Reference no: EM132277293
Question 1. You are given the following probability distribution for the annual sales of Elstop Corporation:
Probability Distribution for Elstop Annual Sales
Probability
|
Sales ($ Millions)
|
0.20
|
275
|
0.40
|
250
|
0.25
|
200
|
0.10
|
190
|
0.05
|
180
|
Sum =1.00
|
|
A. Calculate the expected values of ElStop's annual sales.
B. Calculate the variance of ElStop's annual sales.
C. Calculate the standard deviation of ElStop's annual sales.
Question 2. Suppose we have the expected daily returns (in terms of US dollars), standard deviations and correlations shown in the below.
US Dollar Daily Returns in Percent
|
|
US Bonds
|
German Bonds
|
Italian Bonds
|
Expected Return
|
0.029
|
0.021
|
0.073
|
Standard Deviation
|
0.409
|
0.606
|
0.635
|
Correlation Matrix
|
|
|
|
|
US Bonds
|
German Bonds
|
Italian Bonds
|
US Bonds
|
1
|
0.09
|
0.10
|
German Bonds
|
|
1
|
0.70
|
Italian Bonds
|
|
|
1
|
A. Using the data given above, construct a covariance matrix for the daily returns on US, German, and Italian bonds.
B. State the expected return and variance of return on a portfolio 70 percent invested in US bonds, 20 percent in German bonds, and 10 percent in Italian bonds.
C. Calculate the standard deviation of return for the portfolio in Part B.
Question 3. The variance of a stock portfolio depends on the variances of each individual stock in the portfolio and also the covariance among the stocks in the portfolio. If you have five stocks, how many unique covariance's (excluding variances) must you use in order to compute the variance of return on your portfolio? (Recall that the covariance of a stock with itself is the stock's variance.)
Question 4. Why is the central limit theorem important?
Question 5. What is wrong with and missing from the following statement of the central limit theorem?
Central Limit Theorem. " If the random variables X1, X2, X3,..., Xn, are a random sample of size n from any distribution with finite mean µ and variance σ2, then the distribution of X ¯ will be approximately normal, with a standard deviation of σ/√n."
Question 6. Suppose we take a random sample of 30 companies in an industry of 200 companies. We calculate the sample mean of the ratio of cash flow to total debt for the prior year. We find that this ratio is 23 percent. Subsequently, we learn that the population cash flow to total debt ratio (taking into account of all 200 companies) is 26 percent. What is the explanation for the discrepancy between the sample mean of 23 percent and the population mean of 26 percent?
A. Sampling Error
B. Bias
C. A lack of Consistency