Download BKM Chapter II

Examples of how to adjust the rate of return on a discount money
market instrument calculated on a 360-day year basis (a US T-Bill)
such that it can be compared to a yield instrument whose return is
calculated on a 365-day year (here a US bond).
Q2
A U.S. treasury bill has 180 days to maturity and a price of $9600
per $10000 face value. The bank discount yield, rBD, of the bill is
8%.
 FV  P   360 
rBD  


 FV   n 
a)
Calculate the bond equivalent yield for the Treasury bill.
 FV  P   365 
rBEY  


 P   n 
= (10000 – 9600)/9600 * (365/180)
= .0845  8.45%
b)
[> 8% bank discount yield]
Briefly explain why a t-bill’s bond equivalent yield differs
from (i.e. is greater than) the bank discount yield.
i)
The denominator for the discount yield is the face
value (i.e. 10000) rather than invested value. Thus
the first factor is larger.
ii)
360 vs. 365 days. The numerator in the second factor
is larger.
Q3
A T-bill has a bank discount yield of 6.81% based on the asked
price, and 6.9% based on the bid price. The maturity of the bill is
60 days. Find the bid and asked price of the bill.
Bank Discount Yield:
P = 10000 * [1 – rBD * (n/360)]
Thus,
Pask = 10000 [1 – 0.0681 (60/360)] ≈ $ 9886.5
Pbid = 10000 [1 – 0.069 (60/360)] ≈ $ 9885
Q4
From Q3, calculate the bond equivalent yield and effective annual
yield based on the ask price. Confirm that these yields exceed the
discount yield.
Bond Equivalent Yield:
rBEY = (10000 – P)/ P * (365/n)
|use ask Pask
= (10000 – 9886.5)/9886.5 * (365/60)
≈ 6.98%
[ > 6.81 = rBD]
Effective Annual Yield:
1 + rAY = [1 + (10000 – 9886.5)/9886.5]365/60
1 + rAY = (10000/9886.5)365/60
1 + rAY ≈ 1.0719 => rAY ≈ 7.19%