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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 on

Stock AReturn on

Stock B

120%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:

where

- N = the number of states,
- pi = the probability of state i,
- Ri = the return on the stock in state i, and
- E[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 A

Stock B

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Q: How are variance and standard deviation used as measures of risk for both a security and a portfolio?

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How can the return and standard deviation of a portfolio be deteremined

They are measures of the spread of data.

They are measures of the spread of distributions about their mean.

The standard deviation of the population. the standard deviation of the population.

The standard deviation in a standard normal distribution is 1.

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difference standard deviation of portfolio

How can the return and standard deviation of a portfolio be deteremined

They are measures of the spread of data.

Standard deviation would be used in statistics.

Standard deviations are measures of data distributions. Therefore, a single number cannot have meaningful standard deviation.

They are measures of the spread of distributions about their mean.

Standard Deviation tells you how spread out the set of scores are with respects to the mean. It measures the variability of the data. A small standard deviation implies that the data is close to the mean/average (+ or - a small range); the larger the standard deviation the more dispersed the data is from the mean.

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

It is not. And that is because the mean deviation of ANY variable is 0 and you cannot divide by 0.

The standard deviation is the standard deviation! Its calculation requires no assumption.

It is one of several measures of the spread of data. It is easier to calculate than the standard deviation, which has important statistical properties.

The standard deviation of the population. the standard deviation of the population.

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