You have a portfolio of two assets, X and Y. The returns of X and Y follow a joint probability function as follows:There is a 25% chance that X will return 16% and Y will return 10%; there is a 60% chance that X will return 9% and Y will return 7%; and there is a 15% chance that Y will return 15% and X will return 5%. Find the covariance of X and Y.
Answer(s): D
For a joint probability function, the covariance of X and Y is given by the formula: double summation (over all X, and over all Y) of P(X,Y)*[X - E(X)]*[Y - E(Y)]. E(X) will be 25% * 16% + 60% * 9% + 15% * 5% = 4% + 5.4% + 0.75% = 10.15%. Similarly, we will find that E(Y) = 8.95%. Next, we plug these values into our formula and obtain 25% * (16% - 10.15%) *(10% - 8.95%) + 60% (9% - 10.15%) * (7% - 8.95%) + 15% (5% - 10.15%) * (15% - 8.95%) = -1.79%%.
Which is true of positively skewed distributions?
Answer(s): C
All are true of positively skewed distributions, so the answer is I, II, and III: None of the above is the correct choice.
If you want $1,000,000 when you retire in 25 years, how much must you deposit each month, beginning one month from today, if your funds will earn 9% per year, compounded monthly?
Note that since the deposits are made monthly, there are 300 of them (25 x 12 = 300). On the BAII Plus, press 300 N, 9 divide 12 = I/Y, 0 PV, 1000000 FV, CPT PMT. On the HP12C, press 300 n, 9 ENTER 12 divide i, 0 PV, 1000000 FV, PMT. Note that the answer will be displayed as a negative number. Make sure the BAII Plus has the value of P/Y set to 1.
If alpha equals 0.05 for a two-tailed hypothesis test, how large is the area of rejection in the upper or right tail?
Answer(s): B
If it is a two tailed test, then there is a similar size region in each tail. So 0.05/2 = 0.025.
Two sets of observations, A and B, each contain 160 observations. The variance of data in A equals 198.4 and that of the data in B equals 231.9. The two sets have the same mean. Then, A has a ________ dispersion and a ________ coefficient of variation.
B has a higher variance and hence, a higher dispersion. The coefficient of variation equals the standard deviation divided by the mean. Since A and B have the same mean, B has a higher coefficient of variation.
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