Hedging Financial Risk
Econ 422
Summer 2005
Hedging and Insuring
•
Both hedging and insuring are methods to manage or reduce
financial risk.
•
Insuring involves the payment of a premium (a small certain loss) for
the reduction or elimination of the possibility of a larger loss.
•
Hedging involves a transaction that reduces the risk of financial loss
by giving up the possibility of a gain.
•
Hedging often involves the use of derivative securities.
General Principles of Hedging
•
Assume that you own risky asset A and want to reduce your risk
exposure.
•
Find an asset B whose price is (highly) correlated with that of A, i.e.,
there is a linear relationship between A’s price and B’s.
•
Estimate the parameters of this relationship by running a regression
of A’s price on B’s price:
p
A
=
α
+
δ
p
B
+
ε
,
δ
= cov(p
A
,p
B
)/var(p
B
)
•
Delta measures the sensitivity of expected changes in A’s price to
expected changes in B’s price:
E[p
A
] =
α
+
δ
E[
p
B
]
•
Delta is referred to as the hedge ratio.
General Principles of Hedging,
Cont.
•
If the prices of A and B are perfectly correlated
, with a hedge ratio of
δ
, then
ε
= 0 and you could construct a perfect hedge by selling
(short)
δ
units of B. Thus, your portfolio would have a long position
of one unit of A and a short position of
δ
units of B.
•
If the price of A rises by $1, the price of B (in this case) rises by
($1/
δ
).
•
The value of your portfolio changes by:
$1 
δ
($1/
δ
) = 0
•
You have eliminated the risk
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General Principles of Hedging,
Cont.
•
If the prices of A and B are not perfectly correlated
, then
ε ≠
0 and
you could still construct a hedge by selling (short)
δ
units of B, but
the hedge would not be perfect.
•
Your portfolio would have a long position of one unit of A and a short
position of
δ
units of B.
•
If the price of A rises by $1, the price of B (in this case) rises by
($1/
δ
) on average, but not always.
•
The value of your portfolio changes on average by:
$1 
δ
($1/
δ
) = 0 but not always
•
You have eliminated the risk on average, but not always.
Hedging Using Returns
•
In practice, hedging using regression is usually
done with returns instead of prices, for certain
statistical reasons:
error
A
B
r
r
α
δ
=
+
+
The interpretation of
δ
remains the same:
it is an estimate of the hedge ratio
General Principles of Hedging
(Example)
•
XYZ Corp holds $12.5 million of IBM stock. It wants to reduce the risk
associated with this asset, using a market index as a hedge
instrument.
•
We know based on the CAPM, that IBM’s return is correlated with the
market return and the relationship is
2
ˆ
0.78
0.72
,
0.4
ˆ
ˆ
0.72
IBM
M
M
IBM
r
r
r
R
α
β
ε
ε
δ
β
=
+
+
=
+
+
=
=
=
To construct a hedge, sell 0.72 * $12.5 million = $9 million of the market
index.
•
Q: Is the hedge perfect?
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 Fall '08
 Staff

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