of Corporate Bonds over the Business Cycle. The Review of Financial Studies , 31 (3), 852-897.
DeFusco, R. A., McLeavey, D. W., Pinto, J. E., Runkle, D. E., & Anson, M. J. (2015). Quantitative investment analysis . John Wiley & Sons.
Fernández, A., Schmitt-Grohé, S., & Uribe, M. (2017). World Shocks, World Prices, and Business Cycles: An Empirical Investigation. Journal of International Economics , 108 , S2-S14.
He, J., Ma, C., & Pan, K. (2017). Capacity Investment in Supply Chain with Risk Averse Supplier under Risk Diversification Contract. Transportation Research Part E: Logistics and Transportation Review , 106 , 255-275.
Schmitt, A. J., Sun, S. A., Snyder, L. V., & Shen, Z. J. M. (2015). Centralization Versus Decentralization: Risk Pooling, Risk Diversification, and Supply Chain Disruptions. Omega , 52 , 201-212.
