1. Forward Rates FNCE 4070 Financial 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.