A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the thirdis a money market fund that provides a safe return of 7%. The characteristics of the risky funds are as follows:Stock fund (S)Bond fund (B)Expected Return22%12Standard Deviation32%19The correlation between the fund returns is 0.11.Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio.(Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)Portfolio invested in the stockPortfolio invested in the bondExpected returnStandard deviation

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Answered: A pension fund manager is considering…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Mortgage rates: Following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one day. It is reasonable to assume that the population is approximately normal. 4.752 4.375 4.173 4.675 4.421 4.229 4.128 4.250 3.954 4.295 4.411 Send data to Excel Part: 0/ 2 Part 1 of 2 (a) Construct a 99% confidence interval for the mean rate. Round the answer to at least four decimal places. A 99% confidence interval for the mean rate is
4. Along with interest rates, life expectancy is a component in pricing financial annuities. Suppose that you know that last year average life expectancy was 77 years for your annuity holders. Now you want to know if your clients this year have a longer life expectancy, on average, so you randomly sample n=20 of your recently deceased annuity holders to see actual age at death. Using a 5% level of significance, test whether or not the new data shows evidence of your annuity holders now live longer than 77 years, on average. The data below are the sample data (in years of life): (78,75,83,81,81,77,78,79,79,81,76,79,77,76,79,81,73,74,78,79) a) Does this sample indicate that life expectancy has increased? Test an appropriate hypothesis and state your conclusion (use a 5% level of significance). Be sure to check the necessary assumptions and conditions before conducting your test. b) Construct A 90% confidence interval for the true average age of death for the population of your annuity…
Given the following investment returns from two stocks:Stock A: 5%,6%,7%,9%,23% (mean = 10% and standard deviation = 7.416%)Stock B: 50%,60%,70%,90%,230% (mean = 100% and standard deviation = 74.16%).Which stock has the greatest relative risk? Which stock should a risk seeking investor choose? Two correct answers 1. Stock A has the greatest relative risk. 2. Stock B has the greatest relative risk. 3. Both stocks have the same amount of relative risk. 4. A risk seeking investor should invest in Stock A. 5. A risk seeking investor should invest in Stock B. 6. A risk seeking investor should invest in either of the two stocks since they are equally attractive.
The selling prices of mutual funds change daily. In order to study these changes, a sample of mutual funds was examined and the daily changes in price are listed below. (Round answers to 3 decimal places) 0.32, -0.17, 0.26, -0.03, -0.01, 0.18, 0.33, 0.28, 0.02, -0.29, -0.08, 0.12, 0.07, 0.03, 0.28 a) Using a calculator find Q1, Q3, median and IQR b) Determine the lower and upper fences. (Show work) c) Identify the outliers (if any) in this set
Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.A sample of 80 stocks traded on the NYSE that day showed that 11 went up.You are conducting a study to see if the proportion of stocks that went up is is significantly less than 0.3. You use a significance level of α=0.02α=0.02.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail…
Caterpillar, Inc., manufactures and sells heavy construction equipment worldwide. The performance of Caterpillar’s stock is likely to be strongly influenced by the economy. For example, during the Great Recession, the value of Caterpillar’s stock plunged dramatically. Monthly data for Caterpillar’s risk-adjusted return (R − Rf) and the risk-adjusted market return (RM − Rf) are collected for a five-year period (n = 60). A portion of the data is shown in the accompanying table. (You may find it useful to reference the t table.) Month Year R_Rf RM_Rf Jan 2012 0.0510 0.0403 Feb 2012 -0.0682 0.0304 Mar 2012 -0.0360 -0.0083 Apr 2012 -0.1446 -0.0635 May 2012 -0.0318 0.0387 Jun 2012 -0.0091 0.0117 Jul 2012 0.0188 0.0188 Aug 2012 0.0073 0.0232 Sept 2012 -0.0154 -0.0209 Oct 2012 0.0101 0.0018 Nov 2012 0.0504 0.0062 Dec 2012 0.1036 0.0497 Jan 2013 -0.0619 0.0104 Feb 2013 -0.0595 0.0350 Mar 2013 -0.0273 0.0172 Apr 2013 0.0193 0.0202 May 2013 -0.0390 -0.0154…
A financial analyst is examining the relationship between stock prices and earnings per share. She chooses sixteen publicly traded companies at random and records for each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year and y denoting the current stock price (both in dollars). A scatter plot of her data is shown in Figure 1. Also given is the product of the earnings per share and the current stock price for each of the sixteen stocks. (These products, written in the column labelled "xy ", may aid in calculations.) Earnings per share, x (in dollars) 36.79 49.84 30.65 30.17 17.66 57.66 37.98 20.65 58.67 13.52 41.83 39.28 43.73 Current stock price, y (in dollars) 1.43 1.56 0.81 1.40 0.77 2.64 1.11 0.70 2.18 0.41 1.80 1.05 1.63 ху 52.6097 77.7504 24.8265 42.238 13.5982 152.2224 42.1578 14.455 127.9006 5.5432 75.294 41.244 71.2799 Current stock…
Consider the following quarterly time series. Quarter 1 2 3 4 Year 1 923 Year 2 1,112 1,056 1,156 992 Year 3 1,078 1,243 1,124 1,124 1,254 1,301 1,198 a. Construct a time series plot. What type of pattern exists in the data? b. Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1 = 1 if quarter 1, 0 otherwise; Qtr2 = 1 if quarter 2, 0 otherwise; Qtr3 = 1 if quarter 3, 0 otherwise. c. Compute the quarterly forecasts for next year based on the model developed in part b.
