Actuarial Investments

1
Actuarial Investments

• Shane Whelan
• L527

2
Derivative Markets
3
Derivatives

• A derivative is a financial instrument whose
  value is a function of another asset (the
  underlying). So it is a contract between 2 or
  more parties whose value is derived from another
  asset, e.g., futures, forwards, options, and
  swaps.
• Used to hedge (reduce risk)
• Used to speculate (increase return).
• Also used in portfolio management
• e.g., to increase speed of execution of switch.

4
Forwards Futures

• A forward is a contract between two parties to
  trade a specified asset on a specified date in
  the future at a specified price. Generally a
  non-standardised contract.
• A future is an exchange tradeable contract
  between two parties to trade a specified asset at
  a specified date in the future at a specified
  price. It is a standardised contract and a
  special case of a forward.
• The underlying trades in the cash or spot market
  while the forward/future trades in the futures
  market.
• One party is long the contract (buy the future)
  while the other party the seller of the future
  - is short.
• Delivery of underlying rarely occurs in practice.

5
Operation of Futures Exchanges

• The contract must be standardised by
• Exact details of underlying assets
• Units of underlying of one future contract
• The delivery date
• How the settlement price is to be determined.
• Hence futures traders simply agree contract type
  to to deal, the number of contracts, and the
  price of contract.
• Hence appears exactly like spot market. However
  here no money changes hands at beginning of
  contract.

6
Example Gold Future

• Contract Size 100 troy ounces
• Quality 24 carat ounces
• Currency Sterling
• Delivery Date 3rd Monday in March
• Min. price move 10.
• Let us say that gold prices are 198.7 per troy
  ounce. Then total value of underlying is about
  100198.719,870. So traders agree future price,
  say, 19,980.

7
Example Gold Future

• The min. price movement of a contract is set by
  the exchange and is known as the futures tick
  value. It is 10, say, in this example.
• The smallest movement between quoted prices is
  the tick size.
• This contract would be quoted as 19.98

8
Method of Trading

• Most exchanges use electronic trading systems but
  some still favour face-to-face dealing (known as
  open outcry).
• In open outry, the dealing floor is divided into
  trading areas known as pits a pit of each
  contract type. Traders shout out what they want
  to do and a trade occurs when buyer meets seller.
  
• On either system, the parties to the trade fill
  out clearing slips and give to exchange which
  register deal with exchanges clearing house.
• The clearing house is a party to every trade
  each party now has an obligation to the clearing
  house not one-another. It acts as the
  counter-party, guaranteeing delivery hence credit
  risk of individual participants removed.

9
How Clearing House Manages it Credit Risk Exposure

• Margin Calls
• Initial margin payable to clearing house at start
  of contract.
• Variation margin due (or released) at the end of
  each trading day calculated by marking-to-market
  the contract at the close of each day.
• Hence no big liability to one party on delivery
  day it is spread as smoothly as market daily
  gyrations allow.
• Margin payments are credited with interest.

10
How Clearing House Manages it Credit Risk Exposure

• Margin Calls
• Initial margin payable to clearing house at start
  of contract.
• Variation margin due (or released) at the end of
  each trading day calculated by marking-to-market
  the contract at the close of each day.
• To mark-to-market, the price used is the market
  value of the future at the end of the day.
• Hence no big liability to one party on delivery
  day it is spread as smoothly as market daily
  gyrations allow.
• Margin payments are credited with interest.

11
Margining v- Final Settlement

• In terms of PV, settling on the Settlement Day
  is equivalent to marking-to-market on a daily
  basis. Discuss.

12
Price Limits

• Futures markets generally have price limits.
• A band centring on the previous days close is
  constructed about a futures contract price so, if
  it moves outside the band during the day, the
  market closes for a cooling-off period. Market
  can close limit-up (price hits upper bound) or
  limit-down.
• Closing out a position take the opposite
  position in the same amount on the same contract.
  
• E.g., if long 150 March bund futures then sell
  150 March bund futures so net exposure is now
  zero.
• The Clearing House calculates net exposure of
  each trader and the sum of these gives the open
  interest the number of contracts outstanding at
  any one time.
• Almost everyone closes out prior to delivery
  the formal settlement process in the futures
  market.
• If delivery reached then still normally settled
  for cash the exchange publishes the EDSP (the
  exchange delivery settlement price) which is the
  final settlement price on all outstanding futures.

