What Are the Best Tips for Computing Standard Deviation?
Standard Deviation, also known as the mean square deviation in the Chinese environment, is the square root of the arithmetic mean from the square of the mean deviation, expressed as . It is most commonly used in probability statistics as a measure of the extent of a statistical distribution. The standard deviation is the arithmetic square root of the variance. Standard deviation can reflect the degree of dispersion of a data set. The standard deviation of the two sets of data with the same mean may not be the same.
- Standard deviation ( StandardDeviation ), in
- All numbers are subtracted from the sum of the squares of their averages. The result is divided by the number of groups (or the number is reduced by one, that is, the number of variations), and the obtained value is rooted. The number obtained is the standard for this group of data. difference.
- The dark blue area is a range of values less than one standard deviation from the mean. in
- Standard deviation is the most commonly used form of quantification to reflect the degree of discreteness of a set of data.
- From the perspective of geometry, the standard deviation can be understood as a function of the distance from a point in n-dimensional space to a straight line. As a simple example, there are 3 values in a set of data, X1, X2, X3. They can determine a point P = (X1, X2, X3) in 3D space. Imagine a straight line passing through the origin. If all three values in this set of data are equal, then point P is a point on line L, and the distance from P to L is 0, so the standard deviation is also 0. If these three values are not all equal, the crossing point P is perpendicular to L as the perpendicular PR and PR intersects L at point R, then the coordinates of R are the average of these three values:
- Standard deviation and standard error are both contents of mathematical statistics. Not only are they literally similar, but both represent the degree of dispersion from a certain standard or intermediate value, that is, the degree of variation, but both are There is a big difference.
- Let's start with statistical sampling. In real life or survey research, we often cannot test all members of a certain type of target group to be surveyed, and we can only select some members from all members (that is, samples) to conduct surveys, and then use statistical principles and The method analyzes the obtained data. The result of the analysis is the result of the sample, and then the sample is used to infer the overall situation. Multiple samples can be drawn from a population. The more samples taken, the closer the sample mean to the average of the population data.
- There are four functions STDEV, STDEVP; STDEVA, STDEVPA in Excel, which respectively represent the sample standard deviation and the overall standard deviation; the sample standard deviation including the logical value operation and the overall standard deviation including the logical value operation (excel uses "standard deviation" Text).
- The differences in calculation methods are: sample standard deviation ^ 2 = (sample variance / (number of data-1)); overall standard deviation ^ 2 = (total variance / (number of data)).
- The excel decomposition of the function:
- stdev () function can be decomposed into (assuming the sample data is A1: E10
- Standard deviation refers to an indicator used to statistically measure the difference between a value in a set of values and its average. The standard deviation is used to assess the extent to which prices may change or fluctuate. The larger the standard deviation, the wider the range of price fluctuations, and the greater the fluctuations in the performance of financial instruments such as stocks.
- Calling a function in excel
- "STDEV"
- Estimate the standard deviation of the sample. The standard deviation reflects the relative
Standard Deviation Fund
- In investment funds, the average person pays more attention to performance, but often buys
- Fund Algorithm
- The tool for measuring the degree of fund volatility is Standard Deviation. Standard deviation refers to the degree of possible changes in the fund. The larger the standard deviation, the greater the degree to which the fund's future net worth may change, the smaller the stability, and the higher the risk.
- For example, a fund with a standard deviation of one year is 30%, indicating that the net value of such funds may increase by 30% within a year, but may also fall by 30%. Therefore, if there are two funds with the same rate of return, the investor should choose a fund with a smaller standard deviation (bearing the same risk with less risk and get the same return). Funds (bearing the same risks, but with higher returns). It is recommended that investors include both returns and risks to judge the fund. For example, the second-year yield of A fund is 36%, and the standard deviation is 18%; the second-year yield of B fund is 24%, and the standard deviation is 8%. , But at the same time the risk is greater than the B fund. The "risk return per unit" of fund A is 2 (0.36 / 0.18), while fund B is 3 (0.24 / 0.08). Therefore, the A fund was better based on the return assessment, but after the standard deviation, which is the risk factor adjustment, the B fund was better.
- In addition, the standard deviation can also be used to judge fund attributes. According to Morningstar statistics, the average standard deviation of stock funds is 5.14, the average standard deviation of active funds is 5.04, the average standard deviation of conservatively allocated funds is 4.86, the average standard deviation of ordinary bond funds is 2.91, and the average standard deviation of money funds is 0.19; it can be seen that the more positive the fund, the larger the standard deviation; and if the standard deviation of the fund held by the investor is higher than the average, it means that the risk is higher. Investors may wish to watch the Olympic Games while also Examine the funds in your hand.
