1.1
Asset Management and Derivatives
Lecture 1
1.2
Course objectives
Why an asset management course on
derivatives?
A derivative is an instrument whose value depends on the values of other
more basic underlying variables. Examples: swaps, futures, options, ...
1. They can increase the efficiency of the investment process
2. Their non-linear payoff can be attractive for improving the risk-return profile
of the managed portfolio
3. We can borrow from their hedging/pricing techniques new ways of
managing portfolios
4. They can enlarge the asset classes on which we can invest
1.3
Improve the efficiency
• a quicker way for tactical market timing. Imagine that you are the manager of
an equity fund and you want to take a positive bet on the entire stock market
(+1% on the benchmark). Since you are actually neutral and you want to go
long, you can borrow money and buy all the stocks that are in your portfolio in
the existing proportions. This is a complex operation. The typical shortcut is
through a futures contract.
• if you want to replicate an index where a single stock weights more than the
max allowed by regulators, you have to resort to derivates to reach
synthetically the desired exposure.
• another example of use of derivatives is when you want to hedge your fund
from currency fluctuations.
1.4
Modify risk-return mapping
• traditional long-only asset management has a linear pay-off
• one can use derivative both for going short and for introducing some nonlinearity in a fund which remains in any case essentially long-only
• Apart from the “simple” buying or selling of options either because of
particular views that we have on stock/market or because of arbitrage
opportunities between the cash and the derivatives market, we can use
derivatives to tilt the management result on a given time horizon. This can be
useful if you want a floor on your profits (think about the possibility of lockingin the profits through a put option) ... or if you want a cap (think about the
possibility of improving your return by selling an out-of-the money call option
on a stock held in your portfolio.
• In any case, you may end up buying options also if are not perfectly aware
of it (see convertible bonds). So beware
1.5
new ways of managing money
• Derivatives can be useful to learn new ways of managing money and then
structuring products helpful for more sophisticated clients’ needs.
• The pricing of a derivatives is based on the concept that if market is efficient
there should be no arbitrage opportunities between the cash market and the
derivatives.
• The pricing is then strictly linked to replicating the pay-off of the derivatives
via a portfolio of basic financial instrument. The portfolio has to be managed
dynamically.
• So it is possible to manage a fund in a way that it replicates the pay-off of an
option. This principle is behind portfolio insurance and other dynamic
techniques that are currently used in the asset management industry.
1.6
enlarging the universe
• Many asset classes cannot be invested in, by regulatory reasons and by
objective difficulties inherent to the markets nature. Those asset classes might
be very useful in diversifiyng the portfolio.
• For example, it can be very difficult to access certain emerging markets,
either because they are protected by cumbersome administrative rules or
simply because foreign investors are not allowed to hold them.
• Another example is instead the one of an asset class that cannot be
accessed by an asset manager because of the market’s nature.
•Think about mortgages or loans. This is a market that can be accessed only
by banks. Credit derivatives are a new class of financial instruments that allow
an asset manager to access them.
•Think about re-insurance risks (weather or earthquake risks). ART
instruments can help asset managers to access them
1.7
The Playground
1.8
Derivatives Markets
• Exchange Traded
– standard products
– trading floor or computer trading
– virtually no credit risk
• Over-the-Counter
– non-standard products
– telephone market
– some credit risk
1.9
Types of Traders
• Hedgers
• Speculators
• Arbitrageurs
Some of the large trading losses in
derivatives occurred because individuals
who had a mandate to hedge risks switched
to being speculators
1.10
Hedging Examples
• A US company will pay £1 million for
imports from Britain in 6 months and
decides to hedge using a long position
in a forward contract
• An investor owns 500 IBM shares
currently worth $102 per share. A twomonth put with a strike price of $100
costs $4. The investor decides to hedge
by buying 5 contracts
1.11
Speculation Example
• An investor with $7,800 to invest feels
that Exxon’s stock price will increase
over the next 3 months. The current
stock price is $78 and the price of a 3month call option with a strike of 80 is
$3
• What are the alternative strategies?
1.12
Arbitrage Example
• A stock price is quoted as £100 in
London and $172 in New York
• The current exchange rate is 1.7500
• What is the arbitrage opportunity?
1.13
Forward Contracts
• A forward contract is an agreement to
buy or sell an asset at a certain time in
the future for a certain price (the
delivery price)
• It can be contrasted with a spot
contract which is an agreement to buy
or sell immediately
1.14
How a Forward Contract Works
• The contract is an over-the-counter
(OTC) agreement between 2 companies
• The delivery price is usually chosen so
that the initial value of the contract is
zero
• No money changes hands when
contract is first negotiated and it is
settled at maturity
The Forward Price
• The forward price for a contract is the
delivery price that would be applicable
to the contract if were negotiated
today (i.e., it is the delivery price that
would make the contract worth exactly
zero)
• The forward price may be different for
contracts of different maturities
1.15
1.16
Terminology
• The party that has agreed to
buy has what is termed a
long position
• The party that has agreed to
sell has what is termed a
short position
1.17
Example
• On January 20, 1998 a trader enters
into an agreement to buy £1 million in
three months at an exchange rate of
1.6196
• This obligates the trader to pay
$1,619,600 for £1 million on April 20,
1998
• What are the possible outcomes?