13
Calculation of Fair Value for Future Contract

• Actual price of a future results from interplay
  of supply demand.
• However, the Law of One Price or, equivalently,
  the No-Arbitrage Condition, allow us to compute a
  fair value for future.
• The actual future price should trade very closely
  to the fair priceor arbitrageur gets a free
  lunch.

14
Calculation of Fair Value for Future Contract

• Two ways to manufacture the same economic
  exposure
• Buy future, leaving money on deposit to gain
  interest.
• Buy the underlying and receive whatever income
  the underlying gives prior to the delivery date.
• The price of doing either must be the same
  (otherwise an arbitrage opportunity).
• Hence
• Fair futures price income from underlying
  current cost of underlying interest on deposit.
• i.e., fair futures price underlying interest
  on deposit income from underlying.

15
Terminology

• Deposit interest is sometimes called the cost of
  carry. While income on underlying is the return
  on carry.
• Basis Spot price of underlying futures price.
• At time ? delivery, then basis ? 0

16
Investment Risk Characteristics of Futures

• Derivative are generally not held in their own
  right (i.e., as individual assets) but must be
  considered as part of the overall portfolio.
• Always think in terms of economic exposure the
  quantity of the underlying.
• Term short term contracts that can be rolled
  over to maintain exposure. Volatility a function
  of the underlying.
• Income Capital no income but capital flows
  over term by margining arrangements.
• Security high with exchange-traded futures but
  not complete.

17
Investment Risk Characteristics of Futures

• Marketability excellent. Generally better than
  underlying with higher turnover figures. Dealing
  costs lower than underlying.
• Volatility, if related to margin payment is
  extremely high because of gearing. If related to
  economic exposure then it is same as underlying.
• Expected returns zero as, ignoring the modest
  dealing costs, it is a zero-sum game between
  buyers and sellers ???

18
Options

• Option a contract that gives one party the
  right but not the obligation to buy or sell the
  underlying at or by a future specified date at a
  specified price.
• Define call option put option strike price
  exercise price (option) writer (option)
  premium.
• Is buying a put the same as selling a call?
• 4 exposures with the two option types
• buy a call buy a put
• write a call write a put.
• American option
• can be exercised at any time prior to expiry.
• European option can only be exercised at
  expiry.

19
Traded options

• Traded options contracts that are standardised
  by and traded on an exchange.
• Available on financial future foreign
  currencies short-term interest rates stock
  market indices individual equities commodities.
• Traded generally by open outcry.
• Clearing house becomes party to every trade
  severing link between buyer seller.
• Only one party only pays margin. Which one?
• OTC (over-the-counter) security/derivative is
  one not traded on a recognised exchange.

20
Option Prices

• Option price ultimately set by supply and demand.
  But again we can derive (but not on this course)
  a theoretical price that it generally trades
  near.
• Option value
• Instrinsic value of call greater of zero or
  current price of underlying less exercise price.
• if positive the call option in the money, zero
  then option out of the money
• Time value the choice that can still be
  exercised until expiry give it a time value.
• Option Price Option Premium

21
Option Prices

• Call premium
• Is an increasing function of share price.
• Decays with decreasing time (other things being
  equal), reaching instrinsic value at expiry.
• Deep out of money option not so sensitive to
  share price movements at around exercise price
  it increases by about 0.5 for very 1 move in
  share price.
• What happens when deep in-the-money?

22
Options Position Diagrams

• Position diagrams help to see profit/loss on
  option or option book at expiry, as a function of
  the underlying price.
• Convention has it that
• You allow for premium.
• Ignore dealing costs.
• Ignores interest on premium.
• Draw position diagram of
• Long call option
• Short call option
• Long put option
• Short put option

23
Investment Risk Characteristics of Options

• Term short-term, so roll-over regularly if want
  longer-term exposure.
• Income none but capital flows to writer via
  margining.
• Security as good as the clearing house.
• Marketability very good generally with low
  dealing costs.
• Volatility very high relative to premium.
• Expected return zero as a zero-sum game?

