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Whats the formula for calculating variance?
and another way for expressing it... |
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Definition
Var(X) = E[(X - μ)2]
=E(X2) - [E(X)]2 where μ = E(X) |
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| Chebyshev's inequality - what does it state and whats the formula? |
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Definition
Chebyshev's inequality states that for any set of observations whether sample of population data, and regardless of the shape of the distribution, the percentage of the observations that lie within k standard deviations of the mean is at least 1-1/k2 for all k > 1.
The important thing about Chebyshev's inequality is that it applies to any distribution. |
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| What is relative dispersion and whats a common way of measuring it? |
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Definition
Relative dispersion is the amount of variability in a distribution relative to a reference point or benchmark. It's commonly measured with the coefficient of variation (CV) is is calculated as:
CV = σx / average value of x |
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| Why is the coefficient of variance useful? |
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Definition
| it enables direct comparison of dispersion across different sets of data. |
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Compute the CV for these two investments:
Oceanagold mean monthly return = 2.2%, standard deviation = 3%
Telecom, mean monthly return = 1.7%, standard deviation = 0.8% |
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Definition
CV = σx / average value of x
Oceana gold = .03 / .022
Telecom = .017 / .007 |
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What is covariance?
define the formula for computing covariance of the return of asset i, Ri, and asset j, Rj: |
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Definition
Covariance is the expected value of the product of the deviations of the two random variables from their respective expected values.
Cov(Ri,Rj) = E{[Ri - E(Ri)][Rj - E(Rj)]} |
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| What the formula for the correlation of the returns for asset i and j? |
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Definition
| Corr(Ri,Rj) = Cov(Ri,Rj) / [σ(Ri).σ(Ri)] |
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| Comput the correlation of returns for stocks A and B given that σ2(RA) = .0028 and σ2(RB) = .0124, and that Cov(RA,RB) = 0.0058 |
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Definition
| = .0058 / (.0529 * 0.1114) = 0.9842 |
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| Whats the formula for the variance of a 2 asset portfolio? |
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Definition
| Var(Rp) = wA2.σ2(RA) + wB.σ2(RB) + 2wAwBCov(RA,RB) |
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| What is conditional variance? |
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Definition
| Variance is conditional if the variance of a variable is contingent on another variable. |
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For the last 3 years the retruns fro Acme Corporation common stock have been -9.34%, 23.45%, and 8.92%.
Computer the compounded annual rate of return: |
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Definition
Use geometric mean:
1 + RG = [(-.0934 + 1) * (0.2345+1) * (.0892+1)]1/3
RG = 6.825% |
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Formula for population variance:
and population standard deviation: |
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Definition
sum of [(Xi - µ)2] / N
population std deviation = square root of population variance |
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formula for sample variance:
formula for sample std deviation: |
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Definition
sum of [(Xi - sample mean)2] / n-1
square root of sample variance |
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| How do you calculate sample covariance? |
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Definition
| [Sum to n of: (Xi - sample mean X)*(Yi - sample mean Y)] / n-1 |
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| How do you calculate skewness: |
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Definition
skewness is equal to the sum of the cubed deviation from the mean divided by the sample standard deviation cubed times 1/n.
skewness(Sk) = [[sum(Xi-sample mean x)3] / sample standard deviation3]] all of that is multipled by 1/n |
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a positive skewness value indicates...
a negative skewness value indicates... |
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Definition
a right skewed distribution.
a left skewed distribution |
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How do you calculate kurtosis?
What do positive values of kurtosis indicate?
What do negative values of kurtosis indicate? |
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Definition
Kurtosis is the same formula as for skewness but raised to the 4th power:
kurtosis = [[sum(Xi-sample mean x)4] / sample standard deviation4]] all of that is multipled by 1/n
--- positive values indicate a distribution that is leptokurtic (more peaked, fat tails)
--- negative values indicate a distribution that is platykurtic (less peaked, thin tails). |
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