Using Options and Swaps to Hedge Risk

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Using Options and Swaps to Hedge Risk
You are subject to interest rate risk and wish to
hedge. Alternative Bond Option Hedging
Strategies in Order of Aggressiveness (just
reverse the arguments if Interest Rate Options
are to be used) . 1. Buy Put Options on
Bonds This is the traditional approach to
insuring against interest rate increases. One
pays a premium to avoid the risk that interest
rates will rise and the fixed income securities
you hold will fall in value. If interest rates
rise (fall) you lose (gain) on the bonds but
gain (lose only) on the options (premiums).
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2. Sell Bonds and Buy Bond Call Options This
strategy is similar to strategy 1 but increases
your cash position by selling bonds already
owned and insuring against a large increase in
bond prices. 3. Hold the Bonds You Own and Sell
Bond Call Options This strategy offers some
protection if bond prices fall up to the amount
of the option premiums you receive. You are
still exposed to large drops in bond prices.
Selling options is typically looked on
unfavorably by regulators and boards of
directors.
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4. Marginal Approach - Buy Call Option to Cover
Cash Suppose you hold cash now or expect to
receive cash that would normally be invested in
bonds (insurance premiums). This strategy is to
hold cash and buy options to insure that if
bonds rally (interest rates fall) strongly, then
you have covered your cash position. But any
bonds already owned are exposed. The hedging
process is similar to that described for futures
in the previous lecture except that in addition
to the effect of interest rate changes on the
underlying bond price, the option has a delta
(-?) that measures option price sensitivity to a
bond price change.
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Hedging a Bond with Put Options - Example
You own 100 million of 6-year, 8 coupon bonds
with a 5-year duration selling at par. T-Bond put
options on 100,000 face value of bonds have a
delta of -0.625 and a premium of 3.25 per 100
face value. The underlying bond has a market
value of 96,157 and a 10.1 duration. How do you
hedge? The formula for getting the number of put
option contracts (NP) to buy is NP DAA /
(?)(DB)(B) where B is the market value of the
bond underlying the option and DB is the duration
of the bond. Here NP (5)(100 M) /
(.625)(10.1)(96,157) 824 and Cost
824(3.25)(1000) 2,678,000
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Hedging a Duration Gap with Put Options - Example
Assume that there are put options on Tbonds
covering a face value of 100,000, a market value
of 97,000 and a duration of 8.82. The options ?
-.5 and the premium is 2.5 per 100 face value.
Husky has 100 million in assets with a duration
of 5 and 90 million in liabilities with a
duration of 3. How do you hedge the duration
gap? The formula for getting the number of put
option contracts (NP) to buy is NP DA -
kDLA / (?)(DB)(B) where B is the market value of
the bond underlying the option and DB is the
duration of the bond. Here NP 5 -
(.9)(3)(100 M) / (.5)(8.82)(97,000)
537.7 and Cost 537(2.5)(1000) 1,342,500
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Question If the duration gap was negative
instead of positive, how would you hedge
interest rate risk? Using a No-Cost Collar In the
previous examples, we purchased put options for
2.67 and 1.34 million to construct our hedge.
Boards of directors often find this acceptable
when interest rates actually rise but when
interest rates fall or stay the same, they see
the premium losses as wasteful. An alternative to
only buying put options is to simultaneously sell
call options with the same premium value as the
puts. In this case, if interest rates do nothing
there is no cost. If interest rates rise, the
puts pay off as before plus you gain the
premiums. If interest rates fall, you will lose
on the calls you sold but gain on the underlying
bond (assets).
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Using Interest Rate Swaps to Hedge
A plain vanilla interest rate swap is an
agreement between one party (buyer) who agrees to
pay fixed interest rate payments at periodic
settlement dates on some face (notional) value.
In return, the buyer receives floating rate
payments paid by the other party (seller).
