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Q5 - Summary statistics for returns on two stocks X and Y are listed below.
Mean Variance
Stock X 2.85% 0.005000
Stock Y 5.91% 0.006000
The covariance of returns on stocks X and Y is 0.002800. Consider a portfolio of 30% stock X and 70% stock Y.
What is the variance of portfolio returns?
Please round your answer to six decimal places.
Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.
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- A company has established that the relationship between the sales price for one of its products and the quanlity sokld per month is approximalely p=75-0. 1D (D is the demand or quantity sold per month and p is the price in dollars). The fixed cost is $1,000 per month and the variable cost is $30 per unit produced. a. What is the maximum profit per month for this product? b. What is the range of profitable demand during a month? a. The maximum profit per month for this product is $. (Round to the nearest dollar.) b. The range of profitable demand during a month is from units to units. (Round up the lower limit and down the upper limit to the nearest whole number.)Consider an investment that pays off $700 or $1,600 per $1,000 invested with equal probability. Suppose you have $1,000 but are willing to borrow to increase your expected return. What would happen to the expected value and standard deviation of the investment if you borrowed an additional $1,000 and invested a total of $2,000? What if you borrowed $2,000 to invest a total of $3,000? Instructions: Fill in the table below to answer the questions above. Enter your responses as whole numbers and enter percentage values as percentages not decimals (.e., 20% not 0.20). Enter a negative sign (-) to indicate a negative number if necessary. Invest $1,000 Invest $2,000 Invest $3,000 Expected Value Percent Increase Standard Deviation 1150 S 28 % $ 8 % $ Expected Return N/A Doubled Tripled : #You decide to invest in a portfolio consisting of 21 percent Stock X, 48 percent Stock Y, and the remainder in Stock Z. Based on the following information, what is the standard deviation of your portfolio? State of Economy Normal Boom Probability of State of Economy .84 .16 Return if Stat Stock X Stock Y 10.20% 3.60% 17.50% 25.50%
- If the economy booms, Meyer&Co. stock will have a return of 20.8 percent. If the economy goes into a recession, the stock will have a loss of 13.1 percent. The probability of a boom is 63 percent while the probability of a recession is 37 percent. What is the standard deviation of the returns on the stock? 9.29% 12.43% 13.56% 14.61% 14.61%The following table provides a probability distribution for the random variable x. Excel File: data05-15.xlsx f(x) 3 0.25 0.50 0.25 a. Compute E(x) , the expected value of x. b. Compute o 2, the variance of x (to 1 decimal). c. Compute o, the standard deviation of x (to 2 decimals).Consider the following joint distribution of two random variables X and Y: -2 1 3 ? 0.15 2 0.15 2 0.20 0.30 ? Y|X 2 4 Total 2 Q1a) Calculate the expected value of X, and its standard deviation. Total 0.55 ? ?
- George has projections for the 3 alternative investments in equity shares (stock): What is the Standard Deviation in portfolio 2?A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a rate of 8%. The probability distribution of the risky funds is as follows: Stock fund (S) Bond fund (B) Proportion in Stock Fund The correlation between the fund returns is 0.10. Tabulate the investment opportunity set of the two risky funds. (Round your answers to 2 decimal places.) 0.00 % Expected Return 20% 12 20.00 40.00 60.00 80.00 100.00 Proportion in Bond Fund Standard Deviation 30% 15 100.00 % 80.00 60.00 40.00 20.00 0.00 Expected Return % Standard Deviation %a. A company produces lightbulbs whose life follows a normal distribution, with mean 1200 hours and standard deviation 250 hours. If we choose a lightbulb at random, what is the probability that its lifetime will be between 900 and 1300 hours? (answer in three decimal places) b. An instructor has found that the time spent by students on a particular homework assignment follows a normal distribution with mean 150 minutes and standard deviation 40 minutes. The probability is 0.8 that a randomly chosen student spends less than how many minutes on this assignment. (answer in one decimal place),
- You are at a casino and there are three slot machines you can use to bet on. You must have a return of .5% of higher on what you are betting. Below is the expected returns for each slot machine under various scenarios. What combination of machines do you play to maximize your average return? Decision Variables Data Slot 1 100.0% Monday Tuesday Wednesda Average Slot 2 0.0% Slot #1 8% 4% 5% 5.667% Slot 3 0.0% Slot #2 2% -3% 3% 0.667% Slot #3 6% -2% 4% 2.667% Objective 5.7% Constraints 0.08 >= 0.5% 0.04 >= 0.5% 0.05 >= 0.5% 100.0% .: 100%a. A company produces lightbulbs whose life follows a normal distribution, with mean 1200 hours and standard deviation 250 hours. If we choose a lightbulb at random, what is the probability that its lifetime will be between 900 and 1300 hours? (answer in three decimal places)QUESTION 3 A company sells its products to wholosalers in batches of 10 units only. The daily demand for its product and the respective probabilities are given below. 10 20 30 40 Demand (Units) Probability 0.2 0.2 0.3 0.2 0.1 Assume that the company sells its product at $3.75 per unit. What is the variance of the daily revenue? NOTE: Write your answer using 4 decimal digits. Do not round up or down,
