Ch. 8: Int’l Equity Markets
• Approximately 90% of global equity market
  capitalization is in the developed world.
• Rema...
Emerging Equity Markets
• Most global equity funds allocate ~5% of
  total assets to emerging markets.
• But, this is quit...
Emerging Markets Overview




Notes: (1) Sharpe Ratio = (portfolio return – risk-free rate)/portfolio
standard deviation. ...
How do we measure liquidity?
• Turnover ratio: ratio of stock market
  transactions over a period of time divided
  by the...
Liquidity
• The equity markets of the developed world tend to
  be much more liquid than emerging markets.
• Turnover rati...
Market Concentration
• Concentration ratio = ratio of 10 largest stocks
  traded as a fraction of total market capitalizat...
International Equity Market
            Benchmarks
• Morgan Stanley Capital International Perspective
  (MSCI) = the main ...
World Equity Benchmark Shares
• Each fund is designed to approximate the return
  pattern of a designated MSCI country ben...
Cross-Listing of Shares
• A firm has its equity shares listed on one or
  more foreign exchanges.
• The number of firms do...
Why would a firm cross-list?
1. Expanded investor base
   a. Increased demand for stock  raise price  increase
      mar...
American Depository Receipts
• An ADR is issued by a U.S. Bank, consisting of a
  bundle of shares of a foreign corporatio...
ADRs – more!
• ADRs can be bought or sold just like the stocks of
  U.S. companies, and ADR trades clear and settle
  just...
Types of ADRs
• Sponsored ADRs
  – Created by a bank at the request of the foreign
    company that issued the underlying ...
Unsponsored ADRs
• Created at the request of a US investment bank
  without direct involvement by the foreign issuing
  fi...
Factors Affecting International
          Equity Returns
• Macroeconomic factors
   – Imperfect correlation of internation...
Trends in Equity Issuance
                                                              • Int‘l equity issuance has
      ...
Ch. 9: Futures & Options on
            Forex
• Why do we study these tools?
  – Provide a more comprehensive understandin...
Futures vs. Forwards
     • A futures contract is like a forward contract:
             – It specifies that a certain curr...
Timing: Spot Transaction




                           19
Timing: Forward




                  20
Timing: Futures




 Implies daily changes
 in margin account.



                         21
Standard Features of
           Futures Contracts
• Standardizing Features:
  – Contract Size (varies across exchanges and...
Initial Margin Requirements
• Margin requirements are complex and are not the
  same for writers of options on different t...
Settlement Terminology
• Buyer holds a long position (seller – short).
• If today‘s settlement price is higher than
  yest...
Daily Resettlement: An Example
     • Suppose you want to speculate on a rise in the $/¥
       exchange rate (specificall...
Daily Resettlement: An Example
• Currently $1 = ¥140 and it appears that the
  dollar is strengthening.
• If you enter int...
Daily Resettlement: An Example
• If tomorrow, the futures rate closes at $1 = ¥149,
  then your position‘s value drops.
• ...
Daily Resettlement: An Example
 • The $559.28 comes out of your $3,333.33 margin
   account, leaving $2,774.05
 • This is ...
Basic Futures Terminology
• Open Interest refers to the number of contracts
  outstanding for a particular delivery month....
Open Interest
                                                   •When a contract month first
                            ...
Reversing Trades
• Rare in forward markets – about 90% of all
  contracts lead to eventual delivery of the
  underlying as...
Interest Rate Parity
• FT(¥/$) = S0(¥/$) * [(1+rUS)/(1+r¥)]T
• This theory worked for forwards (remember
  chapter 5?). An...
Eurodollar Interest Rate
                        Futures Contracts
     • Widely used futures contract for hedging short-
...
Reading Eurodollar Futures Quotes
EURODOLLAR (CME)—$1 million; pts of 100%

            Open      High    Low     Settle  ...
Futures Contracts vs. Options
• Futures Contract – you‘ve agreed to
  purchase/sell the contract. No backing out
  but you...
Options
 • An option gives the holder the right, but not
   the obligation, to buy or sell a given quantity
   of an asset...
Currency Futures Options
     • Are an option on a currency futures contract.
     • Exercise of a currency futures option...
Examples of Terminology
• Long on futures contract = buy futures contract.
  (can also go short)
   – Commitment – guarant...
Examples of Terminology (2)
• Long call on futures option = buy option to
  purchase a pre-specified amount of a pre-speci...
Options Contracts: Preliminaries
     • Intrinsic Value
             – The difference between the exercise price of the op...
Currency Options Markets
•   PHLX = Philadelphia Stock Exchange
•   HKFE = Hong Kong Futures Exchange
•   20-hour trading ...
European vs. American options
     • With an American option, you can do
       everything that you can do with a European...
Basic Option Pricing
                      Relationships at Expiry
     • At expiry, an American call option is worth
    ...
Basic Option Profit Profiles:
                       Long Call
                      CaT = CeT = Max[ST - E, 0]

