Standard_Deviation

the annual rate of return of an investment, to measure the investment's volatility, or "risk". Standard deviation in investment standard deviation statistical measure of the degree to which an individual value in a probability distribution tends to vary from the mean of the distribution. It is widely applied in modern portfolio theory , for example, where the past performance of securities is used to determine the range of possible future performances and a probability is attached to each performance. Mutual fund analysts average the returns over three years, then determine the range in which returns have varied from that mean. So, if the mean return is 10% and the range has been +25% to -5%, standard deviation is 15. Standard deviation in business terms standard deviation statistical measure of the degree to which an individual value in a probability distribution tends to vary from the mean of the distribution. From a normal distribution, one standard deviation includes about 66% of the population; two standard deviations include about 95%. When you say that an investment like a stock market index fund has an expected return of 9%, you're saying that in any year there is a chance that your return will be better than 9% and a chance that it will be worse. To get more specific about your chances, you need to specify the expected volatility of the investment, as well as its expected return. The volatility of an investment is given by the statistical measure known as the standard deviation of the return rate. a standard deviation of zero would mean an investment has a return rate that never varies, like a bank account paying compound interest at a guaranteed rate. The Standard Deviation Formula Simple Example of Calculating Standard Deviation Let's say we wanted to calculate the standard deviation for the amounts of gold coins pirates on a pirate ship have. There are 100 pirates on the ship. In statistical terms this means we have a population of 100. If we know the amount of gold coins each of the 100 pirates have, we use the standard deviation equation for an entire population: What if we don't know the amount of gold coins each of the 100 pirates have' For example, we only had enough time to ask 5 pirates how many gold coins they have. In statistical terms this means we have a sample size of 5 and in this case we use the standard deviation equation for a sample of a population: The rest of this example will be done in the case where we have a sample size of 5 pirates, therefore we will be using the standard deviation equation for a sample of a population. Here are the amounts of gold coins the 5 pirates have: 4, 2, 5, 8, 6. Now, let's calculate the standard deviation: 1. Calculate the mean: 2. Calculate for each value in the sample: 3. Calculate : 4. Calculate the standard deviation: The standard deviation for the amounts of gold coins the pirates have is 2.24 gold coins. What Does Standard Deviation Mean' 1. A measure of the dispersion of a set of data from its mean. The more spread apart the data, the higher the deviation. Standard deviation is calculated as the square root of variance. 2. In finance, standard deviation is applied to the annual rate of return of an investment to measure the investment's volatility. Standard deviation is also known as historical volatility and is used by investors as a gauge for the amount of expected volatility Standard deviation is a statistical measurement that sheds light on historical volatility. For example, a volatile stock will have a high standard deviation while the deviation of a stable blue chip stock will be lower. A large dispersion tells us how much the return on the fund is deviating from the expected normal returns.