You are a bank and your customer asks you to quote an agreed-upon rate for a 3*9 FRA.You observe the following rates. $$\begin{array} { c | l }
\text { Maturity } & \text { Rate } \
\hline 3 \text { months ( } 90 \text { actual days) } & 3 \% \
6 \text { months (180 actual days) } & 4 \% \
9 \text { months } ( 270 \text { actual days) } & 5 \%
\end{array}$$ What rate should you quote?

Question

You are a bank and your customer asks you to quote an agreed-upon rate for a 3*9 FRA.You observe the following rates. $$\begin{array} { c | l } 
\text { Maturity } & \text { Rate } \
\hline 3 \text { months ( } 90 \text { actual days) } & 3 \% \
6 \text { months (180 actual days) } & 4 \% \
9 \text { months } ( 270 \text { actual days) } & 5 \%
\end{array}$$ What rate should you quote?

Quizplus · Accepted Answer

The correct rate is the forward rate for 3 months in the future, which is 5.96%. This can be calculated using the formula:$$F_3 = S_3 * (1 + r_3 * \frac{90}{360})$$where:* $$F_3$$ is the forward rate for 3 months in the future* $$S_3$$ is the spot rate for 3 months* $$r_3$$ is the annualized interest rate for 3 monthsPlugging in the values we have:$$F_3 = 3\% * (1 + 4\% * \frac{90}{360}) = 5.96%$$

You Are a Bank and Your Customer Asks You to Quote