# 5. What is the beta of a portfolio consisting

5. What is the beta of a portfolio consisting of one share of each of the following stocks, given their respective prices and beta coefficients? Stock Price BetaA $10 1.4B 24 0.8C 41 1.3D 19 1.8How would the portfolio beta differ if (a) the investor purchased 200 shares of stocks B and C for every 100 shares of A and D and (b) equal dollar amounts were invested in each stock?1.What is the relationship between interest rates and the length of time to maturity? Figures 13.1 through 13.3 give various yield curves for U.S. Treasury securities. What is the current yield curve for U.S. Treasury securities? Possible sources for the answer to this question are Bloomberg (http://www.bloomberg.com under Market Data: Rates & Bonds) or the TreasuryDirect (http://www.treasurydirect.gov under the section on access data).2.How do you purchase a publicly traded bond?3. Portfolio A consists entirely of $1,000 zero coupon bonds that mature in 8, 9, and 10 years. Portfolio B consists of $1,000, 8 percent coupons that mature in 10, 15, and 20 years. a) Based on this information, which portfolio appears to be riskier? Why? b) If the rate of interest on comparable bonds is 8 percent, what are the price and duration of each bond? c) What is the average duration of each portfolio based on each bonds dura- tion? Does this information change your answer to (a)? d) What is the percentage loss for each portfolio if the comparable interest rate rises to 10 percent? e) What does the previous answer imply about the importance of duration to the management of risk?5.As a result of lower interest rates, you are considering refinancing your mort- gage. The existing mortgage has a 12 percent interest rate. The balance owed is $50,000, and the remaining term is 18 years, and your annual payment (i.e., in- terest plus principal) is $6,897. A bank is willing to lend you the money at 10 per- cent to retire the old loan. The term of the new loan will be 18 years, so you are not increasing the number of years required to pay off the mortgage. (There is no reason why the number of years should be the same. If there is a reduction in your mortgage payment, you could restore the original payment and retire the loan quicker. Or you may increase the amount of the loan and use the additional funds to improve the property.) Unfortunately, the bank will charge you an application fee of $500 and an additional fee (points) equal to 2 percent of the amount of the mortgage. There will also be additional costs (e.g., court recording costs of the new mortgage) that are estimated to be $500. To help determine if it is profitable to refinance, answer the following questions. a) What are the total expenses to obtain the new loan? b) How much will you have to borrow to retire the loan when the refinancing expenses are included, and what will be the annual payment required by the new loan? c) What is the difference between the annual payments under the new and the old mortgages? What is the implied course of action?