Question

Treasury securities that mature in 180 days currently sell for $980. At maturity they are worth $1,000. What is the effective annual yield of these securities? What is the bank discount yield of these securities? Which is a more accurate measure and why?

Answer 1

Face Value (F)= $1,000.

Price (P)= $980.

Time to maturity (t)= 180 days

Effective Annual Yield= [(1+HPY)^(365/t)]-1

Where HPY= Holding period Yield

Holding Period Yield (HPY)= (F-P)/P

HPY= $1,000-$980/$980 =$20/$980 = 2.0408%

Effective Annual Yield= [(1+2.0408%)^(365/180)]-1 = (1.020408^ 2.0278)-1= 4.18%

Bank Discount Yield= (F-P/F)*(360/t)

Bank Discount Yield= ($1000-$980/$1,000)*(360/180) = 0.02*2 = 4%

Bank Discount Yield does not take into account the potential for compound returns. Hence the Effective Annual Yield is a more accurate measure.