Floating rates are reset at settlement dates
covering the subsequent period. Only net payments
are actually exchanged. Swaps are equivalent to
an exchange of a series of forward contracts. No
money changes hands initially. There are
standardized contracts for particular periods,
e.g., 5-years, 10-years etc. The contracts have
durations which are the net difference between
the durations of the underlying fixed and
floating rate instruments.
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Example of Interest Rate Swap Cash Flows
Assume 1,000,000 notional principal, Tenor 2
years, semi-annual reset with rate set at the
beginning of period and paid at the end of
period, net from the buyers perspective. --------
--------------------------------------------------
--------------- Date Fixed Fixed
Variable Variable Net Rate Cash Flow
Rate Cash Flow ------------------------------
------------------------------------------- Jan
1 10 9 Jul 1 10 50,000 10 45,000
-5,000 Jan 1 10 50,000 11 50,000
0 Jul 1 10 50,000 12 55,000
5,000 Jan 1 10 50,000 60,000 10,000
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Hedging a Bond with an Interest Rate Swap -
Example
You own 100 million of 6-year, 8 coupon bonds
with a 5-year duration selling at par. Each
15-year swap contract has a notional value of
100,000 involving a fixed rate instrument of
duration 7 years and a floating rate instrument
of duration 1 year. How do you hedge? The
formula for getting the number of swap contracts
(NS) to sell is NS DAA / (DF - Df)(S) where
S is the swaps notional value and DF is the
duration of the fixed instrument and Df is the
duration of the floating. Here NP (5)(100 M) /
(7 - 1)(100,000) 833
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Hedging a Duration Gap with Interest Rate Swaps -
Example
Husky has 100 million in assets with a duration
of 5 and 90 million in liabilities with a
duration of 3. Each 15-year swap contract has a
notional value of 100,000 involving a fixed rate
instrument of duration 7 years and a floating
rate instrument of duration 1 year. How do you
hedge the duration gap? The formula for getting
the number of swap contracts (NS) to sell is
NS DA - kDLA / (DF - Df)(S) where S is the
swaps notional value and DF is the duration of
the fixed instrument and Df is the duration of
the floating. Here NP (5 - (.9)(3))(100 M) /
(7 - 1)(100,000) 383
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Using Total Return Swaps to Hedge Credit Risk
Financial firms often want to hold a particular
companys loans or bonds to maintain a customer
relationship and sell other products even though
the companys credit risk may be higher than the
financial firm prefers. It can hedge the risk it
wishes to avoid through a total return swap. How
the Total Return Swap Works Suppose that you make
a 100 million loan to Yahoo and are worried its
credit quality will fall, reducing the loans
value. You can swap the return on the loan for
the return on a safer asset, say, 1-year Tbills.
The return on the loan is the interest payment
plus a gain or loss in value estimated from the
gain or loss in Yahoos market-traded bonds.
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Total Return Swap - Example
1. You have made a 100 million loan to Yahoo and
simultaneously enter into a total return swap to
pay the loan return to the swap counter-party in
return for the return on the 1-year Tbill. The
loan agreement specifies interest payments of 12
annually. 2. Now suppose that after one year,
the price of Yahoos bonds have dropped from
1000 to 900, a 10 decline. As the swap
requires, your commitment to the counter-party
is Yahoo Loan Total Return 12 - 10
2 100 million (.02) 2 million
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3. If the 1-year Tbill rate is 11, the
counter-partys commitment is 100 million
(.11) 11 million 4. Only net payments are
exchanged so that the counter-party pays you 9
million. This payment helps offset the implied
decline in the loans value. 5. Had Yahoos bonds
increased in value by 10 , you would have ended
up paying the counter-party 100 million (.12
.10 - .11) 11 million 6. Had Yahoos bonds
decreased in value by 1, no payments would be
made under the swap agreement.
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Total return swaps are available for any assets.
For example, suppose you own a stock portfolio
indexed to the London Stock Exchange. You can
swap the total return on the London Stock Market
Index for the total return on Brazilian bonds.
Swapping returns saves the transactions costs of
having to sell a large portfolio and buy other
assets. If you change your mind later, you can
swap back into stocks again without having to pay
transactions fees.