LTCM Observed the Following Ten-Year Swap Spreads on July 1

question 42

Essay

LTCM observed the following ten-year swap spreads on July 1, 1998. You remember that U.S. dollar interest swaps (fixed rate against LIBOR three-month) are quoted as a spread over the Treasury yield (so the fixed rate on the swap is equal to the interest rate on Treasury bonds for the same maturity plus the quote spread). LTCM believes that the normal spread is 40 bp (basis points). The current spread of 80 bp is expected to converge back to normal in three months.
If you borrow securities, you have to deposit as collateral an equivalent amount of cash that is marked-to-market. For example, if you borrow a security that is worth 100, you have to deposit 100; if the value of the security increases to 110, you have to deposit 10 more. Swaps are also marked-to-market and free of default risk. a. What arbitrage using Treasury bonds and swaps could you put in place if you believe that the spread will revert back to its normal level? Be very precise and assume you do the above arbitrage for $100 million. How much of LTCM capital is invested in the arbitrage?
b. Suppose that the spread is still at 80 bp on October 1, but that Treasury yields have moved
up by 40 bp on October 1 (reset date for the floating leg). What is your gain/loss in dollars?
[You only need to provide a rough estimate assuming that the sensitivity (duration) on the Treasury bond and fixed leg of the swap is equal to 10.]
c. Other scenario: How much would you gain (from July 1) if Treasury yields do not move, but
the spread reverts back to 40 bp three months later on October 1 (reset date for the floating leg)? [You only need to provide a rough estimate assuming that the sensitivity (duration) on the Treasury bond and fixed leg of the swap is equal to 10.]

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