Question

Calculate the 90-day Commercial Paper (CP) forward rate starting day 270, if you know the following spot CP rates: 90-day: 2.35% 180-day: 2.42% 270-day: 2.39% 360-day: 2.93% Provide your answer in percent, with four decimals.

Answer 1

Investing for 360 days at the 360-day spot rate should result in the same ending value as investing for 270 days at the 270-day spot rate and reinvesting the proceeds after 270 days at the 90-day spot rate after 270 days.

Ending value of investment (for each $1 invested) = (1 + rate * (number of days / 360))

Let us say the 90-day spot rate after 270 days is R. Then :

(1 + 2.93% * (360 / 360)) = (1 + 2.39% * (270 / 360)) * (1 + R * (90 / 360))

1.0293 = (1 + (0.0239 * 270 / 360)) + (1 + R * (90 / 360))

R = [ [(1 + 2.93% * (360 / 360)) / (1 + 2.39% * (270 / 360))] - 1 ] * (360 / R)

R = 4.4699%