Standard deviation stock analysis
- The fluctuation of the stock price is a manifestation of the risk of the stock market, so the analysis of the stock market risk is to analyze the fluctuation of the stock market price. Volatility represents the uncertainty of future price values. This uncertainty is usually characterized by variance or standard deviation (Markowitz, 1952). The following table is the stock statistics index of China and the United States for certain periods of time. The data of the Chinese stock market is downloaded by the "Qianlong" software. The data of the US stock market is taken from the ECI's "WorldStockExchangeDataDisk". Table 2 Stock Statistics Index
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- By calculation, we can get:
- Performance expectation of Shanghai Composite Index
- SSE Volatility Expectation 0.115643
- Standard & Poor's performance expectations 6.731429
- Expected S & P Volatility 0.068029
- The standard deviation calculation formula is based on the
- Analysis Figure 2
- Standard deviation of the performance of the Shanghai Composite Index 45.2489073
- Standard deviation of Shanghai Stock Volatility 0.063167
- Standard deviation of S & P index performance 21.70647
- Standard deviation of S & P volatility 0.023647
- Because the standard deviation is an absolute value, China and the United States cannot be directly compared through the standard deviation, and the coefficient of variation can be directly compared. Calculated: (Coefficient of variation C · V = (standard deviation SD ÷ average MN) × 100%)
- SSE performance coefficient of variation 2.18926148
- SSE Volatility Coefficient 0.5462
- Standard & Poor's performance coefficient of variation 3.2247
- Standard and Poor's Volatility Coefficient 0.3476
- It can be seen from the comparison that the coefficient of variation of the Shanghai Stock Exchange's volatility is larger than that of the Standard & Poor's.
Application in standard deviation enterprises
- The capital structure refers to the proportional relationship between various funding sources of an enterprise, and is the result of corporate fund-raising activities. The optimal capital structure refers to the capital structure that can minimize the capital cost of an enterprise and maximize the value of the enterprise. The property right ratio, that is, the proportion of borrowed capital and its own capital, is an important variable that reflects the capital structure of an enterprise. The assets of an enterprise are composed of debt funds and equity funds, but their risk levels and returns are different. According to the portfolio theory, diversification of investment can spread out certain risks, so fund providers need to decide the proportion of investment in debt funds and equity funds. In order to ensure the maximum benefits while weighing the risks and benefits.
- diagram
- Assume that an enterprise's funds are obtained by issuing bonds and stocks, and both are risk assets. where the yield of the bond is r D, and the risk is measured by the standard deviation D; the return of the stock is r E, and the risk is E ; the correlation coefficient between the stock and the bond is p DE, and the covariance is COV , r E); the proportion of bonds is w D, and the proportion of stocks is W E ( W D + W E = 1). According to the portfolio theory, the expected rate of return of the company's external investors on the company's investment is E ( r p) = W D E ( r D) + w E E ( r E), and the variance is
- variance
- 1. Corporate debt funds and equity funds are completely positively correlated, that is, the correlation coefficient p DE is 1. The expected return rate obtained by the external investors of the enterprise is E ( r p) = w D E ( r D) + w E E ( r E), and the standard deviation of risk is = w DD + w EE, that is, the standard deviation of the portfolio is equal to The weighted average of the standard deviations of various parts, it is impossible to disperse the investment risk through the investment portfolio. According to the portfolio theory, different proportions of the investment portfolio are the same for investors.
- 2. Corporate debt funds and equity funds are completely negatively correlated, that is, their correlation coefficient is -1. The investor's expected return and its variance are respectively. According to portfolio theory, its portfolio is only valid when the investment ratio is greater than E / (D + E). For corporate fundraising, that is, the proportion of the company's equity funds is E / (D + E), the corporate fundraising ratio is effective, and when the portfolio ratio is E / (D + E), the company s The financing portfolio risk is zero.
- 3. The correlation coefficient between corporate debt funds and equity funds is greater than -1 and less than 1. Theoretically, there is a high degree of correlation between the two financing methods of an enterprise. On the one hand, both financing methods bear systemic risk, and on the other hand, they also bear the same corporate risk. Therefore, from a practical point of view, the degree of correlation between different financing methods of an enterprise cannot be completely positive and negative. For an enterprise, debt funds have a fixed claim on the enterprise, and equity funds have only residual claims on the enterprise. Therefore, the fluctuation of debt funds cannot be as large as that of equity funds. At the same time, the risks of the enterprise will affect both the debt funds and the equity funds of the enterprise, so the correlation coefficient between the debt funds and the equity funds of the enterprise cannot be negative. Correlation coefficients between different financing methods of enterprises are generally between 0-1.
- So what proportion of the company's value will reach the maximum? According to portfolio theory, when E ( r 1)> E ( r 2), and
- Variance 3
- Only when it appears, r 1 is better than r 2. It can be seen that the direct factors that determine the capital structure of enterprises are mainly the returns and risks of different financing methods and the correlation coefficient between them.