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Forward Rates FNCE 4070 Financial Markets and Institutions

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

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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.

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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

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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.

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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

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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

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

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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

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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

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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

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

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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

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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.

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