Problem 3. The following are the monthly rates of return for Madison Cookies and for Sophie Electric during a six-month period. Madison Sophie Month Cookies Electric 1 -0.04 0.07 2 0.06 -0.02 3 -0.07 -0.1 4 0.12 0.15 5 -0.02 -0.06 6 0.05 0.02 Compute the following: a. Average mnthly rate of return Ri for each stock b. Standard deviation of returns for each stock c. Covariance between the rates of return d. The correlation coefficient between the rates of return What level of correlation did you expect? How did your expectations compare with the computed correlation? Would these two stocks be good choices for diversification? Why or Why not? ————————————————————— The following are monthly percentage price changes for four market indexes. Month DJIA S&P 500 Russell 2000 Nikkei 1 0.03 0.02 0.04 4.00 2 9.07 0.06 0.10 (0.02) 3 (0.02) (0.01) (0.04) 0.07 4 0.01 0.03 0.03 0.02 5 0.05 0.04 0.11 0.02 6 (0.06) (0.04) (0.08) 0.06 Compute the following: a. Average monthly rate of return for each index. b. Standard deviation for each index c. Covariance between the rates of return for the following indexes: DJIA – S&P500 S&P 500 – Russell 2000 S&P 500 – Nikkei Russell 2000 – Nikkei d. The correlation coefficients for the same four combinations e. Using the answers from parts (a), (b), and (d), calculate the expected return and standard deviation of a portfolio consisting of equal parts of: (1) the S&P and the Russell 2000, and (2) the S&P and the Nikkei. Discuss the two portfolios. —————————————————————– The standard deviation of Shamrock Corp. stock is 19 percent. The standard deviation of Cara Co. stock is 14 percent. The covariance between these two stocks is 100. What is the correlation between Shamrock and Cara Stock?
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1.) Watters Umbrella Corp. issued 15-year bonds 2 years ago at a coupon rate of 8.8 percent. The bonds make semiannual payments. If these bonds currently sell for 109 percent of par value, what is the YTM?
| Laurel, Inc., and Hardy Corp. both have 6 percent coupon bonds outstanding, with semiannual interest payments, and both are priced at par value. The Laurel, Inc., bond has three years to maturity, whereas the Hardy Corp. bond has 20 years to maturity. |
| If interest rates suddenly rise by 2 percent, what is the percentage change in the price of each bond? |
| Percentage change in price of Laurel, Inc., bond | [removed] % |
| Percentage change in price of Hardy Corp. bond | [removed] % |
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| If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of each bond? |
| Percentage change in price of Laurel, Inc., bond | [removed] % |
| Percentage change in price of Hardy Corp. bond | [removed] % |
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| You purchase a bond with an invoice price of $1,036. The bond has a coupon rate of 8.7 percent, and there are four months to the next semiannual coupon date. |
| What is the clean price of the bond? |
| Wyland Co. wants to issue new 15-year bonds for some much-needed expansion projects. The company currently has 9 percent coupon bonds on the market that sell for $1,070, make semiannual payments, and mature in 15 years. |
| What coupon rate should the company set on its new bonds if it wants them to sell at par? |
| Cavo Corp. has 7 percent coupon bonds making annual payments with a YTM of 6.5 percent. The current yield on these bonds is 6.85 percent. |
| How many years do these bonds have left until they mature? |
| A 10-year annuity of twenty $5,675 semiannual payments will begin 14 years from now, with the first payment coming 14.5 years from now. |
| If the discount rate is 11 percent compounded monthly, what is the value of this annuity five years from now? |
| Value of the annuity | $ [removed] |
| If the discount rate is 11 percent compounded monthly, what is the value three years from now? |
| Value of the annuity | $ [removed] |
| If the discount rate is 11 percent compounded monthly, what is the current value of the annuity? |
| Value of the annuity | $ [removed] |
What is the present value of an annuity of $6,000 per year, with the first cash flow received three years from today and the last one received 25 years from today? Use a discount rate of 7 percent.
| Mike Bayles has just arranged to purchase a $450,000 vacation home in the Bahamas with a 30 percent down payment. The mortgage has a 5.1 percent stated annual interest rate, compounded monthly, and calls for equal monthly payments over the next 30 years. His first payment will be due one month from now. However, the mortgage has an eight-year balloon payment, meaning that the balance of the loan must be paid off at the end of Year 8. There were no other transaction costs or finance charges. |
| How much will Mike’s balloon payment be in eight years? |
| A prestigious investment bank designed a new security that pays a quarterly dividend of $4.00 in perpetuity. The first dividend occurs one quarter from today. |
| What is the price of the security if the stated annual interest rate is 4.5 percent, compounded quarterly? |
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