Consider the following information on a yield curve (where t = 0 is now) Time (i

Question

Consider the following information on a yield curve (where t = 0 is now)

                Time (in years) to Maturity (TTM)             Effective Annual Rate                   

1                                                                                                     .01                                              

2                                                                                                     .015

3                                                                                                     .02

4                                                                                                     .0225

5                                                                                                     .0235

Part 1: Using this yield curve, calculate the present value of the following payment streams:

a.       $100 at t = 1,

b.      $100 at t = 2,

c.       $100 at t = 3,

d.      $100 at t = 4,

e.      $100 at t = 5,

f.        $100 at t = 1 and $100 at t = 4

g.       $200 at t = 2 and $200 at t = 5

Part 2: Also using the above yield curve, calculate the forward rate for the one-year yield next year at t = 1.    If you take your answer to b above divided by your answer to a above and then subtract 1, do you get the same answer?

Part 3: Consider the following two strategies for getting a return over three years:

Strategy 1: Invest for three years at the three year rate;

Strategy 2: invest at the two-year rate for two years and then roll over into the one-year rate in two years.

You can calculate a forward rate for the one-year rate in two years (at t = 2) by considering the one-year rate in two years that would make you indifferent between Strategy 1 and Strategy 2. What is that forward rate?

Explanation / Answer

Part 1

a.$100 at t = 1, Present Value = 99.0099

b.$100 at t = 2, Present Value = 97.06617

c.$100 at t = 3, Present Value = 94.23223

d.$100 at t = 4, Present Value = 91.48433

e.$100 at t = 5, Present Value = 89.035

f.$100 at t = 1 and $100 at t = 4 Present Value = 190.4942

g.$200 at t = 2 and $200 at t = 5 Present Value = 372.2024

Part 2

Forward rate = 9.1584. This is calculated as 1.015^2 = 1.01*(1+forward rate)

Yes if wetake our answer to b above divided by our answer to a above and then subtract 1we get the same answer which is shown below

{(1.015^2)/1.01}-1 = 0.091584

Part 3

Use the above formula for calculating the forward rate for one year rate in two years

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