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##### FIN 473 Problem Set Assignment

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Question;1.Consider a portfolio consisting of 4 different bonds with market values as in the Table below.Bond A B C DMod. Duration (years) 2 7 8 14Market value($) 13 27 60 40a. What is the modified duration of the portfolio? Show that the modified duration of a portfolio of bonds is the (portfolio) weighted average of the individual bond durations.b. Suppose interest rates falls by 50 bp for all maturities. Compute an approximate percentage change in the value of the portfolio.(10p)2. Consider the two semi-annual bonds E and F described in the table below.Bond E FCoupons 8% 9%Yield to maturity 8% 8%Maturity (years) 2 5Face value $100 $100Price $100 $104.055Now assume interest rates increases by 100 bp.a. Calculate the price of the bonds.b. Approximate the price using duration.c. Approximate the price using both duration and convexity.d. Comment on the accuracy and explain why one of the approximations are better than the other.e. Without calculations, indicate whether the duration of the two bonds would be higher or lower if the yield to maturity is 10% rather than 8%.(10p)3. Consider a bond with par value $100, coupon rate 6% and 10 years to maturity.a. Using Microsoft Excel produce a printout of a table and a graph of the PVBP corresponding to required yields in the range 1%-16% with intervals of 1% (place yield on the horizontal axis of the graph).b. Repeat part a. for Macauley duration.c. Give a brief explanation of your findings.Note: It is the same bond used for the Excel exercises of previous problem set.(6p)4. True-False: Suppose the spread between the yields at two different maturities narrows. Then it is profitable to have a short position in the bond with lower maturity and a long position in the bond with higher maturity. Explain your answer. (4p)5. Consider three zero-coupon bonds with 2, 10, and 30 years to maturity and with required yields 4%, 7%, and 9%, respectively.a. Calculate the price and modified duration of the three bonds using annual compounding.b. How can a trader use convexity to set up a profitable trade in case she expects the yield curve to move in a parallel way? (Hint: assume a short position of 100 10 year bonds and then solve the system of two linear equations in two unknowns)c. Using Excel, produce a print-out of a table with the trade positions values and the trade profit generated by parallel yield curve shifts of 250 bp in steps of 50 bp.d. Now assume that the yield curve does not shift in a parallel way but instead flattens for the shorter maturities. More precisely assume y2 increases 1%, y10 decreases 1% and y30 remains unchanged. What are the trade positions values and the trade profit in this case? (14p)6. True-False. At each date an investor can choose between a one year and a two year zero-coupon bond. Assume that she wants to make a two year horizon investment and that she expects the one year rate, one year from now, to be higher than the current one year rate. Then she should investin one year bonds twice (now and in one year) rather than directly in the two-year bond. Explain your answer. (6p)7.Determine the annual cash flows from an investment in a 4-year, 3% annual TIP bond with an original principal of $1000, given a 2% inflation rate each year for the next four years. (5pts)YearInflationInflation-AdjustedPrincipalTIP CashFlow12342%2%2%2%$1020.00$1040.40$1061.21$1082.43$30.60$31.21$31.84$32.47 + $1082.43

Paper#48493 | Written in 18-Jul-2015

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