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Q-3.et X and Y be two random variables representing the annual returns of two different portfolios. If E[X] = 3, E[Y] = 4 and E[XY] = 11, then what is Cov[X, Y]?
A.-1
B.0
C.11
D.12
Solution: A
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Q-5.Which type of distribution produces the lowest probability for a variable to exceed a specified extreme value X which is greater than the mean assuming the distributions all have the same mean and variance?
AA leptokurtic distribution with a kurtosis of 4
BA leptokurtic distribution with a kurtosis of 8
CA normal distribution
DA platykurtic distribution
Solution: D
A is incorrect. A leptokurtic distribution has fatter tails than the normal distribution. The kurtosis indicates the level of fatness in the tails, the higher the kurtosis, the fatter the tails. Therefore, the probability of exceeding a specified extreme value will be higher.
B is incorrect. Since answer A. has a lower kurtosis, a distribution with a kurtosis of 8 will necessarily produce a larger probability in the tails.
C is incorrect. By definition, a normal distribution has thinner tails than a leptokurtic distribution and larger tails than a platykurtic distribution.
D is correct. By definition, a platykurtic distribution has thinner tails than both the normal distribution and any leptokurtic distribution. Therefore, for an extreme value X, the lowest probability of exceeding it will be found in the distribution with the thinner tails.
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