Part%20

1

• Part III
• Valuation, Hedging, and Speculation

2
Pricing of a Forward Contract

• How do we decide as to what price we should
  transact at in the future, when we enter into a
  forward contract?
• Let us first review a forward contract.
• It entails an obligation on the part of the short
  to make delivery of the asset on a future date,
  and an equivalent obligation on the part of the
  long to take delivery.

3
Pricing (Cont)

• From the perspective of the short, if he buys the
  asset at the market price prevailing at the
  outset and simply holds on to it, he is assured
  of a selling price at the time of delivery by
  virtue of the contract.

4
Pricing (Cont)

• So if the difference between the forward price as
  per the contract and the spot price at the
  outset, were to exceed the cost of carrying the
  asset until delivery, then there would exist an
  arbitrage opportunity.
• Thus the relationship between the spot price and
  the forward price at any point in time, is a
  function of the carrying cost.

5
An Asset That Pays No Income

• Consider an asset that pays no income.
• Examples include stocks that are unlikely to pay
  any dividends or bonds that are not scheduled to
  pay any coupons.
• In this case the cost of carrying the asset is
  purely the interest cost.
• That is, if the spot price is S, the interest
  cost is rS.

6
No Income (Cont)

• This interest cost is an actual expenditure if
  funds are borrowed to purchase the asset, else it
  is an opportunity cost.
• Consequently the lack of potential for arbitrage
  would imply that
• F S rS

7
Cash and Carry Arbitrage

• What would be the consequence if
• F gt S rS
• If so, an arbitrageur would borrow and buy the
  asset and go short in a forward contract to
  deliver at a future date.
• At the time of delivery he would receive F,
  return S rS, which represents the loan plus
  interest, and pocket the difference.

8
Arbitrage (Cont)

• Such a strategy is called Cash and Carry
  Arbitrage.
• To rule it out, we require that
• F S ? rS ? F ? S(1r)

9
Illustration

• Assume that TISCO is currently selling for Rs 100
  per share, and is not expected to pay any
  dividends for the next six months.
• The price of a forward contract for one share of
  TISCO to be delivered after six months is Rs 106.
• An arbitrageur is able to borrow at the rate of
  5 for six months.

10
Illustration (Cont)

• In this case, the arbitrageur can borrow
• Rs 100 and acquire a share, and simultaneously
  go short in a forward contract to deliver the
  share after six months for Rs 106.
• The rate of return on investment is
• (106 100)
• -------------- 0.06 ? 6
• 100

11
Illustration (Cont)

• The borrowing cost it must be remembered is only
  5.
• Consequently cash and carry arbitrage is
  profitable.
• This is because the contract is overpriced, that
  is
• F gt S(1r)

12
Cash and Carry Arbitrage (Cont)

• The rate of return obtained from a cash and carry
  arbitrage strategy is called the Implied Repo
  Rate.
• Thus cash and carry arbitrage is profitable only
  if the Implied Repo Rate exceeds the borrowing
  rate.

13
Synthetic T-Bill

• By engaging in a cash and carry strategy, the
  arbitrageur has ensured a payoff of
• Rs 106 after six months for an initial
  investment of Rs 100.
• Therefore it is as if he has bought a Zero Coupon
  Bond with a face value of Rs 106 for a price of
  Rs 100.

14
Synthetic T-Bill

• Thus, a combination of a long position in the
  asset and a short position in the forward
  contract, is equivalent to a long position in a
  Zero Coupon instrument.
• Such a Zero Coupon instrument is called a
  Synthetic T-Bill.

15
Synthetic T-Bill (Cont)

• Symbolically
• Spot Forward Synthetic T-Bill
• The negative sign indicates a short position in
  the forward contract.
• Thus if we have a natural position in two out of
  the three assets, we can artificially create a
  position in the third.

16
Arbitrage-The Longs Perspective

• We have seen that if F gt S rS then it can be
  exploited by an arbitrageur by going short in a
  forward contract.
• However, what if F lt S rS?
• This too represents an arbitrage opportunity.
• However to exploit it, one would have to take a
  long position in a forward contract.

