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Homework answers / question archive / The market one-year, strip (zero) spot rate is 4

The market one-year, strip (zero) spot rate is 4

Finance

The market one-year, strip (zero) spot rate is 4.5%, and the forward rate from year one to year two (meaning for lending/borrowing money in a year for one more year) is 3.5%. Today, an individual is willing to lend or borrow money for two years at an annual rate of 4.6%. Is there an arbitrage opportunity? If yes describe it.

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Here in order to determine whether there is any arbitrage opportunity we first calculate the spot rate in year 2.

The forward rate after 1 year for 1 year should be equal to

= (1 + spot rate Year 2) ^2/ (1+Spot rate year 1) – 1

So, the spot rate for year 2 would be calculated as

((1 + 0.035) *(1 + 0.045))^(1/2) – 1

= 0.03998

Or = 4.00%

Now here there is an arbitrage opportunity because the spot rate for 2 year as calculated from the forward rate for 1 year after 1 year is 4.00% but the borrowing and lending in the market for 2 years is at 4.60% so here the arbitrage opportunity arises and investors can take the advantage by borrowing and investing.