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How are variance and standard deviation used as measures of risk for both a security and a portfolio?
Wiki User
∙ 10y ago
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
Wiki User
∙ 10y ago
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How can he return and standard deviation of a portfolio be determined?
How can the return and standard deviation of a portfolio be deteremined
What type of measures are the range and the standard deviation?
They are measures of the spread of data.
What do the variance and the standard deviation measure?
They are measures of the spread of distributions about their mean.
Why do we use mean absolute deviation?
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.
How do you calculate risk on a two-asset portfolio?
For a two-asset portfolio, the risk of the portfolio, σp, is: 2222p1122112212222p11221212121212σ=wσ+wσ+2wσwσρorσ=wσ+wσ+2wwcovcov since ρ=σσ where σi is the standard deviation of asset i's returns, ρ12 is the correlation between the returns of asset 1 and 2, and cov12 is the covariance between the returns of asset 1 and 2. Problem What is the portfolio standard deviation for a two-asset portfolio comprised of the following two assets if the correlation of their returns is 0.5? Asset A Asset B Expected return 10% 20% Standard deviation of expected returns 5% 20% Amount invested $40,000 $60,000
Difference Standard Deviation of a portfolio?
difference standard deviation of portfolio
How can he return and standard deviation of a portfolio be determined?
How can the return and standard deviation of a portfolio be deteremined
What type of measures are the range and the standard deviation?
They are measures of the spread of data.
How do you find highest standard deviation in given number?
Standard deviations are measures of data distributions. Therefore, a single number cannot have meaningful standard deviation.
What do the variance and the standard deviation measure?
They are measures of the spread of distributions about their mean.
What does standard deviation show us about a set of scores?
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.
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
Why standard deviation scores over mean deviation as a more accurate measures of dispersion?
It is not. And that is because the mean deviation of ANY variable is 0 and you cannot divide by 0.
Why do we use mean absolute deviation?
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.
If the standard deviation decreases does the mean decrease?
Not necessarily. The standard deviation measures (in simplified terms) how different the numbers are from each other, while the mean is their average. If the standard deviation decreases, it means the numbers are closer to each other, it doesn't change how big the numbers are.
How do you calculate risk on a two asset portfolio?
For a two-asset portfolio, the risk of the portfolio, σp, is: 2222p1122112212222p11221212121212σ=wσ+wσ+2wσwσρorσ=wσ+wσ+2wwcovcov since ρ=σσ where σi is the standard deviation of asset i's returns, ρ12 is the correlation between the returns of asset 1 and 2, and cov12 is the covariance between the returns of asset 1 and 2. Problem What is the portfolio standard deviation for a two-asset portfolio comprised of the following two assets if the correlation of their returns is 0.5? Asset A Asset B Expected return 10% 20% Standard deviation of expected returns 5% 20% Amount invested $40,000 $60,000
How do you calculate risk on a two-asset portfolio?
For a two-asset portfolio, the risk of the portfolio, σp, is: 2222p1122112212222p11221212121212σ=wσ+wσ+2wσwσρorσ=wσ+wσ+2wwcovcov since ρ=σσ where σi is the standard deviation of asset i's returns, ρ12 is the correlation between the returns of asset 1 and 2, and cov12 is the covariance between the returns of asset 1 and 2. Problem What is the portfolio standard deviation for a two-asset portfolio comprised of the following two assets if the correlation of their returns is 0.5? Asset A Asset B Expected return 10% 20% Standard deviation of expected returns 5% 20% Amount invested $40,000 $60,000
