Floaters and Inverse Floaters

1
Floaters and Inverse Floaters

• Investments
• Ning Gong

2
Floaters

• A floater is a fixed income instrument whose
  coupon fluctuates with some designated reference
  rate.
• A floating rate note (FRN) is a floater issued by
  a corporate or agency borrower.
• In Australia, the 90-day bills rate is often used
  as a reference rate.

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Inverse Floaters

• An inverse floaters (or reverse floater) coupon
  fluctuates inversely with its reference
• With each coupon payment, the floating rate is
  reset for the next period according to the
  formula
• floating rate fixed rate coupon leverage
  reference rate
• The multiplier is called the coupon leverage.
  Often, it is equal to 1, but not always. If it
  exceeds 1, the instrument is called a leveraged
  inverse floater.

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Q.5, HW 5

• The total interest paid on a floater and inverse
  floater has to be supported by the bond class
  worth of 100 million with a coupon rate of 7.5
  from which they are created. Suppose the coupon
  rate for the floater is
• T-bill rate 0.50
• And the inverse floater takes the form
• a b T-bill rate.
• The proportion of issues should be floater is
  estimated at 75. Then what is the appropriate
  inverse floater coupon rate? Furthermore, if the
  floor on the inverse floater is set to be zero,
  what is the cap for the floater?

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Answer

• It has to be (in terms)
• w( T-bill 0.50) (1-w) (a b T-Bill)
  7.5. (1)
• To hedge against the interest rate risk, the
  investment banker would like to set
• w T-bill (1-w) b T-bill 0
• Since w 75, b 3.
• Substituting this back to (1),
• a 28.5.
• Since b gt 1, so it is a leveraged inverse floater.

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Cap and Floor

• It is natural to set a floor of zero for inverse
  floaters.
• Now, if the floor on the inverse floater is zero,
  the threshold T-bill rate, r, would be
• 28.5 3 r 0, r 9.5
• so the cap on the floater would be r 0.5
  10.

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Durations of Floaters

• The price of a floater is P0 P1 P2 100
  if the spread is not changed and the cap or floor
  is not reached.
• Thus, it somehow is similar to the zero-coupon
  bond The price for the next coupon payment is
  100.
• The duration is the length between the coupon
  payment dates, say, six months for semi-annual
  coupon bonds.

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Duration for Inverse Floaters

• Because 0.75 Floaters 0.25 Inv. Floaters
  Coupon bonds
• Using the property of portfolios duration
• 0.75 0.5 0.25 D_inv D _ coupon
• If the coupon bond has 5 years to maturity, then
  D_coupon 4.26 years.
• D_inv 15.54 years!
• The duration of an inverse floater is longer than
  its effective maturity!