You are given a risk-free rate of 5% per year, a portfolio return of 15% per year, and a standard deviation of portfolio return of 16% per year. What is the Sharpe measure of risk-adjusted performance?
Answer(s): A
The Sharpe measure of risk-adjusted performance is equal to (rbar_p - rbar_f)/sigma_p, where rbar_p is the mean portfolio return, rbar_f is the mean risk-free return, and sigma_p is the standard deviation of portfolio return. In our case, we have (15% - 5%) / 16% = 10/16 = 5/8 = 0.625.
An analysis of the grades on the first test in History 101 revealed that they approximate a normal curve with a mean of 75 and a standard deviation of 8. The instructor wants to award the grade of A to the upper 10 percent of the test grades. What is the dividing point between an A and a B grade?
Answer(s): C
First we need to find the z value for an area under the curve representing 40%. (This is because we are looking for the top 10%). From the table z = 1.282. Therefore using the z formula we have 1.282 = X-75/8. We find that x = 85.25
If you owe $5,000 today and will repay it with 8 annual payments of $900 beginning next year, what is the annual interest rate, compounded annually, that you are paying?
Answer(s): D
On the BAII Plus, press 8 N, 5000 PV, 900 +/- PMT, 0 FV, CPT I/Y. On the HP12C, press 8 n, 5000 PV, 900 CHS PMT, 0 FV, i. Note that the PMT must be entered with a sign that is opposite that given the PV.
Distributions X and Y have the same coefficients of variation. If the mean of X is twice the mean of Y and the standard deviation of X is 5, the standard deviation of Y is ________.
coefficient of variation = standard deviation/mean. If the mean of Y is M, then the coefficient of variation of X is 5/(2M) and that of Y is (standard deviation of Y)/M. Given that these two are equal, 5/(2M) = (standard deviation of Y)/M. Therefore, standard deviation of Y = 5/2 = 2.5.
Consider the following list of numbers:6, 4, 3, 8, 3, 3, 5, 9, 11, 4For this list, the mean, the median and the mode are given respectively by:
The sum of the 10 numbers is 56. The mean is 56/10 = 5.6. The most common number is 3, which is the mode.Since there is an even number (10) of numbers in the list, the median is the average of the 5th and 6th numbers when the list is arranged in an ascending order. The median is therefore equal to (4 + 5)/2 = 4.5.
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