24
Forwards Swaps

• Forwards swaps are OTC instruments (synthesised
  by investment banks). They are bespoke, less
  liquid, less transparent, and credit risk is a
  major factor.
• Institutional investors mostly use these
  instruments for hedging foreign currency exposure
• Generally run to delivery
• No margining unless specified in special contract
• As with futures, it is straightforward to price
  forwards.

25
Swaps

• Swap a contract between 2 parties under which
  they agree to exchange a future series of
  payments according to an agreed formula.
• e.g. two different currencies (a currency swap)
• e.g., two different types of interest payments
  (an interest rate or coupon swap)
• In both cases they are bundles of forward
  agreements so straightforward to price but must
  make allowance for credit risk.

26
Example Interest Rate Swap

• In a plain vanilla interest rate swap, company B
  agrees to pay company A cash flows equal to
  interest at a predetermined fixed rate on a
  notional principle for a number of years. At the
  same time, company A agrees to pay company B cash
  flow equal to interest at a floating rate on the
  same notional principal for the same period of
  time in the same currrency.
• Note that the notional principal is used only for
  the calculation of interest payments. The
  principal itself is not exchanged.
• The swap contract has the effect of transforming
  the nature of the liabilities or assets. In the
  example, company B can use the swap to transform
  a floating-rate loan into a fixed-rate loan.
• Usually, two non-financial companies deal with a
  financial intermediary which is remunerated by
  the difference between the value of a pair of
  offsetting transactions, providing neither client
  defaults on their swap.
• The intermediary has two separate contracts, one
  with company A and the other with company B.  

27
Example Interest Rate Swap

• In practice, it is unlikely that two companies
  will contact an intermediary at the same time and
  want to take opposite positions in exactly the
  same swap. For this reason, a large financial
  institution will be prepared to enter into a swap
  without having an offsetting swap with another
  counterparty in place. This is known as
  warehousing swaps.
• If we assume no possibility of default (e.g.,
  collateralised), an interest-rate swap can be
  valued as
• a long position in one bond compared to a short
  position in another bond, since the notional
  principal is the same in both cases.
• Alternatively, as a portfolio of forward rate
  agreements.

28
Risk of Swaps

• to either party
• market risk the risk that market conditions
  change to their detriment,
• credit risk the other party defaults (when NPV
  of contract is positive).

29
Credit Derivatives

• Another way of managing credit risk is by using
  credit derivatives credit derivatives are
  contracts where the payoff depends partly on upon
  the creditworthiness of one (or more) commercial
  (or sovereign) entities.
• The most common types of credit derivative is the
  credit default swap
• Credit default swaps A contract that provides a
  payment if a particular event occurs. The party
  that buys the protection pays a fee to the
  seller. If the credit event occurs within the
  term of the contract a payment is made from the
  seller to the buyer, otherwise it no payment is
  made by seller. There are two ways to settle a
  claim under a credit default swap
• A pure cash payment, representing the fall in the
  market price of the defaulted security. However,
  the market value may be difficult to
  determine/agree.
• A more robust method is, perhaps, the exchange of
  both cash and a security (physical settlement).
  The protection seller pays the buyer the full
  notional amount and receives, in return, the
  defaulted security.
•         

30
Credit Derivatives

• Main Use of Credit default swaps Lenders who
  have reached their internal credit limit with a
  particular client, but wish to maintain their
  relationship with that client can use credit
  default swaps. Main users of credit default swaps
  are banks.
• Other credit derivative instruments
• Total return swaps Here, the total return from
  one asset (or group of assets) is swapped for the
  return on another. This enables financial
  institutions to swap one type of exposure for
  another. In the absence of counterparty risk,
  the value of a total return swap is the
  difference between the values of the assets
  generating the returns on each side of the swap.
  A total return swap is normally structured so
  that it is worth zero initially.
• Credit spread options An option on the spread
  between the yields earned on two assets, which
  provides a payoff whenever the spread exceeds
  some level (the strike spread).
• A credit-linked note consists of a basic
  security plus an embedded credit default swap.
  They provide a useful way of stripping and
  repackaging credit risk.

31
ASIDE Dont forget the Web

• A great source of information
• www.cme.com
• www.liffe.com
• www.nyse.com
• www.ise.ie
• Etc.