         ...
Basic Option Profit Profiles:
                       Short Call
                      CaT = CeT = Max[ST - E, 0]

        ...
Basic Option Pricing
                      Relationships at Expiry
     • At expiry, an American put option is worth
     ...
Basic Option Profit Profiles:
                        Long Put
                      PaT = PeT = Max[E - ST, 0]

         ...
Basic Option Profit Profiles:
                        Short Put
                      PaT = PeT = Max[E - ST, 0]

        ...
Currency Futures Options




The #s in the ‗call‘ and ‗put‘ columns denote the premium for a call or put expiring
in the s...
Test Theory: Expiration Value of an
     American Call Option (~Ex 9.4)
• CaT = CeT = Max[ST - E, 0]
• Given that the stri...
Currency Futures Options




The #s in the ‗call‘ and ‗put‘ columns denote the premium for a call or put expiring
in the s...
Test Theory: Expiration Value of an
      American Put Option (~Ex 9.5)
• PaT = PeT = Max[E - ST, 0]
• Given that the stri...
Market Value, Time Value and
Intrinsic Value for an American Call
                              CaT > Max[ST - E, 0]
     ...
Interpretation of Graph
• Intrinsic Value – you only care about it
  when you make a profit. Hence, this line
  was trunca...
How is a call (or put) priced?
•  Given that CaT > Max[ST - E, 0], the market
   value of this call will be greater or equ...
One Very Important Caveat
• When we discuss whether to exercise a call or put
  at expiration we examine only the marginal...
Sailing in Uncharted Waters?
•    How do you decide to go long/short a call/put or
     to buy a contract vs. an option?
 ...
Hedging Your Bets
• Suppose you aren‘t sure which way an exchange
  rate will move. Could go up or down. If you
  guess wr...
European Option Pricing
                           Relationships
Consider two investments:
1 Buy a call option on the Brit...
European Option Pricing
                           Relationships
            • When the option is in-the-money both
      ...
European Option Pricing
                           Relationships
            • Using a similar portfolio to replicate the
...
Option Value Determinants
                                         Call Put
1.      Exchange rate (S)                  +  ...
Portfolio Evaluation (1)
      • Imagine a simple world where the dollar-euro
        exchange rate is S0($/ ) = $1 today ...
Portfolio Evaluation (2)
      • A call option on the euro with exercise price
        S0($/ ) = $1 will have the followin...
Portfolio Evaluation (3)
Borrow the present value of $.90 today and buy 1.
Your net payoff in one period is either $.20 or...
Portfolio Evaluation (4)
• In this example, the portfolio has twice the
  option‘s payoff so the portfolio is worth twice ...
Portfolio Evaluation (5)
      • The most important lesson to draw from this is
        that a position can be replicated ...
Technical Extension
• We‘ve determined the lower bounds on call & put
  premiums but have not figured out exact pricing.
•...
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  1. 1. Ch. 8: Int’l Equity Markets • Approximately 90% of global equity market capitalization is in the developed world. • Remaining 10% of global equity market capitalization is in emerging markets. • Emerging markets are growing faster but have greater volatility. 1
  2. 2. Emerging Equity Markets • Most global equity funds allocate ~5% of total assets to emerging markets. • But, this is quite sizeable in relation to the market capitalization of emerging stock markets. • Example: In 2001 total emerging market exposure of global equity funds was approximately US$108bn – or about the size of Korea‘s total market capitalization! Source: IMF Global Financial Stability Report, June 2002 2
  3. 3. Emerging Markets Overview Notes: (1) Sharpe Ratio = (portfolio return – risk-free rate)/portfolio standard deviation. Indicates whether returns reflect wise investments or excess risk. (2) Why divide data at ‘94? Mexico crisis. Source: http://www.imf.org/external/pubs/ft/GFSR/2002/02/pdf/chp4.pdf 3
  4. 4. How do we measure liquidity? • Turnover ratio: ratio of stock market transactions over a period of time divided by the size, or market capitalization , of the market. • Higher ratio  more liquid market, easier to trade equities. • Liquidity refers to how quickly an asset can be sold without a major price concession. 4
  5. 5. Liquidity • The equity markets of the developed world tend to be much more liquid than emerging markets. • Turnover ratio varies markedly over time and across markets (e.g. US 71% in ‘94… 98% in ‘98) • Sharp swings might reflect external macro or political factors that influence local demand for equities. – Example: Hong Kong was 55% in ‘94, 35% in ‘95, 37% in ‘96, 118% in ‘97 and then 60% in ‘98! 5
