FIN 685: Risk Management
Topic 2: How Do We Deal with Risk?
Why Should We Care?
Larry Schrenk, Instructor

Why Manage Risk? Why Hedge?

Digression: Non-Linearity

What is Hedging?

How to Hedge
– Linear Risk
– Non-Linear Risk
Why Manage Risk? Why Hedge?
– Commodity price risk
– Equity market risk
– Interest rate risk
– Foreign exchange rate risk
– Credit risk
– Weather risk

Hedging is Irrelevant or Wasteful
– Diversified shareholders don’t care about
firm-specific risks (CAPM)
– Since markets are efficient, risk
management does not add to firm value
– Active risk management wastes resources
– Agency cost
– Increase risk when competitors do not
hedge
5 (of 26)

Hedging creates Value
– Transaction Costs
• Helps ensure that cash is available for positive NPV
investments
• Reduces dependence on (expensive) external finance
• Reduces probability of financial distress
• Firms should focus on core business
– Non-Linearity
• Reduces tax obligation
– No Diversification
• A company whose owners are not well diversified
may benefit from hedging. (example: privately
owned)
6 (of 26)
Overall, Firms’ Behavior Diverse
 50% of surveyed firms do use derivatives
for risk management

– especially large firms (83%), and
– especially for FX risk.

Mainly hedging, but some speculation.
– 1998 Wharton/CIBC World Markets Survey of
Financial Risk Management by US NonFinancial Firms
7 (of 26)

Speculating
– Speculators in futures markets do not own or
control the underlying commodity.
– They invest in futures markets to try and capture
profits from price movements/price forecasting.
– The major attraction of speculative investors to the
futures market is the leverage made possible by the
margin system.

There are three major ways in which to
invest as a speculator in the futures
markets
– Short Term
– Long Term
– Spreading

The most celebrated of all day traders are
the scalpers (also known as locals)
– Mostly exchange members
– Trade on very small price movements and
concentrate on a large volume of trade to
generate income
– Locals usually end the day without holding
any open position, i.e., they offset all the
trade by the end of the day.
Spreading involves price relationships in
two or more markets and tries to take
advantage of any abnormality.
 Spread investing is relatively less risky
because gains made on either the buy or
sell side are usually offset by losses on
other side.
 Spreader will spread temporal, spatial,
form and substitutional relationships.


Temporal Spread: Relationships
Involving Carrying Charges such as
Storable Commodities

Spatial Spread: Price Relationship
between Gold trading in New York
Futures Gold and Chicago Futures Gold

Substitutional Spread: Near Substitutes
Digression: Non-Linearity

It is essential to appreciate the
importance of this non-linearity, i.e.,
‘curvature’

Non-linearity is our worst enemy!
Lawrence P. Schrenk

First, consider a linear relationship.
– The slope (rise over run) is 1
– If the x value increases by one, then the y value
increases by one–everywhere.
Lawrence P. Schrenk

In a linear relationship, all we need to
know is the slope to predict how a
change in x will affect the value of y.

In particular, we do not need to know the
current value of x in order to predict how
a change in x will affect the value of y.
Lawrence P. Schrenk

Now consider a non-linear relationship.
– There are an infinite number of slopes
Lawrence P. Schrenk

In a non-linear relationship:
– No one slope characterizes the entire
relationship
– We DO need to know the current value of x in
order to predict how a change in x will affect
the value of y.
– Any prediction will be
• Only an approximation, and
• Only ‘locally’ valid.
Lawrence P. Schrenk

We can estimate the slope at any point.
A
– The yellow tangent line has the slope of the
tangent point (A).
Lawrence P. Schrenk
But the more x changes, the less valid is
the prediction of y based upon the slope
at x0.
 The accuracy of any prediction will
depend upon:

– The magnitude of the change in x, and
– The degree of convexity in the relationship.
Lawrence P. Schrenk
What is Hedging?

“…can be defined as the exposure of a
company’s earnings, cashflow or market
value to external factors such as interest
rates, exchange rates, or commodity
prices.” Tufano and Headley, “Why
Manage Risk?”
"the design, development and
implementation of innovative financial
instruments and processes, and the
formulation of creative solutions to
problems in finance“ John Finnerty (1988)
 "the development and creative
application of financial technology to
solve financial problems and exploit
financial opportunities." IAFE


…a financial position taken to diminish
exposure to a risk.

Hedging versus Speculating

Hedging as Insurance

Hedging-Active; Diversification-Passive

Static Hedge
– Long Term Position
• How Long Does It Last?

Dynamic Hedge
– Rebalancing
• Cost versus Benefit

Forward (and Futures) Contracts

Options

Swap Contracts
– Not Here

An Forward (and Futures) Contract is the
Agreement to Buy or Sell a Quantity of an
Asset at (or within) a Specified Period of
Time at a Specified Price.

