Question

Suppose a bank enters a repurchase agreement in which it agrees to buy Treasury securities from a correspondent bank at a price of $24,995,000, with the promise to buy them back at a price of $25,000,000. a. Calculate the yield on the repo if it has a 7-day maturity. b. Calculate the yield on the repo if it has a 21-day maturity.

Answer 1

Solution:

The formula for calculating the yield on repo is

= [ ( Repurchase price - Purchase price ) / Purchase price ] * ( 360 / Maturity Period )

a. Calculation of yield on repo if it has a 7 – day maturity :

As per the information given in the question we have

Purchase price of treasury securities = $ 24,995,000

Repurchase price or Buy back price of treasury securities = $ 25,000,000

Maturity Period = 7 days

Applying the above values in the formula we have

= [ ( $ 25,000,000 - $ 24,995,000 ) / $ 24,995,000 ] * ( 360 / 7 )

= [ ( $ 5,000 ) / $ 24,995,000 ] * ( 360 / 7 )

= 0.0002 * 51.428571

= 0.010288

= 0.0103 ( when rounded off to four decimal places )

= 1.03 %

Thus the yield on the repo if it has a 7 – day maturity = 1.03 %

b. Calculation of yield on repo if it has a 21 – day maturity :

As per the information given in the question we have

Purchase price of treasury securities = $ 24,995,000

Repurchase price or Buy back price of treasury securities = $ 25,000,000

Maturity Period = 21 days

Applying the above values in the formula we have

= [ ( $ 25,000,000 - $ 24,995,000 ) / $ 24,995,000 ] * ( 360 / 21 )

= [ ( $ 5,000 ) / $ 24,995,000 ] * ( 360 / 21 )

= 0.0002 * 17.142857

= 0.003429

= 0.0034 ( when rounded off to four decimal places )

= 0.34 %

Thus the yield on the repo if it has a 21 – day maturity = 0.34 %