  6. 6. Market Concentration • Concentration ratio = ratio of 10 largest stocks traded as a fraction of total market capitalization of all equities traded. • When this is high, it may be harder to diversify a portfolio within the country as there are fewer investment opportunities. • Emerging markets tend to be much more concentrated. A small # of firms have greater impact on local market. • Example: China was 18% in ‘98 but the Philippines was 55% at same time. 6
  7. 7. International Equity Market Benchmarks • Morgan Stanley Capital International Perspective (MSCI) = the main benchmark. – Monthly index covering 23 national stock market indices from developed countries. – Includes 85% of market cap of each industry within the country. All stocks are market-value weighted. (Effective since 2002; book says 60%.) – Also publishes regional and global indices. – Used by most funds/banks to recommend international investment strategy. ―Overweight relative to MSCI.‖ – http://www.msci.com/equity/index.html 7
  8. 8. World Equity Benchmark Shares • Each fund is designed to approximate the return pattern of a designated MSCI country benchmark index. • Country-specific baskets of stocks designed to replicate the country indexes of 14 countries. • WEBS are subject to U.S. SEC and IRS diversification requirements. Trade as shares on the American Stock Exchange. • Low cost, convenient way for investors to hold diversified investments in several different countries. • Trading since March 1996. 8
  9. 9. Cross-Listing of Shares • A firm has its equity shares listed on one or more foreign exchanges. • The number of firms doing this has exploded in recent years. 9
  10. 10. Why would a firm cross-list? 1. Expanded investor base a. Increased demand for stock  raise price  increase market liquidity. b. Make hostile takeovers more difficult and less likely. 2. Increases name recognition in a market  stimulate local demand for company‘s services. 3. Increases name recognition in other markets & to other customer groups  easier for the firm to raise capital in the future. 10
  11. 11. American Depository Receipts • An ADR is issued by a U.S. Bank, consisting of a bundle of shares of a foreign corporation that are being held in custody overseas. The foreign entity must provide financial information to the sponsor bank. • Offers U.S. investors a convenient way to add global exposure to their portfolios. – Lower administrative costs. – Avoid foreign taxes on each transaction. 11
  12. 12. ADRs – more! • ADRs can be bought or sold just like the stocks of U.S. companies, and ADR trades clear and settle just like U.S. stock trades. • ADRs are listed on either the NYSE, AMEX, or Nasdaq. • ADRs do not eliminate the currency and economic risks for the underlying shares in another country. • In early ‘90s about 60% of int‘l equity issues were in the form of ADRs; closer to 80% in ‘00-‘02. 12
  13. 13. Types of ADRs • Sponsored ADRs – Created by a bank at the request of the foreign company that issued the underlying security. – Largely a historical anomaly now. – (Not important to us.) • Unsponsored ADRs – Levels I, II and III 13
  14. 14. Unsponsored ADRs • Created at the request of a US investment bank without direct involvement by the foreign issuing firm. • Level I: Most basic type of ADR. Foreign companies either don‘t qualify or don‘t wish to list on an exchange. Trade on the OTC market. Does not have to comply with US GAAP or full SEC disclosure. • Level II: Listed on an exchange or quoted on Nasdaq. Slightly more requirements from the SEC. • Level III: Most prestigious! Issuer floats a public offering on a US exchange. 14
  15. 15. Factors Affecting International Equity Returns • Macroeconomic factors – Imperfect correlation of international business cycles (not all countries experience ups/downs at same time). – Weak influence. • Exchange rates – Cross-correlation of equity and forex markets is low but positive. • Industrial Structure – Some countries are more similar  greater correlation of equity market movement • Politics and sentiment 15
  16. 16. Trends in Equity Issuance • Int‘l equity issuance has far exceeded domestic issuances in recent years. • Enables top-quality emerging market companies to raise capital at lower cost. • But, might dampen efforts to develop local equity markets. Source: http://www.imf.org/external/pubs/ft/GFSR/2002/02/pdf/chp4.pdf 16
  17. 17. Ch. 9: Futures & Options on Forex • Why do we study these tools? – Provide a more comprehensive understanding of the foreign exchange markets. – Risk-management. – Potential profit-making tool. 17
