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How is expected rate of return calculated from average rate of return on investment and standard deviation?
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How are variance and standard deviation used as measures of risk for both a security and a portfolio?
Risk reflects the chance that the actual return on an investment may be very different than the expected return. One way to measure risk is to calculate the variance and standard deviation of the distribution of returns.Consider the probability distribution for the returns on stocks A and B provided below.StateProbabilityReturn onStock AReturn onStock B120%5%50%230%10%30%330%15%10%320%20%-10%The expected returns on stocks A and B were calculated on the Expected Return page. The expected return on Stock A was found to be 12.5% and the expected return on Stock B was found to be 20%.Given an asset's expected return, its variance can be calculated using the following equation:whereN = the number of states,pi = the probability of state i,Ri = the return on the stock in state i, andE[R] = the expected return on the stock.The standard deviation is calculated as the positive square root of the variance.Note: E[RA] = 12.5% and E[RB] = 20%Stock AStock B
If you square standard deviation you get this term?
Variance. However, in fact the standard deviation is calculated from the variance, not in the order that the question seems to suggest.
How do you calculate expected variation?
Mean 10.70 Standard Deviation 0.030101868
What would it mean if a standard deviation was calculated to equal 0?
A standard deviation of zero means that all the data points are the same value.
How do you calculate the expected value when you know the standard deviation?
You cannot; there is insufficient information.
Can a standard deviation be calculated for a median?
no.
What is the purpose of finding the standard deviation of a data set?
The purpose of obtaining the standard deviation is to measure the dispersion data has from the mean. Data sets can be widely dispersed, or narrowly dispersed. The standard deviation measures the degree of dispersion. Each standard deviation has a percentage probability that a single datum will fall within that distance from the mean. One standard deviation of a normal distribution contains 66.67% of all data in a particular data set. Therefore, any single datum in the data has a 66.67% chance of falling within one standard deviation from the mean. 95% of all data in the data set will fall within two standard deviations of the mean. So, how does this help us in the real world? Well, I will use the world of finance/investments to illustrate real world application. In finance, we use the standard deviation and variance to measure risk of a particular investment. Assume the mean is 15%. That would indicate that we expect to earn a 15% return on an investment. However, we never earn what we expect, so we use the standard deviation to measure the likelihood the expected return will fall away from that expected return (or mean). If the standard deviation is 2%, we have a 66.67% chance the return will actually be between 13% and 17%. We expect a 95% chance that the return on the investment will yield an 11% to 19% return. The larger the standard deviation, the greater the risk involved with a particular investment. That is a real world example of how we use the standard deviation to measure risk, and expected return on an investment.
Is the expected value the same as the standard deviation?
No. The expected value is the mean!
Can standard deviation be calculated for non normal data?
Standard deviation can be calculated using non-normal data, but isn't advised. You'll get abnormal results as the data isn't properly sorted, and the standard deviation will have a large window of accuracy.
Annualized standard deviation?
http://www.hedgefund.net/pertraconline/statbody.cfmStandard Deviation -Standard Deviation measures the dispersal or uncertainty in a random variable (in this case, investment returns). It measures the degree of variation of returns around the mean (average) return. The higher the volatility of the investment returns, the higher the standard deviation will be. For this reason, standard deviation is often used as a measure of investment risk. Where R I = Return for period I Where M R = Mean of return set R Where N = Number of Periods N M R = ( S R I ) ¸ N I=1 N Standard Deviation = ( S ( R I - M R ) 2 ¸ (N - 1) ) ½ I = 1Annualized Standard DeviationAnnualized Standard Deviation = Monthly Standard Deviation ´ ( 12 ) ½ Annualized Standard Deviation *= Quarterly Standard Deviation ´ ( 4 ) ½ * Quarterly Data
Does variance and standard deviation assume nominal data?
No. Variance and standard deviation are dependent on, but calculated irrespective of the data. You do, of course, have to have some variation, otherwise, the variance and standard deviation will be zero.
How are variance and standard deviation used as measures of risk for both a security and a portfolio?
Risk reflects the chance that the actual return on an investment may be very different than the expected return. One way to measure risk is to calculate the variance and standard deviation of the distribution of returns.Consider the probability distribution for the returns on stocks A and B provided below.StateProbabilityReturn onStock AReturn onStock B120%5%50%230%10%30%330%15%10%320%20%-10%The expected returns on stocks A and B were calculated on the Expected Return page. The expected return on Stock A was found to be 12.5% and the expected return on Stock B was found to be 20%.Given an asset's expected return, its variance can be calculated using the following equation:whereN = the number of states,pi = the probability of state i,Ri = the return on the stock in state i, andE[R] = the expected return on the stock.The standard deviation is calculated as the positive square root of the variance.Note: E[RA] = 12.5% and E[RB] = 20%Stock AStock B
If you square standard deviation you get this term?
Variance. However, in fact the standard deviation is calculated from the variance, not in the order that the question seems to suggest.
What is the standard deviation of a treasury bill that has a expected return of 10.5?
ddd
How do you calculate expected variation?
Mean 10.70 Standard Deviation 0.030101868
What would it mean if a standard deviation was calculated to equal 0?
A standard deviation of zero means that all the data points are the same value.
How do you calculate the expected value when you know the standard deviation?
You cannot; there is insufficient information.
