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).
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.
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.
Hedging a Bond with Put
Options - Example
You own $100 million of 6-year, 8% coupon bonds with a 5year 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
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 option’s  = -.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 - kDL]A / ()(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
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).
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.
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 buyer’s 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
Hedging a Bond with an
Interest Rate Swap - Example
You own $100 million of 6-year, 8% coupon bonds with a 5year 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 swap’s 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
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 - kDL]A / (DF - Df)(S)
where S is the swap’s 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
Using Total Return Swaps to
Hedge Credit Risk
Financial firms often want to hold a particular company’s
loans or bonds to maintain a customer relationship and sell
other products even though the company’s 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 loan’s 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 Yahoo’s market-traded bonds.
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 Yahoo’s
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
3. If the 1-year Tbill rate is 11%, the counter-party’s
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 loan’s value.
5. Had Yahoo’s bonds increased in value by 10 %, you would
have ended up paying the counter-party:
$100 million (.12 + .10 - .11) = $11 million
6. Had Yahoo’s bonds decreased in value by 1%, no
payments would be made under the swap agreement.
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.