  18. 18. Futures vs. Forwards • A futures contract is like a forward contract: – It specifies that a certain currency will be exchanged for another at a specified time in the future at prices specified today. • A futures contract is different from a forward contract: – Futures are standardized contracts trading on organized exchanges with daily resettlement through a clearinghouse. Source: McGraw/Hill 18
  19. 19. Timing: Spot Transaction 19
  20. 20. Timing: Forward 20
  21. 21. Timing: Futures Implies daily changes in margin account. 21
  22. 22. Standard Features of Futures Contracts • Standardizing Features: – Contract Size (varies across exchanges and currencies but is constant over time; look at p.211) – Delivery Month (March, June, Sept, Dec.) – Daily resettlement  ―marked-to-market‖ daily at the settlement price (closing price). 22
  23. 23. Initial Margin Requirements • Margin requirements are complex and are not the same for writers of options on different types of contracts. • Margin requirements are subject to change, and may vary between brokerage firms. • Held as collateral by broker. • Usually ~2-4% of contract value paid in cash or T- bills. • Account balance fluctuates because of daily resettlement. • Margin amount is the same for short & long positions. 23
  24. 24. Settlement Terminology • Buyer holds a long position (seller – short). • If today‘s settlement price is higher than yesterday‘s, the buyer has a positive settlement for the day. This means the futures price of the underlying asset has increased. A long position in the contract is now worth more. • Exact opposite for the seller. • Thus, this is a zero-sum game. 24
  25. 25. Daily Resettlement: An Example • Suppose you want to speculate on a rise in the $/¥ exchange rate (specifically you think that the dollar will appreciate). Currency per U.S. $ equivalent U.S. $ Wed Tue Wed Tue Japan (yen) 0.007142857 0.007194245 140 139 1-month forward 0.006993007 0.007042254 143 142 3-months forward 0.006666667 0.006711409 150 149 6-months forward 0.00625 0.006289308 160 159 Currently $1 = ¥140. The 3-month forward price is $1=¥150. Source: McGraw/Hill 25
  26. 26. Daily Resettlement: An Example • Currently $1 = ¥140 and it appears that the dollar is strengthening. • If you enter into a 3-month futures contract to sell ¥ at the rate of $1 = ¥150 you will make money if the yen depreciates. The contract size is ¥12,500,000 • Your initial margin is 4% of the contract value: $1 $3,333.33 .04 ¥12,500,00 0 Source: McGraw/Hill ¥150 26
  27. 27. Daily Resettlement: An Example • If tomorrow, the futures rate closes at $1 = ¥149, then your position‘s value drops. • Your original agreement was to sell ¥12,500,000 and receive $83,333.33 • But now ¥12,500,000 is worth $83,892.62 $1 $83,892 .62 ¥12,500,00 0 ¥149 You have lost $559.28 overnight. Source: McGraw/Hill 27
  28. 28. Daily Resettlement: An Example • The $559.28 comes out of your $3,333.33 margin account, leaving $2,774.05 • This is short of the $3,355.70 required for a new position. $1 $3,355.70 .04 ¥12,500,00 0 ¥149 • Your broker will let you slide until you run through your maintenance margin. Then you must post additional funds (variation margin) or your position will be closed out. This is usually done with a reversing trade. Source: McGraw/Hill 28
  29. 29. Basic Futures Terminology • Open Interest refers to the number of contracts outstanding for a particular delivery month. • Open interest is a good proxy for demand for a contract. • Some refer to open interest as the depth of the market. The breadth of the market would be how many different contracts (expiry month, currency) are outstanding. 29
  30. 30. Open Interest •When a contract month first starts trading, open interest is technically zero. •Open interest increases over time, until positions are liquidated heading into expiration. •―Total open interest‖ is the total number of outstanding positions in all the delivery months of a futures market. •Liquidity implies at least 5,000 outstanding contracts. 30 http://www.activetradermag.com/futuresbasics.htm
  31. 31. Reversing Trades • Rare in forward markets – about 90% of all contracts lead to eventual delivery of the underlying assets. • Commonplace in futures markets – only about 1% of all contracts lead to delivery! – This reflects the regularity of buyers purchasing offsetting positions and high liquidity. 31
  32. 32. Interest Rate Parity • FT(¥/$) = S0(¥/$) * [(1+rUS)/(1+r¥)]T • This theory worked for forwards (remember chapter 5?). And now we can use it again! – Why? If it doesn‘t hold then there exists an opportunity to arbitrage differences between the futures and forwards markets. 32