An Option Contract Gives the Right (but Not
the Obligation) to Buy Or Sell to Buy or Sell a
Quantity of an Asset at (or within) a Specified
Period of Time at a Specified Price.
– A Call Option is the Right to Buy.
– A Put Option is the Right to Sell.

Perfect Hedge: All Risk Eliminated

Cross Hedging: Hedged and Hedge
Assets Do Not Match Exactly.
– Different Assets
– Different Characteristics
– Different Time Periods

Selective Hedging

A long hedge is appropriate when you know
you will purchase an asset in the future and
want to lock in the price.


Example: An insurance company plans to buy Tbills two months from now and faces the risk that
the price of the bills may increase (interest rates
may fall). Hedge: buy T-bill futures.
A short hedge is appropriate when you know
you will sell an asset in the future & want to
lock in the price.

Example: An oil producer agrees to sell 50,000
bbl/mo for each of the next 6 months at spot prices.
Presently, the price of oil is $48.50/bbl, but it may
fall over the next 6 months. Hedge: Sell a strip of
crude oil futures.


A U.S. firm that has an export sale to U.K. with
payment to be made in British pounds faces
the risk that pound, relative to dollar, will
depreciate.
Example: At the current rate of $1.4 per pound,
U.S. exporter has agreed to receive 100,000
pounds ($140,000) for the merchandise. If the
exchange rate changes to $1.35, the exporter
still receive 100,000 pounds. But exchange rate
fluctuations has reduced his profit by $5,000.
Example of Short Foreign Hedge with British Pounds
______________________________________________________________________________________
Date
Jan. 1
Cash position
Future Hedge
____________________________________________________________
U.S. firm agrees to sale in pound.
Sell one contract of pound futures at $1.4
Sale price 100,000 pounds
(current exchange rate $1.4/pound)
Dollar Appreciating
May 1
Receives 100,000 pounds
Converts to U.S. dollars at
$1.35 and receives $135,000
buy pound futures at $1.35
$5,000 loss
Net Hedge Price=
Dollar Depreciating
May 1
Receives 100,000 pounds
Converts to U.S. dollars at
$1.45 and receives $145,000
$5,000 gain
buy pound futures at $1.45

Eliminate all risk in an underlying risky
investment, so risk free.
Payoff on underlying
asset
Payoff on hedged
position
Payoff on hedge

Pricing (Discount Basis)
– (1 – discount x (91/360) x $1million

Mar 19 w/ 27 days to Maturity priced at a
discount of 4.68.

Price on $1 million Face:
– (1 – 0.0468(27/360)) x 1,000,000 = $996,490

Delivery of 91-day T-Bill at maturity date.

So, a March futures delivers a June T-Bill.

Pricing on a discount basis, but quoted %.

Feb. 19, March 95.02, so discount = 4.98
91 

100   4.98

360

 1,000,000  $987,412
100

Previous T-Bill futures has us buy:
– $25mill / $987,412 = 25.3187 contracts

If rates at delivery are 5.5%, T-Bills cost:
– (1-(.055*91/360)) x $1mill = $986,097

Futures lost:
– (986,097 - 987,412) x 25.3187 = (33294), leaving
$24,966,706 for T-Bills

But this still buys us:
– $ 24,966,706 / $986,097 = 25.3187 $1 mill. T-Bills

If rates at delivery are 4.5%, T-Bills cost:
– (1-(.045*91/360))*$1mill = $988,625

Futures gained:
– (988,625 - 987,412)*25.3187 = +30,712,

Leaving $25,030,712 for T-Bills
– This just buys us:
– $25,030,712/$988,625 = 25.3187 $1 mill. T-Bills

So, whether rates go up or down, buying
March T-Bill futures locks in delivery.
(Hedge initiated at time t1 and closed out
at time t2)
Futures
Price
Spot
Price
Time
t1
t2

Basis is the difference between
spot & futures

Basis risk arises because of the
uncertainty about the basis when
the hedge is closed out
Choose a delivery month that is as close
as possible to, but later than, the end of
the life of the hedge
 When there is no futures contract on the
asset being hedged, choose the contract
whose futures price is most highly
correlated with the asset price. This is
known as cross hedging.

Proportion of the exposure that should optimally
be hedged is:
sS
h*  r
sF
where
h* is the optimal hedge ratio,
sS is the standard deviation of DS, the change in the
spot price during the hedging period,
sF is the standard deviation of DF, the change in the
futures price during the hedging period
r is the coefficient of correlation between DS and DF.
To hedge the risk in a portfolio the
number of contracts (N*) that
should be shorted is
P
N*  b
A
where P is the value of the
portfolio, b is its beta, and A is the
value of the assets underlying one
futures contract

The effectiveness of a hedge is measured
by r2.
– Perfect Hedge:
• r = 1 → r2 = 100%

Desire to be out of the market for a short
period of time.
– Hedging may be cheaper than selling the
portfolio and buying it back.