17
Reverse Cash and Carry Arbitrage

• Under such circumstances, the arbitrageur would
  have to short sell the asset and invest the
  proceeds at the risk-less rate.
• He would have to simultaneously go long in a
  forward contract to reacquire the asset at a
  predetermined price.
• Such a strategy is called Reverse Cash and Carry
  Arbitrage.

18
Short Sales

• What is a short sale?
• It entails the borrowing of an asset from another
  party in order to sell it.
• The borrower or the short-seller is responsible
  for eventually returning the asset to the lender.

19
Short sales (Cont)

• He must also compensate the lender for any cash
  flows that he would have received from the asset
  had he not parted with it.
• This is because the lender continues to be the
  owner of the asset and is consequently entitled
  to the lost income.

20
Illustration ofReverse cash and carry arbitrage

• Assume that shares of TISCO are selling at Rs 100
  each and that the company is not expected to pay
  any dividends for the next six months.
• Let the price of a forward contract that calls
  for the delivery of one share of TISCO six months
  hence be Rs 104.

21
Illustration (Cont)

• Consider an arbitrageur who can lend money at a
  rate of 5 for six months.
• He can short sell a share of TISCO, receive Rs
  100 and invest it at 5 for six months.
• He can simultaneously go long in a forward
  contract to acquire the share after six months
  for Rs 104.

22
Illustration (Cont)

• The effective borrowing cost is
• (104 100)
• ------------- 0.04 ? 4
• 100
• Which is less than the lending rate of 5.

23
Illustration (Cont)

• Consequently reverse cash and carry arbitrage is
  profitable.
• This is because F lt S(1r), or in other words the
  contract is under priced.
• The cost of borrowing funds using a reverse cash
  and carry strategy is called the Implied Reverse
  Repo Rate.

24
Illustration (Cont)

• Thus reverse cash and carry is profitable only if
  the Implied Reverse Repo Rate is less than the
  lending rate.
• What the arbitrageur has effectively done is that
  he has sold a zero coupon instrument with a face
  value of Rs 104 for a price of Rs 100.

25
Illustration (Cont)

• Thus, a short position in the asset combined with
  a long position in the forward contract is
  equivalent to a short position in a zero coupon
  instrument.

26
The No-Arbitrage Condition

• In order to rule out cash and carry arbitrage, we
  require that
• F ? S(1r)
• In order to rule out reverse cash and carry
  arbitrage we require that
• F ? S(1r)
• Hence to rule out both forms of arbitrage it
  must be the case that F S(1r)

27
Hedging with Futures

• Consider a person who owns an asset.
• Technically speaking he is said to have a long
  position in the asset.
• His worry will always be that the price of the
  asset will decline by the time he is ready to
  sell it.
• Such a person can hedge by going short in a
  futures contract.

28
Illustration

• Gaurav owns 100 kg of rice which he wishes to
  sell after 3 months.
• His worry is that the price will fall by then.
• Assume that he can go short in a futures contract
  at a price of Rs 12 per kg.
• If he were to take a short position in such a
  contract he is assured of an amount of
• Rs 1200 irrespective of what the price is three
  months hence.

29
Illustration

• Remember that a short futures position is an
  obligation to sell.
• Hence while he is assured of a sum of
• Rs 1200, he cannot take advantage of the
  situation if the market price after three months
  were to be greater than Rs 12 per kg.

30
An Options Hedge

• On the contrary assume that Gaurav had bought a
  put option for hedging.
• If the market price of the asset were to fall, he
  can exercise the put and sell at the
  pre-specified price as per the options contract.
• However if the market price were to rise, he can
  forego the option to exercise, and simply sell
  the asset in the spot market.

31
Illustration

• Assume that Gaurav has bought a put option which
  gives him the right to sell at Rs 12 per kg after
  three months.
• If the spot market price after three months is
  less than Rs 12, he will exercise the option and
  sell at Rs 12.
• However if the spot market price is greater than
  Rs 12, then he will sell at the market price.

32
Illustration (Cont)

• Thus he is assured of a minimum price of Rs 12
  per kg.
• Notice that he cannot be forced to exercise the
  option, since an option is a right and not an
  obligation.

