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## Friday, December 13, 2013

(Adapted from Jeff’s lecture notes. [[hull]] P156 example is similar.)

Primary Market Financing available to borrowers AA and BB are
 AA BB fixed rate 7% 7.5% <= AA’s real advantage floating rate Libor + 1% Libor 1.24% needs to borrow floating fixed

Note BB has lower credit rating and therefore higher fixed/floating interest costs. AA’s real, bigger advantage is “fixed”, BUT prefers floating. This mismatch is the key and presents a golden opportunity.

Paradoxically, regardless of L being 5% or 10% or whatever, AA and BB can both save cost by entering an IRS.

To make things concrete, suppose each needs to borrow \$100K for 12M. AA prefers a to break it into 4 x 3M loans. We forecast L in the near future around  6 ~ 6.5%.

-- The strategy –
BB to pay 6.15% to, and receive Libor from, AA. So in this IRS, AA is floating payer.
Meanwhile, AA to borrow from Market fixed 7% (i.e. \$7k interest) <= AA's advantage
Meanwhile, BB  to borrow from market L + 1.24% (i.e. L+1.25K) <= BB's advantage
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To see the rationale, it’s more natural to add up the net INflow --

AA: -L+6.15  -7 = -L-0.85. This is a saving of 15bps
BB:   L -6.15  -L-1.24 = -7.39. This is a saving of 11bps

Net net, AA pays floating (L+0.85%) and BB pays fixed (7.39%) as desired.

Notice in both markets AA enjoys preferential treatment, but the 2 "gaps" are different by 26 bps i.e. 50 (fixed) ~ 24 (floating). AA and BB Combined savings = 26 bps is exactly the difference between the gaps. This 26 bps combined saving is now shared between AA and BB.
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Fake [1] Modified example
 AA BB fixed rate 7% 7.5% floating rate Libor + 1% Libor 1.74% <= AA’s real advantage needs to borrow fixed floating
-- The strategy –
AA to pay 5.85% to and receive Libor from BB.
Meanwhile, BB  to borrow fixed 7.5%
Meanwhile, AA to borrow L + 1% <= AA's advantage

Net inflow:
AA:  L -5.85 -L-1 = -6.85, saving 15 bps
BB: -L+5.85-7.5 = -L-1.65, saving 9 bps

[1] [[Hull]] P156 points out that the credit spread (AA - BB) reflects more in the fixed rate than the floating rate, so usually, AA's advantage is in fixed. Therefore this modified example is fake.
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The pattern? Re-frame the funding challenge -- “2 companies must have different funding needs and gang up to borrow \$100K fixed and \$100k floating total, but only one half of it using AA’s preferential rates. The other half must use BB’s inferior rates.

In the 2nd example, since AA’s advantage lies _more_ in floating market, AA’s floating rate is utilized. BB’s smaller disadvantage in fixed is accepted.

It matter less who prefers fixed since it’s "internal" between AA and BB like 2 sisters. In this case, since AA prefers something (fixed) other than its real advantage (float), AA swaps them "in the family". If AA were to prefer floating i.e. matching her real advantage, then no swap needed.

Q: Why does AA need BB?
A: only if AA needs something other than its real advantage. Without BB, AA must borrow at its lower advantage (in “fixed” rate market), wasting its real advantage in floating market.