Transcript This paper... - Villanova University

Forwards, Futures, and their
Applications
The Oldest Derivative:
Forward Contracts

Forward Contracts – Obligates its owner to buy (if
in a “long” position) or sell (if in a “short” position) a
given asset on a specified date at a specified price
(the “forward price”) at the origination of the
contract.

Two Key Features:



Credit risk is two-sided (i.e., both buyer and seller of the
forward can default on the deal).
No money is exchanged until the forward’s maturity date.
The above features increase default risk and restricts
2
the availability and liquidity of these contracts.
Futures Contracts
Futures Contracts – Similar to Forwards. Obligates
its owner to buy (if in a “long” position) or sell (if in a
“short” position) a given asset on a specified date at
a specified price (the “futures price”) at the
origination of the contract.
 Key Features:


Credit risk is two-sided but is reduced substantially because
of two mechanisms:
1) marking-to-market (daily settling up of the account), and
2) margin requirements (i.e., a good-faith deposit).


Standardized contract specifies exact details of term, asset,
contract size, delivery procedures, place of trading, etc.
Clearinghouse reduces transaction costs and de-couples
buyer from seller by providing anonymity.
3
Forward Contract Characteristics
Forwards can be created on all types of financial
assets (FX, interest rates, commodities, stock prices).
 Can require physical delivery or cash-settled.
 The expected NPV of an at-market forward is zero.
 Notional principal is used to determine cash flows but
is not paid/received at maturity.
 Most liquid within 1-2 year maturities.
 Most frequently used with FX transactions by larger
corporations with international exposures.

4
Profit Calculations on a Forward
Contract



Profit on a forward contract is related to the
difference between the price of the underlying asset
at the forward’s maturity (time = T) and the forward
price (initially specified at the onset of the contract at
time = 0).
Profit = L/S Indicator * (PT – PF0) * Number of units
where,
L/S indicator = +1 if in a long position or
-1 if in a short position.
The objective is to use the forward’s profit to offset
any losses in the underlying asset’s position.
5
Hedging Strategies
If you are long the underlying asset (i.e., increases in the
asset’s price increase firm value), then you can enter into
a forward contract to sell (or “short”) the asset at the
forward price. This can hedge changes in the asset’s
price.
 A classic example is a farmer producing an agricultural
commodity. He/she is long wheat and is worried about
price declines so he/she hedges by selling wheat in the
forward market.
 Conversely, if you are short the underlying asset, then you
should buy (or “go long”) the asset. For example, a baker
consumes wheat and is worried about increases in wheat
prices. So, should buy wheat at the forward price.

6
Principles of Forward Pricing

A cynic: “Someone who knows the price of
everything but the value of nothing”.
There are costs and benefits to all derivatives and
underlying assets.
 Storage and insurance costs of the underlying
asset.
 Opportunity costs (forgone interest, missed
opportunities).
 Benefits such as income generation (e.g., dividends
on a stock) and having the asset on-hand (e.g., a
“convenience yield” for commodities).

7
Principles of Forward Pricing (cont.)
Forward Price = FP0 = P0 + FV(cost of asset
ownership) – FV(benefits of asset ownership)
 Forward prices must be arbitrage-free.
 If FP0 > P0 + FV(costs) – FV(benefits)
then,
1. Sell the forward at FP0,
2. Borrow proceeds equal to P0 and buy asset in spot
market (at P0),
3. Receive income on long position in the asset.
4. At maturity, you reverse your actions to lock in a
riskless profit (receive income, pay back loan, and
sell asset at FP0).

8
Principles of Forward Pricing (cont.)
If FP0 < P0 + FV(costs) – FV(benefits)
then,
1. Buy/go long the forward at FP0,
2. Borrow the asset (and pay any interest on this
borrowing),
3. Sell the asset immediately in the spot market (at
P0) and invest proceeds equal to P0 in riskless
asset,
4. At maturity, reverse your actions to lock in a
riskless profit (recoup investment in riskless asset,
pay for underlying asset at FP0, and return
borrowed asset with interest).

9
FX Risk: Calculate the indirect quotations for
euros and Swedish krona
Euro:
 Krona:

Euro
Swedish krona
1 / 0.8000 =
1 / 0.1000 =
1.25
10.00
Indirect Quotes:
Direct Quote:
# of Units of
U.S. $ per foreign Foreign Currency
currency
per U.S. $
0.8000
1.25
0.1000
10.00
10
What is a cross rate?

A cross rate is the exchange rate between
any two currencies not involving U.S. dollars.

In practice, cross rates are usually calculated
from direct or indirect U.S. rates. That is, on
the basis of U.S. dollar exchange rates.
11
Calculate the two cross rates
between euros and krona.
Euros
Dollars
×
Dollar
Krona
= 1.25 x 0.1000
= 0.125 euros/krona
Cross Rate =
Cross Rate =
Krona
Dollar
Dollars
× Euros
= 10.00 x 0.8000
= 8.00 krona/euro
12
Example of International
Transactions

Assume a firm can produce a liter of orange
juice in the U.S. and ship it to Spain for
$1.75.

