1 / 14

Forward Rates

Forward Rates. FNCE 4070 Financial Markets and Institutions. Market Data. T-Bills 26W 0.130% 52W 0.175% T-Note 2 year Coupon rate 0.25% Semi-Annual Yield 0.273%. T- NotePricing. As there are 4 cashflows in a 2-year T-Note we need 4 discount factors to price the note

zahi
Download Presentation

Forward Rates

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Forward Rates FNCE 4070Financial Markets and Institutions

  2. Market Data • T-Bills • 26W 0.130% • 52W 0.175% • T-Note • 2 year • Coupon rate 0.25% • Semi-Annual Yield 0.273%

  3. T-NotePricing • As there are 4 cashflows in a 2-year T-Note we need 4 discount factors to price the note • These are the 6M, 1Y, 18M and 2Y • We could simply use the s.a. yield to determine a PV but we do not get any term structure information from this. • For example, short term rates are lower than longer term rates. The T-Note price gives information about the relationship but we cannot determine that information from the s.a. yield directly.

  4. Goal • In order to view the yield curve we need to look at consistent rates. • The natural choice for rates is the YTM for a discount bond for a given maturity • An alternate view would be to look at Expected 6M T-Bill prices for 6M, 1Y and 18M. • We need enough rates to value a 2 year T-Note • The rates we need are the 6M, 1Y, 18M and 2Y rates

  5. What we already know • Given the T-Bills we can easily compute the 6M and 1Y YTM. • We can also easily compute the discount factor for a cashflow received on these dates.

  6. What we need to figure out • To create the yield curve we are trying to • Come up with the yield to maturity for 18M and 2Y • Come up with forward T-Bill rates (the first is straightforward) • Start date 6M, 1Y, 18M • End date 12M, 18M, 2Y • These are equivalent representations

  7. Forward T-Bill rates • To figure out Forward T-Bill rates we need • Forward discount factors • Represent the value of 1 dollar paid at the end date as of the start date

  8. Forward T-Bill Rate • The expected Discount Rate for the 6M T-Bill starting in 6M time is straightforward

  9. The Problem • We still need to find two rates • Expected T-Bill starting in 12M and maturing in 18M • Expected T-Bill starting in 18M and maturing in 24M • Alternatively • Expected YTM for 18M • Expected YTM for 24M

  10. The Problem cont • We have a single equation that we have not used. • Or alternatively – we have three pieces of market data and 4 unknowns necessary for pricing our T-Bond

  11. Assumption • We will assume that the 6M T-Bill starting in 12M time will have an expected discount rate that is the average of the 6M T-Bill starting in 6M time and the 6M T-Bill starting in 18M time

  12. Pricing the T-Note • If you price using discount factors you find • Otherwise you use a standard s.a. yield calculation

  13. Discount Factors • The missing discount factors can be derived from: • The missing discount factors from these equations can be derived from the T-Bill discount ratediscount factor formula

  14. Final Solutions • We then use the solver from excel to price the T-Note using discount factors and using s.a. yield calculation and iterate on the T-Bill prices until they match.

More Related