The James Bond Fund is a mutual fund (open-end investment company) with an objective of maximizing income from a widely diversified corporate bond portfolio. The fund has a policy of remaining invested largely in a diversified portfolio of investment-grade bonds. Investment-grade bonds have high investment quality and receive a rating of Baa or better by Moody's, a bond rating service. The fund's investment policy states that investment-grade bonds are to be emphasized, representing at least three times the amount of junk bond holdings. Junk bonds pay high nominal returns but have low investment quality, and they receive a rating of less than Baa from Moody's. To maintain the potential for high investor income, at least 20% of the fund's total portfolio must be invested in junk bonds. Like many funds, the James Bond Fund cannot use leverage (or borrowing) to enhance investor returns. As a result, total bond investments cannot total more than 100% of the portfolio. Finally, the current expected return for investment-grade (I) bonds is 9%, and it is 12% for junk (J) bonds.
A. Using the inequality form of the constraint conditions, set up and interpret the linear programming problem that the James Bond Fund would use to determine the optimal portfolio percentage holdings of investment-grade (I) and junk (J) bonds. Also formulate the problem using the equality form of the constraint conditions. (Assume that the fund managers have decided to remain fully invested and therefore hold no cash at this time.)
B. Use a graph to determine the optimal solution, and check your solution algebraically. Fully interpret solution values.
C. Holding all else equal, how much would the expected return on junk bonds have to fall to alter the optimal investment policy determined in Part B? Alternatively, how much would the return on investment-grade bonds have to rise before a change in investment policy would be warranted?
D. In anticipation of a rapid increase in interest rates and a subsequent economic downturn, the investment committee has decided to minimize the fund's exposure to bond price fluctuations. In adopting a defensive position, what is the maximum share of the portfolio that can be held in cash given the investment policies stated in the problem?© BrainMass Inc. brainmass.com October 16, 2018, 8:15 pm ad1c9bdddf
Solution in excel file
Regression and business
(See attached file for full problem description with diagrams)
2. The following sample observations were randomly selected.
Determine the coefficient of correlation and the coefficient of determination. Interpret.
3. Bi-lo Appliance Stores has outlets in several large metropolitan areas. The general sales manager
plans to air a commercial for a digital camera on selected local TV stations prior to a sale starting
on Saturday and ending Sunday. She plans to get the information for Saturday-Sunday digital
camera sales at the various outlets and pair them with the number of times the advertisement was
shown on the local TV stations. The purpose is to find whether there is any relationship between
the number of times the advertisement was aired and digital camera sales. The pairings are:
a. What is the dependent variable?
b. Draw a scatter diagram.
c. Determine the coefficient of correlation.
d. Determine the coefficient of determination.
e. Interpret these statistical measures.
14. Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a
relationship between the number of client contacts and the dollar amount of sales. To document
this assertion, Mr. McWhinney gathered the following sample information. The X column indicates
the number of client contacts last month, and the Y column shows the value of sales ($ thousands)
last month for each client sampled.
a. Determine the regression equation.
b. Determine the estimated sales if 40 contacts are made.
16. We are studying mutual bond funds for the purpose of investing in several funds. For this particular
study, we want to focus on the assets of a fund and its five-year performance. The question
is: Can the five-year rate of return be estimated based on the assets of the fund? Nine mutual
funds were selected at random, and their assets and rates of return are shown below.
a. Draw a scatter diagram.
b. Compute the coefficient of correlation.
c. Compute the coefficient of determination.
d. Write a brief report of your findings for parts b and c.
e. Determine the regression equation. Use assets as the independent variable.
f. For a fund with $400.0 million in sales, determine the five-year rate of return (in percent).
6. The yield on a 30-year treasury note at the end of each year since 1990 is recorded below. Compute
a five-year weighted moving average using weights of .1, .1, .2, .3 and .3, respectively.
Describe the trend in yield.