According to a high-profile realtor, houses in the sleepy town of Sun Beach have shown higher appreciation over the past three years than have houses in the bustling town of North Arden. To test the realtor's claim, an economist has found twelve recently sold homes in Sun Beach and twelve recently sold homes in North Arden that were owned for exactly three years. The following table gives the appreciation (expressed as a percentage increase) for each of the twenty- four houses. Appreciation rates in percent Sun Beach 12.5, 12.2, 10.4, 12.9, 6.5, 15.0, 10.1, 10.6, 12.1, 10.8, 10.4, 9.1 North Arden 9.2, 10.7, 9.7, 7.8, 9.7, 12.1, 9.4, 6.1, 7.8, 9.3, 4.6, 11.0 Send data to calculator v Assume that the two populations of appreciation rates are normally distributed and that the population variances are equal. Can we conclude, at the 0.05 level of significance, that houses in Sun Beach have higher appreciation over the past three years than houses in North Arden? Perform a one-tailed test.…
Below are percentages for annual sales growth and net sales attributed to loyalty card usage at 74 Noodles & Company restaurants. Annual Sales Growth (px;) and Loyalty Card Usage (px; of Net Sales)(n = 74 restaurants) Store Growth% Loyalty% Store Growth% Loyalty% 1 -7.8 0.7 38 7.3 1.5 2 -6.9 2.5 39 7.4 1.7 3 -5.1 1.6 40 7.7 2.3 4 -4.7 1.4 41 8.0 2.0 5 -3.8 2.5 42 8.0 1.6 6 -1.7 1.5 43 8.3 1.9 7 -1.7 2.6 44 8.4 2.0 8 -1.6 2.4 45 8.6 2.2 9 -1.1 2.2 46 8.6 1.6 10 -1.0 1.9 47 8.7 0.9 11 0.4 1.2 48 8.9 1.7 12 0.6 0.5 49 9.4 1.6 13 0.6 2.1 50 9.5 1.3 14 1.0 1.3 51 9.5 2.1 15 1.3 2.0 52 10.5…
Arbor Systems and Gencore stocks both have a volatility of 44%. Compute the volatility of a portfolio with 50% invested in each stock if the correlation between the stocks is 0.00. If the correlation is 0.00, the volatility of the portfolio is%. (Round to one decimal place.)
A financial analyst is examining the relationship between stock prices and earnings per share. She chooses fifteen publicly traded companies at random and records for each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year and y denoting the current stock price (both in dollars). A scatter plot of her data is shown in Figure 1. Also given is the product of the earnings per share and the current stock price for each of the fifteen stocks. (These products, written in the column labelled "xy ", may aid in calculations.) Earnings per Current stock price, y (in dollars) share, x (in dollars) xy 37.59 1.19 44.7321 y 56.02 2.70 151.254 20.21 0.75 15.1575 X 41.33 0.91 37.6103 19.90 0.63 12.537 58.72 2.37 139.1664 43.33 1.45 62.8285 42.61 1.77 75.4197 13.72 0.52 7.1344 37.29 1.39 51.8331 30 30.12 0.93 28.0116 49.34 1.59 78.4506 Earnings per share (in…

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