Suppose that you want to construct a 2-year maturity forward loan commencing in 3 years. The face value of each bond is $1,000. Maturity (Years) 1 2 3 Price $ 996.04 895.89 833.92 772.80 675.18 Required: a. Suppose that you buy today one 3-year maturity zero-coupon bond with face value $1,000. How many 5-year maturity zeros would you have to sell to make your initial cash flow equal to zero (specifically, what must be the total face value of those 5-year zeros)? b. What are the cash flows on this strategy in each year? c. What is the effective 2-year interest rate on the effective 3-year-ahead forward loan? d. & e. Confirm that the effective 2-year forward interest rate equals (1 + £4) *(1 + f5)-1. You therefore can interpret the 2-year loan rate as a 2-year forward rate for the last two years. Alternatively, show that the effective 2-year forward rate equals (1+y5) 5+ (1+y3)² - 1

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
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Suppose that you want to construct a 2-year maturity forward loan commencing in 3 years. The face value of each bond is $1,000.
Maturity
(Years)
1
2
3
4
5
Price
$ 996.04
895.89
833.92
772.80
675.18
Required:
a. Suppose that you buy today one 3-year maturity zero-coupon bond with face value $1,000. How many 5-year maturity zeros would
you have to sell to make your initial cash flow equal to zero (specifically, what must be the total face value of those 5-year zeros)?
b. What are the cash flows on this strategy in each year?
c. What is the effective 2-year interest rate on the effective 3-year-ahead forward loan?
d. & e. Confirm that the effective 2-year forward interest rate equals (1 + f4) ×(1 + f5)-1. You therefore can interpret the 2-year loan
rate as a 2-year forward rate for the last two years. Alternatively, show that the effective 2-year forward rate equals
(1 + y5) 15 + (1+y3) ³. - 1
Transcribed Image Text:Suppose that you want to construct a 2-year maturity forward loan commencing in 3 years. The face value of each bond is $1,000. Maturity (Years) 1 2 3 4 5 Price $ 996.04 895.89 833.92 772.80 675.18 Required: a. Suppose that you buy today one 3-year maturity zero-coupon bond with face value $1,000. How many 5-year maturity zeros would you have to sell to make your initial cash flow equal to zero (specifically, what must be the total face value of those 5-year zeros)? b. What are the cash flows on this strategy in each year? c. What is the effective 2-year interest rate on the effective 3-year-ahead forward loan? d. & e. Confirm that the effective 2-year forward interest rate equals (1 + f4) ×(1 + f5)-1. You therefore can interpret the 2-year loan rate as a 2-year forward rate for the last two years. Alternatively, show that the effective 2-year forward rate equals (1 + y5) 15 + (1+y3) ³. - 1
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