Question
Assume that the following Treasury yield curve is in existence. Time in Years Time in Periods Coupon Rate YTM Price Theoretical Semi-Annual Spot Rate Theoretical
Assume that the following Treasury yield curve is in existence.
Time in Years | Time in Periods | Coupon Rate | YTM | Price | Theoretical Semi-Annual Spot Rate | Theoretical Annual Spot Rate | Implied Semi-annual forward rate | Implied Annual Forward Rates |
0.5 | 1 | 0.00% | 4.50% | $97.79951 | 2.25% | 4.50% | 2.55022% | 5.1004401% |
1 | 2 | 0.00% | 4.80% | $95.36743 | 2.40% | 4.80% | 4.80000% | 6.3514618% |
Show that the actual futures price (BEY of 4.9%) is incorrect using a zero-cost investment strategy involving the spot market and the futures market. (Of course, if the futures price is correct, this zero cost strategy will also have zero profit.) Show the actual dollar cash flows at time 0 and at the expiration of the futures contract.
Time 0: Borrow at the [ Select ] ["six month spot rate", "one year spot rate", "six month forward rate", "1 year forward rate"] +$ [ Select ] ["$97,513.20", "$97,608.59", "$100,000", "$95,367.43"]
Buy the [ Select ] ["one year futures contract", "six month futures contract", "six month treasury bill", "one year Treasury bill"] -$ [ Select ] ["$97,608.59", "$100,000", "$95,367.43", "$97,513.20"]
Net cash flow $ [ Select ] ["$0", "$95,367.43", "$97,608.59", "$97,513.20"]
[ Select ] ["Buy", "Sell"] the six-month futures contract
At expiration in 6 mo: Pay back the loan plus interest -$ [ Select ] ["$97,608.59", "$95,367.43", "$97,513.20", "$100,000"]
[ Select ] ["Sell", "Buy"] the bond we own to fulfill the futures contract +$ [ Select ] ["$95,367.43", "$97,608.59", "$97,513.20", "$100,000"]
Net cash flow +$ [ Select ] ["$97,513.20", "$0", "$97,608.59", "$95.39"]
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