Desire to hedge systematic risk
– Appropriate when you feel that you have
picked stocks that will out peform the
market.
Similar to hedging a portfolio
 Does not work as well because only the
systematic risk is hedged
 The unsystematic risk that is unique to
the stock is not hedged



May want to be out of the market for a while.
Hedging avoids the costs of selling and
repurchasing the portfolio
Suppose stocks in your portfolio have an
average beta of 1.0, but you feel they have
been chosen well and will outperform the
market in both good and bad times. Hedging
ensures that the return you earn is the risk-free
return plus the excess return of your portfolio
over the market.
We can use a series of futures contracts to
increase the life of a hedge
 Each time we switch from 1 futures
contract to another we incur a type of
basis risk

Your company has contracted to buy 100,000 bushels of corn in
four months at the then current spot rate (sS = 15%). If you
have the following forward contacts available, which is the
most effective hedge? Also, calculate the optimal hedge
ratio, hedge effectiveness and optimal number of contracts.
Contract
A
B
C
D
s
10%
20%
10%
30%
r
.94
.81
.80
.75
bushels/contract
1,000
1,000
500
1,000
expiration
3 months
5 months
6 months
5 months
Use B, since it has the highest r of those
contracts expiring after the close of the
desired hedge.
ss
0.15
 0.81
 0.6075
 Ratio: h*  r

sF


0.20
Effectiveness: r   0.81  65.61%
2
Contracts:
N*  b
2
P
100,000
 0.6075
 60.75
A
1,000
Your company has contracted to buy 100,000 lbs. of lard in six
months at the then current spot rate (sS = 25%). If you have
the following forward contacts available, which is the most
effective hedge? Also, calculate the optimal hedge ratio,
hedge effectiveness and optimal number of contracts.
Contract
A
B
C
D
s
10%
20%
10%
30%
r
bushels/contract expiration
1.0
1,000
5 months
.90
1,000
9 months
1.0
500
8 months
.95
1,000
5 months
Use B, since it has the highest r of those
contracts expiring after the close of the
desired hedge.
ss
0.25
h*  r
1
 2.5
 Ratio:

sF


Effectiveness:
Contracts:
0.10
r  1  100%
2
2
P
100,000
N *  b  2.5
 5,000
A
50

Your company, headquartered in the U.S.,
supplies auto parts to Jaguar PLC in Britain.
You have just signed a contract worth ₤18.2
million to deliver parts next year. Payment is
certain and occurs at the end of the year.
– The $/₤ exchange rate is currently S($/₤) =
1.4794.
– How do fluctuations in exchange rates affect
dollar ($) revenues? How can you hedge this
risk?
52 (of 26)
Now
0
S($/₤) = 1.4794
One Year
1
F12($/₤) = 1.4513
CF = ₤18.2 million
$ ???
53 (of 26)
1.
Do not Hedge
2.
Hedge with Futures/Forward Contracts
3.
‘Hedge’ with Option Contracts

Expected Cash Flow
– E[S1($/₤)] = F1($/₤) = 1.4513
– Expected Cash Flow =
1.4513 x ₤18.2 million = $26.41 million

Risk
– Upside FX Exposure:
– Downside FX Exposure:

Yes
Yes
Cost of Hedge Position: $0
55 (of 26)
Cash Flow ($)
$28.21
$27.30
$26.41
$25.48
$24.57
1.35
1.40
1.45
1.50
1.55
S1($/₤)
56 (of 26)

Known Cash Flow
– E[S1($/₤)] = F1($/₤) = 1.4513
– Lock in Revenues
1.4513 x ₤18.2 million = $26.41 million

Risk
– Upside FX Exposure:
– Downside FX Exposure:

No
No
Cost of Hedge Position: Minimal
57 (of 26)
Cash Flow ($)
$28.21
$27.30
$26.41
$25.48
$24.57
1.35
1.40
1.45
1.50
1.55
S1($/₤)
58 (of 26)

The relevant option has three possible strike
prices:
Put Options
Strike
1.35
1.40
1.45
Min. Rev.
Premium
Cost (×18.2 M)
$24.6 M
$25.5 M
$26.4 M
$0.012
$0.026
$0.047
$221,859
$470,112
$862,771
59 (of 26)

Minimum Cash Flow
– E[S1($/₤)] = F1($/₤) = 1.4513
– Lock in Minimum Revenue
1.4513 x ₤18.2 million = $26.41 million

Risk
– Upside FX Exposure:
– Downside FX Exposure:

Yes
No
Cost of Hedge Position: $862,771
60 (of 26)
Value ▪
Cash Flow ($)
$28.21
Profit ▪
$27.30
$26.41
-$862,771
$25.48
$24.57
1.35
1.40
1.45
1.50
1.55
S1($/₤)
61 (of 26)
Cash Flow ($)
$28.21
$27.30
Forward Market Hedge
$26.41
$25.48
$24.57
1.35
1.40
1.45
1.50
1.55
S1($/₤)
62 (of 26)