Term
| What are the four moments of a distribution? |
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Definition
1st = mean
2nd = variance
3rd = skewness
4th = kurtosis |
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Term
| Formula for calculating variance? |
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Definition
| Var(X) = E[(X - µ)2] = E(X2) - [E(X)2] |
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Term
| What does Chebyshev's Inequality state and what's the formula for it? |
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Definition
states that for any set of observations, whether sample or population data and regardless of the type of distribution, the % of the observations that lie within k standard deviations of the mean =
1 - 1/(k2)
where k > 1 |
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Term
| Whats the CV and how do you calculate it? |
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Definition
Coefficient of Variation is a relative measure of dispersion - it's lets direct comparisons of dispersion across different sets of data
CV = σx / mean X
Standard deviation of X / mean of X |
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Term
| What is covariance and what's the formula for calculating it? |
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Definition
Covariance shows how two random variables (such as asset returns) are related.
Covariance is the expected value of the product of the deviattions of the two random variables from their respective means.
Cov(Ri,Rj) = E{[Ri - E(Ri)][Rj - E(Rj)]} |
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Term
| Whats the formula for the correlation coefficient? |
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Definition
| Corr(Ri,Rj) = Cov(Ri,Rj) / σ(Ri) σ(Rj) |
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Term
| How do you calculate variance of a 2-asset portfolio (what's the formula)? |
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Definition
| Var(Rp) = wA2 σ2(RA) + wB2 σ2(RB) + 2wAwBCov(RA,RB) |
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Term
| When should the geometric mean be used and how do you calculate it? |
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Definition
Used when calculating investment returns over multiple periods or when measures compound growth rates.
Formula for geometric mean for non-returns set data is:
G = (X1 times X2 times X3 ... times Xn)1/n
If calculating GM for a returns data set add 1 to each value and then subtract 1 from the result, i.e.:
Greturns_data = ((1+X1) times (1+X)2 times (1+X3) ... times (1+Xn))1/n |
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Term
| How do you calculate sample variance? |
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Definition
| It's population variance (sum of squared deviations from the mean) but instead of using n in the denominator use n-1 |
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Term
How does a positive skew affect mean, median, mode?
What about a negative skew? |
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Definition
Positive skew - mean is most affected (pulled to the right), then median, then mode.
Also, for negative skew mean is most affected (pulled to the left), then median, then mode. |
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Term
| What does leptokurtic mean? |
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Definition
| a distribution which is more peaked than normal (higher kurtosis than 3). It will have more returns clustered around hte mean and more returns with large deviations from the mean (fatter tails). This is perceived as an increase in risk. |
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Term
| What does platykurtic refer to? |
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Definition
| A distribution that is less peaked (kurtosis < 3) than normal. This will have not fat tails and thus perceived to have less risk. |
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Term
| Interpret a skewness number... what does a negative numer mean, a positive numer...? |
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Definition
When a distribution is right skewed, skewness is positive because the deviations above the mean are larger on average
A negative number means it's a left skewed (negative) distribution.
Skewness if raised to the 3rd power (see Schweser book 1 page 160) |
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Term
| To interpret kurtosis it is measured relative to... |
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Definition
the kurtosis of a normal distribution which is 3.
Positive values of excess kurtosis indicate a leptokurtic distribution.
Negative values of excess kurtosis indicate a platykurtic distribution. |
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