Standard deviation of returns estimates volatility and risk in investments using statistical principles. The bell curve represents the probability distribution of outcomes, with deviations from the average becoming less likely. A larger standard deviation means more volatility, and returns are more likely to be close to the average.
The standard deviation of returns is a way of using statistical principles to estimate the level of volatility in stocks and other investments, and therefore the risk involved in buying them. The principle is based on the idea of a bell curve, where the central high point of the curve is the average or expected percentage of the average value that the stock is most likely to return to the investor in a given period of time. Following a normal distribution curve, as one moves further and further away from the average expected return, the standard deviation of the returns increases the realized gain or loss on the investment.
In most man-made and natural systems, bell curves represent the probability distribution of actual outcomes in situations involving risk. One standard deviation away from the average constitutes 34.1% of the actual results above or below the expected value, two standard deviations away constitute an additional 13.6% of the actual results, and three standard deviations away from the average constitute another 2.1% of the results. . What this really means is that when an investment does not return the expected average amount, approximately 68% of the time it will be off by one standard deviation point higher or lower, and 96% of the time it will be off by two standard deviations. points Almost 100% of the time, the investment will deviate by three points from the average, and beyond this, growth in the level of loss or gain for the investment becomes extremely rare.
Probability therefore predicts that a return on investment is much more likely to be close to the average expected return than farther from it. Despite the volatility of any investment, if it follows a standard deviation of returns, 50% of the time, it will return the expected value. What is even more likely is that 68% of the time it will be within one deviation of the expected value, and 96% of the time it will be within two points of the expected value. Calculating returns is a process of plotting all these variations on a bell curve, and the more often they are far from the average, the greater the variation or volatility of the investment.
One can try to visualize this process with real numbers for the standard deviation of the returns using an arbitrary percentage return. An example would be a stock investment with an average expected rate of return of 10% with a standard deviation of returns of 20%. If the stock follows a normal probability distribution curve, this means that 50% of the time, that stock will actually return a 10% return. However, it is more likely that, 68% of the time, the stock is expected to lose 20% of that rate of return and return 8% value, or earn an additional 20% of return value and return a real rate of 12%. In general, it is even more likely that 96% of the time, the stock can lose or gain 40% of its return value for two points of deviation, which means that it would return between 6% and 14%.
The larger the standard deviation of returns, the more volatile the stock is to increasing positive gains and increasing losses, so a standard deviation of returns of 20% would represent much more variation than one of 5%. As the variance moves away from the center of the bell curve, it becomes less and less likely to occur; however, at the same time, all possible outcomes are taken into account. This means that, at three standard deviations, almost all possible real-world situations plot to 99.7%, but only 2.1% of the time the actual return on an investment falls three deviations from the average, which, in the case of the example , it would be a return of about 4% or 16%.
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