33
Hedging a Short Position

• If you have a short position in the asset, it
  means that you have made a sale transaction
  without owning the asset.
• Thus you have to procure it at the prevailing
  market price.
• Consequently your worry is that prices would have
  increased by the time you acquire the asset.

34
Hedging with Futures

• Such an investor can hedge by going long in a
  futures contract.
• This way he can lock in a price at which he can
  acquire the asset, and will therefore be
  protected against rising prices.

35
Illustration

• Vinayak has short sold a share of TISCO and is
  required to buy it back after 2 weeks.
• His worry is that the share price will have risen
  by then.
• Assume that he can go long in a futures contract
  at a price of Rs 105.
• If so he can be assured of being able to buy at
  this price.

36
Illustration (Cont)

• However, if the market price after 2 weeks were
  to be less than Rs 105, he will be unable to take
  advantage of the situation.
• This is because a futures contract is an
  obligation.

37
Hedging with Options

• The situation would be different if Vinayak were
  to use a call option for hedging.
• If the market price after 2 weeks were to be
  higher, he can exercise the option and buy at the
  pre-specified price as per the contract.
• However, if the market price were to be lower, he
  can forget the option and buy at the prevailing
  market price.

38
Illustration

• Assume that Vinayak has bought call options which
  give him the right to buy shares of TISCO at Rs
  105 per share.
• If the market price after 2 weeks is greater than
  Rs 105 then he will exercise the option and buy
  at Rs 105.
• Otherwise he will simply buy at the market price.

39
Futures or Options?

• As you can see, although both futures and options
  facilitate hedging, they work differently and are
  not substitutes for each other.
• Futures contracts lock in the price at which the
  hedger can buy or sell the asset.
• Options however give protection on one side,
  while permitting the hedger to benefit from
  favourable price movements on the other side.

40
Futures or Options?

• If options give one-sided protection without
  precluding the hedgers ability to benefit from
  favourable price movements on the other, then why
  would any one use futures for hedging?

41
Why Futures?

• When a futures contract is entered into, the
  futures price is set in such a way that the value
  of the contract to both the parties is zero.
• Thus neither party need pay to get into a futures
  position.
• Both of them have to post margins. But this is a
  performance bond and not a cost.

42
Options

• In the case of an option, whether it is a call or
  a put, the buyer has to pay a price to the writer
  at the outset, in order to acquire the right.
• This price is called the Option Price or the
  Option Premium.
• This amount cannot be recovered if the buyer were
  to decide not to exercise the option subsequently.

43
Option Prices and Exercise Prices

• The option price should not be confused with the
  exercise price.
• The exercise price is what the option holder has
  to pay per unit of the asset, if he decides to
  exercise the option.
• Thus, in our example, the price of Rs 105
  that was payable per share of TISCO by Vinayak
  was the exercise price.

44
The Hedgers Choice

• The hedger can either pay nothing and lock in a
  price to buy or to sell, using a futures
  contract.
• Or else he can pay and acquire an option. In this
  case if the market moves against him, he can
  exercise the option. Else if it moves in his
  favour, he can forget the option and transact at
  the spot price.

45
The Hedgers Choice (Cont)

• Thus options and futures are not interchangeable
  from the standpoint of hedging.
• The choice of the instrument would consequently
  depend on the individual investor.

46
Speculation

• Unlike hedgers who are trying to avoid risk,
  speculators wish to consciously take on risk.
• A speculator will take on either a long or a
  short position depending on his hunch as to
  whether the market is going to rise or to fall.
• If he calls the market right, he can make
  enormous profits.

47
Speculation (Cont)

• Else if he reads the market wrong, he can make
  substantial losses.
• Speculation is not the same as Gambling from an
  economics standpoint.
• Gambling means to take on a risk for the sheer
  thrill of risk taking, irrespective of whether or
  not the returns are commensurate.

48
Speculation (Cont)

• Speculation on the other hand means the taking of
  a Calculated Risk.
• A speculator will take a bet on the market only
  if he perceives the expected return to be
  commensurate with the level of risk involved.

49
Speculating With Futures

• Consider an investor who is of the view that the
  market is going to rise.
• One way for him to speculate would be to buy the
  asset in the spot commodity and hold it.
• However if he buys the asset in the spot
  commodity, he would have to pay the full price of
  the asset.

