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T-bill Interest Rates to Determine Future Contract Rates

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Suppose the current yields to maturity on 3 month and 6 month T-Bills are 4.0 percent and 5.0 percent, respectively (yields will need to be converted to 90-day returns).
(a) In perfectly efficient markets and risk-neutral pricing, what yield should you expect to find on a 3 month T-bill forward contract deliverable in 3 months?
(b) Show that for the forward yield calculated in (a) the 6 month returns on (i) a 6 month spot bill and (ii) 3 month spot and 3 month futures bills are the same.
(c) Explain what factors would lead to a rejection of (b).

NOTE: From the term structure of interest rates recall: (look at attachment for proper symbol representation)
(1 + oy2)2 = (1 + oy1)(1 + 1F1)
where oy2 = the cash 6 month bill (two period) yield,
oy1 = the cash 3 month bill (one period) yield,
1F1 = the 3 month (one period) forward yield one period from now.

ALSO, in the futures market:
(1 + oy2)2 = (1 + oy1)(1 + 1y1f),
where 1y1f = the 3 month futures yield on futures contracts due in three months.

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Solution Summary

This solution uses T-bill interest rates to determine Forward and Future contract rates in a step-by-step calculation, with all workings showed on an excel file.

Solution provided by:
  • MBA, Merage School of Business, Univ of Cal, Irvine
  • BA, Univ of Cal, Irvine
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