Question

1. Suppose a 3-month Treasury Note has a holding period return, or r_f (T), of 1.5%.
   1. What is the APR?
   2. What is the EAR?
   3. If instead of a 3-month maturity, assume that T is now incredibly small and 1/T goes to infinity. What is EAR in this scenario?

Answer 1

Suppose a 3-month Treasury note has a holding period return, or rf (T), of 1.5%. Holding period return is the return Treasury note for 3-months

Annual Percentage rate (APR) = holding period return/ (time period in year)

And effective annual rate (EAR) = [(1+ holding period return) ^ 1/time period in year] -1

Where,

Holding period return= 1.5%

Time period in year = 3 months or 3/12 = 0.25 year

Therefore,

Annual Percentage rate (APR) = 1.5%/0.25 = 6.0%

And effective annual rate (EAR) = [(1+1.5%) ^1/0.25] -1

= 1.0614 -1 = 0.0614 or 6.14%

If instead of a 3-month maturity, assume that T is now incredibly small and 1/T goes to infinity. In this scenario we can assume that effective annual rate (EAR) is compounding continuously

And effective annual rate (EAR) with continuous compounding = e^ nominal interest rate -1

Where, nominal interest rate is Annual Percentage rate (APR) = 6.0%

Therefore, effective annual rate (EAR) with continuous compounding = e^0.06 -1

= 1.0618 -1 = 0.0618 or 6.18%