50
Speculating With Futures (Cont)

• Paying the full price means incurring substantial
  costs or opportunity costs.
• In addition, if the commodity is a physical
  asset, the investor would have to take the hassle
  of storing it and insuring it.
• All this can be avoided if he were to speculate
  using the futures market.

51
Speculating With Futures (Cont)

• The principle involved is the same.
• Such a speculator is betting that the market is
  going to move up.
• So instead of buying the asset in the spot
  market, he can take a long position in the
  futures market.

52
Speculating With Futures (Cont)

• If the spot price were to rise the speculator
  will obviously realize a profit since he can
  acquire the asset at the initial futures price,
  and sell it at the terminal spot price.

53
Speculating With Futures (Cont)

• The advantage of speculating with futures is that
  the entire value of the asset need not be paid in
  order to acquire a long position.
• All that the speculator has to do is to deposit
  the required margin.
• Secondly, because of the high volumes of
  transactions involved, transactions costs are
  much lower in futures markets.

54
Illustration

• Let us assume that the current futures price for
  a contract calling for delivery of rice three
  months hence is Rs 12 per kg.
• Abhishek, a speculator, is of the opinion that
  the price three months hence will be at least Rs
  15.
• He therefore chooses to speculate by going long
  in a futures contract, which we will assume is
  for 100 kg of rice.

55
Pitfalls

• Remember, a long futures position is an
  obligation to buy.
• If Abhishek were to have read the market wrong,
  and the price after 3 months were to be Rs 9 per
  kg, then he would incur a loss of Rs 300.

56
Pitfalls (Cont)

• This is because while he still has to acquire the
  rice at Rs 12 per kg, he can only sell it for Rs
  9.
• Thus speculation with futures can lead to
  substantial gains if one forecasts price
  movements accurately, but can lead to substantial
  losses otherwise.

57
Illustration (Cont)

• If he is right, and the market price three months
  hence turns out to be Rs 16 per kg, then he
  can simply sell the rice at this price after
  taking delivery under the futures contract.
• He will obviously make a profit of Rs 400
  on the deal.

58
Using Options for Speculation

• It turns out that a speculator like Abhishek
  could have used an options contract too for
  speculation.
• Since he expects the market to rise, he ought to
  go in for a call option.
• If the market does indeed rise, he can acquire
  the asset by exercising the call and paying the
  exercise price, and then sell it at the market
  price.

59
Illustration

• Let us assume that call options are available on
  rice for delivery three months hence, with an
  exercise price of Rs 12.
• Assume that each contract is for 100 kg and that
  Abhishek buys one contract.
• If his hunch is right and the prevailing market
  price after three months is Rs 16, then he
  will exercise his option.

60
Illustration (Cont)

• When he exercises, he will acquire 100 kg at Rs
  12 per kg.
• The rice can then be sold at Rs 16 per kg.
• Thus in this case too he will make a profit of Rs
  400.

61
The Difference

• In the case where Abhishek speculated with
  futures, the cost of reading the market wrong
  were significant.
• If the terminal price were to be Rs 9 per kg, he
  would lose Rs 300.
• If it were to be Rs 6 per kg, he would lose even
  more, that is, Rs 600.

62
The Difference (Cont)

• Speculating with options is clearly different.
• If the terminal price of rice were to be Rs 9 per
  kg, then Abhishek will simply refrain from
  exercising.
• If so, the amount that he will lose is the option
  premium that was paid initially to take the
  position.

63
The Difference (Cont)

• If we assume that the option premium per kg of
  rice is Rs 0.75, then the amount that is lost
  will be Rs 75 if the options are not exercised.
• This will be the case if the terminal asset price
  is less than or equal to Rs 12.
• This amount of Rs 75, is the maximum possible
  loss for Abhishek.

64
Interchangeable?

• A speculator who uses futures contracts has to to
  deposit only a small margin.
• However to speculate using options, you have to
  pay a premium that is non-refundable.
• In our illustration the premium was Rs 0.75
  per kg.

