PRMIA Exam 8006 Topic 6 Question 27 Discussion

The bond equivalent yield for a treasury bill can be calculated as [(Future value - Present value)/Present value x 365/days to maturity]. In this case this works out to ($100-$98)/$98 * 365/90 = 8.28%

[Why do we use 365 days and not 360? And is there a different way to calculate treasury bill yields?

The answer to this question is that there are alternate ways to calculate these yields. For the exam, I would suggest that you calculate according to one method, see if you get an answer that matches, and pick that. I found the below on the NY Fed's website - a very clear example: (http://newyorkfed.org/aboutthefed/fedpoint/fed28.html)

The Discount Yield Method

The following formula is used to determine the discount yield for T-bills that have three- or six-month maturities:

Discount yield = [(FV - PP)/FV] * [360/M]

FV = face value

PP = purchase price

M = maturity of bill. For a three-month T-bill (13 weeks) use 91, and for a six-month T-bill (26 weeks) use 182

360 = the number of days used by banks to determine short-term interest rates (the investment yield method is based on a calendar year: 365 days, or 366 in leap years).

Example

What is the discount yield for a 182-day T-bill, auctioned at an average price of $9,659.30 per $10,000 face value?

Discount yield = [(FV - PP)/FV] * [360/M]

FV = $10,000 PP = $9,659.30 M = 182

Discount yield = [(10,000) - (9,659.30)] / (10,000) * [360/182]

Discount yield = [340.7 / 10,000] * [1.978022]

Discount yield = .0673912 = 6.74%

For the 13-week bill, the same formula would be used, dividing 360 by a maturity of 91 days rather than 182 days.

The Investment Yield Method

When comparing the return on investment in T-bills to other short-term investment options, the investment yield method can be used. This yield is alternatively called the bond equivalent yield, the coupon equivalent rate, the effective yield and the interest yield.

The following formula is used to calculate the investment yield for T-bills that have three- or six-month maturities:

Investment yield = [(FV - PP)/PP] * [365 or 366/M]

Example

What is the investment yield of a 182-day T-bill, auctioned at an average price of $9,659.30 per $10,000 face value?

Investment yield = [(FV - PP)/PP] * [365/M]

FV = $10,000 PP = $9,659.30 M = 182

Investment yield = [(10,000 - 9,659.30) / (9,659.30)] * [365/182]

Investment yield = [340.70] / 9,659.30] * [2.0054945]

Investment yield = .0707372 = 7.07%

For the 13-week bill, the same formula can be used, dividing 365 (or 366) by a maturity of 91 days.