Question

1. Use the par yield curve below to price the cash flows given in the left-most column. Quote the price to the closest penny.

Period	Maturity (yrs)	Yield (BEY %)	CF ($)
1	0.5	0.5	10
2	1	2	20
3	1.5	3	100
4	2	4	-30
5	2.5	5	50
6	3	6	50
7	3.5	7	100
8	4	7.5	200
9	4.5	8	0
10	5	8.4	1,000

2. Give and describe the no-arbitrage table to price a 2-year zero coupon loan 2 years from now, accounting for the actions of all parties. For concreteness sake, use the par yield curve in question 1. What is the lockable, annualized rate for such a loan?

3. Briefly describe the expectations hypothesis, and how the liquidity preference theory accounts for the observation that the yield curve tends to be upward sloped, rather than what is predicted by the expectations hypothesis.

Answer 1

Because of multiple questions, solution is provided to the first question only

1. We need to discount the cash flow using the par yield for each period. Since the yield provided BEY is annualized and our periods are semi-annual periods, we will have to divide the yield by 2.

The formula to price the cash flows =

ΣCFl/(1 + S(1)] Σ

Substituting the given values in this formula, we can calculate the price to be equal to $1073.85. Please refer to the attached screenshot from Excel workbook.

Since S(t) is given in % terms, we will have to divide the value by 100 to convert it into decimal.

] Period Maturity Yield (BEY %CF ($) CF(t) / lyrs) |s(t) |CF(t) |[1 +S(t)/2/100)]^t 1] 0.5| | 0.5| 10 9.94] [ 1 |2| 20] 19.61| | 3| 1.5[ 3| 100L. 95.63| | 41 2| 41 -30 -27.72 | 5 2.5| | 44.19] 3L | 6l 50] 41.৪7| 7| 100] 78.60| 7.5| 200| 144.94] | ৪| ol | 0.00] ৪.4] 1,000 662.71] Total 1,073.45] 50 ফিলিলিলিত 3.5) 4.5/