If the firm wants a 50% markup on the
product, what should the juice sell for in
Spain?
Target price = ($1.75)(1.50)=$2.625
Spanish price = ($2.625)(1.25 euros/$)
= € 3.28
13
Example (continued)

Now the firm begins producing the orange juice
in Spain. The product costs 2.0 euros to
produce and ship to Sweden, where it can be
sold for 20 krona.

What is the dollar profit on the sale?
2.0 euros * (8.0 krona/euro) = 16 krona
20 - 16 = 4.0 krona profit.
Dollar profit = 4.0 krona * (0.1000 $ per krona)
= $0.40
14
What is exchange rate risk?

Exchange rate risk is the risk that the value of
a cash flow in one currency translated from
another currency will decline due to a change
in exchange rates.
15
Currency Appreciation and
Depreciation

Suppose the exchange rate goes from 10
krona per dollar to 15 krona per dollar.

A dollar now buys more krona, so the dollar
is appreciating, or strengthening.

The krona buys less dollars, so the krona is
depreciating, or weakening.
16
Affect of Dollar Appreciation

Suppose the profit in krona remains
unchanged at 4.0 krona, but the dollar
appreciates, so the exchange rate is now 15
krona/dollar.

Dollar profit = 4.0 krona / (15 krona per
dollar) = $0.267

Strengthening dollar hurts profits from
international sales.
17
Forward FX rate contracts

FX forward contract – agree on an exchange rate
today to exchange one currency (e.g., the Japanese
yen) for another currency (e.g., the U.S. dollar) at
some time in the future.

Interest Rate Parity determines the forward FX rate
that makes the E(NPV) = 0.

Covered Interest Arbitrage ensures that Interest
Rate Parity holds.

Conceptually equivalent to a pair of zero coupon
bonds.
18
FX forward rates…


Forward exchange rate determined by the current spot FX
rate and the riskless interest rates in the two countries.
The interest rate parity relation can be summarized by:
T
(
1

r
)
2
Ft P  St 
(1  r1 )T


Where, r1 = interest rate for the country that has its
currency in the denominator of the FX rate (e.g., U.S. dollar
if FX rate is expressed as Yen / dollar).
r2 = interest rate for country whose currency is in the
numerator of the FX rate.
19
Application for 6-month Colon / U.S.
Dollar FX forward rate:


To synthesize the current Colon / Dollar 6-month forward
exchange rate, we must use the current spot FX rate and
the (near) riskless interest rates of the two countries.
This interest rate parity relation can be summarized by:
F0P1/ 2


(1  r2 )1/ 2
(1.0895)1/ 2
 S0 
 499.4 
 520.9
1/ 2
1/ 2
(1  r1 )
(1.0015)
Where, r1 = the U.S. dollar interest rate because the FX
rate is expressed as Colones / U.S. Dollar).
r2 = the interest rate in Colones).
20
Interest Rate Parity and the “Box”

Forward FX rates can be replicated by
following the lines around a box that links
spot rates, forward rates, and interest rates.
U.S. $T
U.S. $0
ForwardT
Spot0
ColonesT
Colones0
21
Application of how to synthesize a
Short Colon / Dollar Forward FX Rate

A Short Colones position can be synthesized
by: 1) borrowing in Colones at 8.95% for 6
months, 2) investing in U.S. Dollars at 0.15%
for 6 months at the Spot FX rate of 499.4.
U.S. $T
ForwardT=520.9
+1.00151/2
U.S. $0
ColonesT
-1.08951/2
Spot0=499.4
Colones0
22
Forward Interest Rates (FRAs)

Forward Interest Rate Agreement – agree on an interest
rate today to receive (or pay) at some time in the
future.

Forward Interest Rates are implicit in spot yield curves.

This is due to a “no arbitrage” argument that says that
the return on, say, a two-year bond must be equivalent
to the return on a “roll-over” strategy of investing in a 1year bond and rolling it over into another 1-year bond at
the beginning of the second year.
23
FRA pricing

You can use interest rates from the spot yield
curve to derive forward rates as follows:
 (1 0 Rk )
Rk  
j
j
(
1

R
)
 0 j
k





(k  j )
1
Where, R’s with a prefix of “0” are spot rates
and j = the term of the FRA and k = the start
date of the FRA.
24
Currency Risk and Forward Pricing Examples

Link to Forward Pricing Excel file:

FM 12 Ch 26 Mini Case.xls
(Brigham & Ehrhardt file)
25
Futures Contracts

Similar to Forward contracts but are more structured
and standardized than forwards.

Futures contract is a legally binding obligation to buy
or sell a specified quantity of a specific asset at a
specified date in the future.

Standardization features: contract specifies a
homogeneous asset, maturity date, contract size,
delivery mechanism, and minimum “tick” size.
26
Futures Contracts (cont.)

