Fin 7000 problem set 2 37557

Question

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Problem 1: Fill in the table below for each of the following interest rates:

 

Compounding PV of $1000

Case Stated Annual Rate Periods Per Year Effective Annual Rate at t = 2

1 .12 1

2 .12 2

3 .12 4

4 .12 12

5 .12 24

6 .12 infinity

 

Problem 2:

 

The effective annual rate is 3% (i.e., re = .03). What is the stated rate for compounding semi-annually that is associated with this effective rate?That is, solve for rs such that 1+re = (1+(rs/2))2 given re = .03.

 

Problem 3:

 

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:

 

  1. $100 at t = 1,

  2. $100 at t = 2,

  3. $100 at t = 3,

  4. $100 at t = 4,

  5. $100 at t = 5,

  6. $100 at t = 1 and $100 at t = 4

  7. $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?