65
Interchangeable? (Cont)

• If the terminal market price were to be
• Rs 11.25 or above then speculating with futures
  will be more profitable than speculating with
  options.
• If the price were to be between Rs 11.25 and
• Rs 12, then the loss from the futures position
  would be less than or equal to Rs 75 for 100 kg.
• In this price range, the loss from the options
  position would be Rs 75, which represents the
  entire premium, since the options will not be
  exercised.

66
Interchangeable? (Cont)

• If the terminal market price were to exceed Rs
  12, then both the options as well as the futures
  position would be profitable.
• However, once the cost of the options is
  deducted, the futures position would lead to a
  greater profit of Rs 75.
• If the terminal market price were to be less than
  Rs 11.25 per kg then the loss from the options
  position would be Rs 75.

67
Interchangeable? (Cont)

• The maximum possible loss from the futures
  position is Rs 1125, since the lowest possible
  market price for the asset is Rs 0.
• Thus futures and options are not interchangeable
  from the standpoint of speculation, although they
  both facilitate speculation.

68
Speculation by Bears

• A person who anticipates that the market will
  move up is a Bull.
• He can speculate by either going long in futures,
  or by buying call options.
• An investor who anticipates that the market will
  fall is called a Bear.
• A Bear can speculate by going short in futures or
  by buying put options.

69
Bears Futures Contracts

• Consider a person who feels that the market is
  going to fall.
• He can speculate by going short in futures.
• If his hunch turns out be right, he can acquire
  the underlying asset at the terminal market price
  and deliver it under the contract at the initial
  futures price, which by assumption is higher.

70
Illustration

• Nisha is a speculator like Abhishek.
• However she feels that the price of rice after
  three months will not be more than Rs 9 per kg.
• The current futures price is Rs 12 per kg.
• She can take a speculative position by going
  short in a futures contract.

71
Illustration (Cont)

• Assume that her hunch is right and that the
  market price at the end of three months is Rs 8.
• She can now acquire the asset in the spot market
  for Rs 8 and deliver as per the contract at Rs
  12, thereby making a profit of Rs 400 for 100 kg.

72
Bears Options

• It turns out that Nisha could have used options
  too for speculation.
• Assume that put options are available for the
  delivery of rice three months hence at an
  exercise price of Rs 12 per kg. Let the option
  premium be Rs 0.50 per kg.
• If Nisha buys put options equivalent to 100 kg,
  and if the market price after three months is Rs
  8 per kg, then she can buy in the market at Rs 8
  and deliver as per the contract at Rs 12.

73
Interchangeable?

• In our example, if the terminal asset price were
  to be Rs 8, then both futures as well as options
  lead to a profit of Rs 400.
• However there are certain points to be noted.
• Firstly, after the option premium is taken into
  account, the profit from the options strategy
  will be less.

74
Interchangeable? (Cont)

• Secondly if the market were to have risen instead
  of declining then Nisha would have simply
  refrained from exercising the put options, and
  her loss would have been restricted to the
  initial premium of Rs 50.
• However, had she chosen a futures contract for
  hedging, in principle, her loss could have been
  much higher.

75
Interchangeable? (Cont)

• For instance, if the terminal asset price were to
  be Rs 15 per kg, then if Nisha had used a futures
  position, she would have to buy at Rs 15 and
  deliver as per the contract at
• Rs 12, thereby making a loss of Rs 300.
• However had she chosen options for speculation,
  she would have lost only Rs 50.

76
Interchangeable (Cont)

• On the contrary for any asset price less than or
  equal to Rs 12.50, the profit from the futures
  position would be higher.
• If the asset price were to be between Rs 12 and
  Rs 12.50, the loss from the futures position
  would be less than or equal to Rs 50.

77
Interchangeable (Cont)

• In such a scenario the options would not be
  exercised and the loss would be equal to the
  initial premium of Rs 50.
• If the terminal asset price were to be less than
  Rs 12 per kg, the profit from the futures
  position would always be Rs 50 more than the
  profit from the options position.

78
Interchangeable (Cont)

• Once again, while options and futures both
  facilitate speculation by Bears, they are not
  interchangeable, in the sense that one strategy
  does not dominate the other for all possible
  types of investors.