1.18
Profit from a
Long Forward Position
Profit
K
Price of Underlying
at Maturity, ST
1.19
Profit from a
Short Forward Position
Profit
K
Price of Underlying
at Maturity, ST
1.20
Futures Contracts
• Agreement to buy or sell an asset for a
certain price at a certain time
• Similar to forward contract
• Whereas a forward contract is traded
OTC a futures contract is traded on an
exchange
1.21
Exchanges Trading Futures
•
•
•
•
•
•
Chicago Board of Trade
Chicago Mercantile Exchange
BM&F (Sao Paulo, Brazil)
LIFFE (London)
TIFFE (Tokyo)
and many more (see list at end of book)
1. Gold: An Arbitrage
Opportunity?
• Suppose that:
- The spot price of gold is US$300
- The 1-year forward price of gold
is US$340
- The 1-year US$ interest rate is
5% per annum
• Is there an arbitrage opportunity?
1.22
1.23
2. Gold: Another Arbitrage
Opportunity?
• Suppose that:
- The spot price of gold is US$300
- The 1-year forward price of gold
is US$300
- The 1-year US$ interest rate is
5% per annum
• Is there an arbitrage opportunity?
1.24
The Forward Price of Gold
If the spot price of gold is S & the forward price
for a contract deliverable in T years is F, then
F = S (1+r )T
where r is the 1-year (domestic currency) riskfree rate of interest.
In our examples, S=300, T=1, and r=0.05 so that
F = 300(1+0.05) = 315
1.25
Gold Example
• For the gold example,
F0 = S0(1 + r )T
(assuming no storage costs)
• If r is compounded continuously instead
of annually
F0 = S0erT
When an Investment Asset
Provides a Known Dollar
Income (page 58)
F0 = (S0 – I )erT
where I is the present value of the
income
1.26
When an Investment Asset
Provides a Known Dividend
Yield
F0 = S0 e(r–q )T
where q is the average dividend yield
during the life of the contract
1.27
Valuing a Forward Contract
1.28
Page 59
• Suppose that
K is delivery price in a forward contract &
F0 is forward price that would apply to the
contract today
• The value of a long forward contract, ƒ, is
ƒ = (F0 – K )e–rT
• Similarly, the value of a short forward contract
is
(K – F0 )e–rT
1.29
Stock Index
• Can be viewed as an investment asset
paying a continuous dividend yield
• The futures price & spot price
relationship is therefore
F0 = S0 e(r–q )T
where q is the dividend yield on the
portfolio represented by the index
1.30
Stock Index
(continued)
• For the formula to be true it is
important that the index represent an
investment asset
• In other words, changes in the index
must correspond to changes in the
value of a tradable portfolio
• The Nikkei index viewed as a dollar
number does not represent an
investment asset
1.31
Index Arbitrage
• When F0>S0e(r-q)T an arbitrageur buys
the stocks underlying the index and
sells futures
• When F0<S0e(r-q)T an arbitrageur buys
futures and shorts or sells the stocks
underlying the index
1.32
Index Arbitrage
(continued)
• Index arbitrage involves simultaneous
trades in futures & many different stocks
• Very often a computer is used to
generate the trades
• Occasionally (e.g., on Black Monday)
simultaneous trades are not possible
and the theoretical no-arbitrage
relationship between F0 and S0 may not
hold
1.33
Hedging Using Index Futures
• To hedge the risk in a portfolio the
number of contracts that should be
shorted is
P
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
1.34
Changing Beta
• What position in index futures is
appropriate to change the beta of a
portfolio from b to b*
1.35
Futures and Forwards on
Currencies
• A foreign currency is analogous to a security
providing a continuous dividend yield
• The continuous dividend yield is the foreign
risk-free interest rate
• It follows that if rf is the foreign risk-free
interest rate
F0  S0e
( r rf ) T
1.36
Futures on Consumption Assets
F0  S0 e(r+u )T
where u is the storage cost per unit
time as a percent of the asset value.
Alternatively,
F0  (S0+U )erT
where U is the present value of the
storage costs.
1.37
The Cost of Carry
• The cost of carry, c , is the storage cost plus
the interest costs less the income earned
• For an investment asset F0 = S0ecT
• For a consumption asset F0  S0ecT
• The convenience yield on the consumption
asset, y , is defined so that
F0 = S0 e(c–y )T
1.38
Futures Prices & Expected
Future Spot Prices
• Suppose k is the expected return
required by investors on an asset
• We can invest F0e–r T now to get ST
back at maturity of the futures
contract
• This shows that
F0 = E (ST )e(r–k )T
Futures Prices & Future Spot
Prices
• If the asset has
– no systematic risk, then
k = r and F0 is an unbiased
estimate of ST
– positive systematic risk, then
k > r and F0 < E (ST )
– negative systematic risk, then
k < r and F0 > E (ST )
1.39
1.40
1. Oil: An Arbitrage
Opportunity?
Suppose that:
- The spot price of oil is US$19
- The quoted 1-year futures price of
oil is US$25
- The 1-year US$ interest rate is
5% per annum
- The storage costs of oil are 2%
per annum
• Is there an arbitrage opportunity?
1.41
2. Oil: Another Arbitrage
Opportunity?
• Suppose that:
- The spot price of oil is US$19
- The quoted 1-year futures price of
oil is US$16
- The 1-year US$ interest rate is
5% per annum
- The storage costs of oil are 2%
per annum
• Is there an arbitrage opportunity?