Institutional Features that:



Reduce credit risk, and
Improve liquidity
Five key elements:





Standardized contract on homogeneous asset
Daily settlement of positions (like a series of forwards)
Margin requirements (good faith deposit that reduces credit
risk)
Price limits (restricts daily movement in futures price to be
within margin requirement)
Clearinghouse (de-couples buyer and seller by providing
anonymity and reduces counterparty risk)
27
Pricing of Futures Contracts

Pricing reflects the spot price, P0, plus the “cost of
carry”, c, (which includes the risk-free rate, rf).

F0 = P0 + c = P0 * (1 + rf)T
if the only component of c is a constant risk-free
rate.

No arbitrage requirement enforces the above relation

Other factors can affect the cost of carry, c, such as
storage and insurance costs, as well as
interest/dividend income on the underlying asset.
28
Features of Futures Prices

The concept of Basis is a key factor when
determining the effectiveness of a hedge:
Basist = Ft - Pt
See Spreadsheet File.

According to the cost-of-carry model, the basis
should correspond to the cost of carry variable, c.

Over time, futures prices will tend to converge
toward the price implied by c.

Also, the futures price will converge to the spot price
at the futures contract’s expiration (FT = PT).
29
Basis Risk
Perfect hedges are difficult to construct due to basis
risk.
 Basis Risk is the risk that the payoff profile of the
hedging instrument is not exactly equal to the firm’s
risk profile associated with a specific financial asset.
 Four primary sources of basis risk:






Changes in the convergence rate of FT to PT
Changes in the factors affecting c,
Random deviations in c,
Mismatches between the hedging instrument and the
underlying asset exposure (cross-hedge basis risk)
Note: basis risk goes to zero if hedge’s maturity
exactly equals the underlying asset’s purchase/sale
date.
30
Cross-hedge Basis Risk

Cross-hedge is used when there is no hedging
instrument that is identical to the underlying asset
exposure (e.g., use T-bond futures to hedge a corp.
bond portfolio).

Cross-hedge Basist = (Ft,X – Pt,X) + (Pt,X - Pt,Y)
where,
X = asset that is used for hedging purposes,
Y = underlying asset exposure to the firm.

Three factors that affect the above basis risk:
1) Maturity mismatch, 2) Liquidity, 3) Credit risk.
31
Hedging Applications of
Forwards and Futures




Forward contracts are normally best for situations
where the contract details (size, maturity, underlying
asset) need to be tailored to a specific set of firm
cash flows.
Forwards are usually more cost-effective for larger
firms with good credit ratings and special needs that
suit “custom-tailoring”.
Futures are less flexible than forwards in terms of
tailoring the payoffs to fit a firm’s exposures.
However, futures are much more liquid than forwards
and have much less credit risk.
32
Hedging Prerequisites

“Appropriates” – specifies the details of the
financial exposure that the firm plans to hedge (e.g.,
What security?, What time/maturity?, How much?).

Hedging Strategies:





Do Nothing – easiest strategy (but can be very costly!).
Lock in price today – use forwards or futures to hedge
exposure fully (100% of exposure is covered).
Lock in price today for some of the exposure - less than
100% coverage can be cheaper.
Cross-hedge – when derivative is not available for the firm’s
underlying financial exposure.
Note: hedging substitutes Basis Risk for Price Risk.
33
Cross-Hedging Example

Cross-hedge: Use New Mexican Peso Futures to
hedge against changes in Colon / U.S. Dollar rate).

Find Futures Contract with closest correlation to
underlying exposure – Usually use a regression:
PC.R. Exchange Rate = a + b * PMexican Exchange Rate + e
(choose the future that has the highest adj. R2,
e.g., our R2 = .333 and b = 0.023 for the peso)

Divide total exposure by standard futures contract size
(0.5M pesos) to get “raw” number of contracts needed.
e.g., {[400M colones x 0.023] / 0.5M} = 18.4  19.
34
Cross-Hedging Example (continued)
Assume: Peso devalues from 11.1 to 12.3 per U.S. dollar
and Colon devalues from 513 to 570 per U.S. dollar.
Initial Value of 400M Sale: $0.780M = 400M / (513 / $1)
Ending Value of Sale:
$0.702M = 400M / (570 / $1)
Loss due to Devaluation: $0.078M (-10.0%)
Initial SHORT Futures:
$0.856M = (19 x 0.5M) / 11.1
Ending SHORT Futures:
$0.772M = (19 x 0.5M) / 12.3
Gain due SHORT Futures: $0.084M (+9.8%)
Net Change in Total Value: +$0.006M = +0.084 – 0.078
35
Calculating the Overall Effect of a
Hedge

Calculate Change in Underlying Asset Position
– Multiply the spot price at maturity times quantity of
the underlying position
– Then subtract initial asset value (at t=0) from the
above figure.

Calculate the Hedge’s Profit/Loss
Hedging Profit/Loss = L/S Indicator * (FT – F0) *
Number of Futures Contracts * Futures Contract size
Note: must replace FT with PT if there is no basis risk

Add the two figures together to get net effect:
Net Change in Value = D Underlying + D Hedge
36