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Name the parts of a US Treasury coupon bond and contrast it with Treasury STRIPS, taking in how P-STRIPS and C-STRIPS differ.

FRM® Part I · Valuation and Risk Models · Pricing Conventions, Discounting, and Arbitrage · FRM1.VR.9.d

The idea

A US Treasury coupon note or bond has a par (face) value repaid at maturity, a stated annual coupon rate, a maturity date, and coupons paid every six months. Each coupon is calculated as Coupon = coupon rate × par ÷ 2, which is half the annual amount. Notes mature in 2 to 10 years and bonds beyond that. Treasury STRIPS are zero-coupon securities that exist because a coupon security is separated into its individual cash flows, each of which then trades alone. A C-STRIP comes from a coupon payment and a P-STRIP from the principal payment. On the maturity date the final coupon becomes a C-STRIP and the principal a P-STRIP, and the two can trade at slightly different prices. A STRIP's duration equals its maturity, which is longer than the duration of a coupon bond of the same maturity. The exam favours counting the pieces and telling the two kinds apart.

Formulas

Semiannual coupon on a US Treasury note or bond

Coupon = c × F ÷ 2

c
the stated annual coupon rate
F
the par (face) value

Treasury coupons are paid every six months, so the stated annual rate is halved. Using the full annual rate doubles the payment.

A practice question

From the question bank, with the reason each wrong option is wrong.

A US Treasury note has a face value of USD 100,000 and a coupon rate of 4.5%. Each coupon payment is:

  1. USD 2,250 - correct
  2. USD 4,500Why not: Pays the whole annual coupon at each date instead of half, since Treasuries pay semiannually.
  3. USD 1,125Why not: Divides by four, as for a quarterly payer.
  4. USD 2,225Why not: Converts 4.5% to an equivalent semiannual rate, 1.045^0.5 - 1, rather than splitting the stated rate in half.

A Treasury coupon is coupon rate x par / 2 = 0.045 x 100,000 / 2 = 2,250. The stated rate is simply halved.

A harder one

A dealer strips USD 10 million face value of a newly issued 5-year Treasury note with a 6% coupon. Which STRIPS pay on the maturity date?

  1. One C-STRIP paying USD 10.3 millionWhy not: Merges the final coupon and principal into one coupon strip.
  2. One P-STRIP paying USD 10.3 millionWhy not: Merges the final coupon and principal into one principal strip.
  3. A P-STRIP paying USD 10 million and a C-STRIP paying USD 0.3 million - correct
  4. A C-STRIP paying USD 10 million and a P-STRIP paying USD 0.3 millionWhy not: Swaps the labels, assigning the principal to the C-STRIP and the coupon to the P-STRIP.

The final semiannual coupon is 0.06 x 10 / 2 = 0.3 million, which becomes a C-STRIP; the 10 million principal becomes a P-STRIP. They pay on the same date.

The hardest tier

A three-year C-STRIP trades at 91.00 per 100 face value. Its semiannually compounded yield is closest to:

  1. 3.30%Why not: Uses simple interest, (100 / 91 - 1) / 3, with no compounding.
  2. 3.17% - correct
  3. 6.39%Why not: Takes the three-year root and doubles it, treating three years as three half-year periods.
  4. 1.58%Why not: Uses six half-year periods but forgets to double the periodic rate to annualise it.

A zero compounds over six half-years: 91 x (1 + y/2)^6 = 100, so y = 2 x ((100 / 91)^(1/6) - 1) = 2 x 0.01584 = 3.17%.

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