  33. 33. Eurodollar Interest Rate Futures Contracts • Widely used futures contract for hedging short- term U.S. dollar interest rate risk. • The underlying asset is a hypothetical $1,000,000 90-day Eurodollar deposit—the contract is cash settled. – This means profits/losses are realized in the margin account based on the final settlement price on the last day of trading. Source: McGraw/Hill 33
  34. 34. Reading Eurodollar Futures Quotes EURODOLLAR (CME)—$1 million; pts of 100% Open High Low Settle Chg Yield Open Settle Change Interest June 94.69 94.69 94.68 94.68 -.01 5.32 +.01 47,417 Eurodollar futures prices are stated as an index number of three- month LIBOR calculated as F = 100-LIBOR. The closing price for the June contract is 94.68 thus the implied yield is 5.32 percent = 100 – 94.68 The change was .01 percent of $1 million (1 basis point) representing $100 on an annual basis. Since it is a 3-month contract one basis point corresponds to a $25 price change. Source: McGraw/Hill 34
  35. 35. Futures Contracts vs. Options • Futures Contract – you‘ve agreed to purchase/sell the contract. No backing out but you can offset or exit a position by buying/selling to someone else. – Buy = long; sell = short. • Option – contract that gives you the right but not the obligation to purchase/sell something at pre-specified terms. No commitment. 35
  36. 36. Options • An option gives the holder the right, but not the obligation, to buy or sell a given quantity of an asset in the future, at prices agreed upon today. • Calls vs. Puts: – Call options – right to buy an asset at some time in the future at prices agreed upon today. – Put options – right to sell an asset at some time in the future at prices agreed upon today. Source: McGraw/Hill 36
  37. 37. Currency Futures Options • Are an option on a currency futures contract. • Exercise of a currency futures option results in a long futures position for the holder of a call or the writer of a put. • Exercise of a currency futures option results in a short futures position for the seller of a call or the buyer of a put. • If the futures position is not offset prior to its expiration, foreign currency will change hands. Source: McGraw/Hill 37
  38. 38. Examples of Terminology • Long on futures contract = buy futures contract. (can also go short) – Commitment – guarantees you a certain quantity of a certain currency on a specific date. • Intuition: – Similar to forward in many respects. – Lower transaction costs because it is a standardized commodity. – Easy to re-sell. 38
  39. 39. Examples of Terminology (2) • Long call on futures option = buy option to purchase a pre-specified amount of a pre-specified foreign currency at a pre-set price on an agreed upon date. (can also go short) • Intuition: – Preserve flexibility. – Leeway to change your opinion about a currency‘s trajectory over a specified time-frame. – Limits downside potential. 39
  40. 40. Options Contracts: Preliminaries • Intrinsic Value – The difference between the exercise price of the option and the spot price of the underlying asset. • Speculative Value – The difference between the option premium and the intrinsic value of the option. Option Intrinsic + Speculative = Premium Value Value Source: McGraw/Hill 40
  41. 41. Currency Options Markets • PHLX = Philadelphia Stock Exchange • HKFE = Hong Kong Futures Exchange • 20-hour trading day. • OTC volume is much bigger than exchange volume. (~ 46x) Why? Regulatory restrictions – great explanation on p. 217. • Trading is in six major currencies against the U.S. dollar. (Australian dollar, British pound, Canadian dollar, Japanese yen, Swiss franc, Euro) 41
  42. 42. European vs. American options • With an American option, you can do everything that you can do with a European option—this option to exercise early has value. CaT > CeT = Max[ST - E, 0] PaT > PeT = Max[E - ST, 0] Source: McGraw/Hill 42
  43. 43. Basic Option Pricing Relationships at Expiry • At expiry, an American call option is worth the same as a European option with the same characteristics. • If the call is in-the-money, it is worth ST – E. • If the call is out-of-the-money, it is worthless. CaT = CeT = Max[ST - E, 0] Source: McGraw/Hill 43
  44. 44. Basic Option Profit Profiles: Long Call CaT = CeT = Max[ST - E, 0] profit ST E+C E loss Source: McGraw/Hill 44
  45. 45. Basic Option Profit Profiles: Short Call CaT = CeT = Max[ST - E, 0] profit E ST E+C loss Source: McGraw/Hill 45
  46. 46. Basic Option Pricing Relationships at Expiry • At expiry, an American put option is worth the same as a European option with the same characteristics. • If the put is in-the-money, it is worth E - ST. • If the put is out-of-the-money, it is worthless. PaT = PeT = Max[E - ST, 0] Source: McGraw/Hill 46
  47. 47. Basic Option Profit Profiles: Long Put PaT = PeT = Max[E - ST, 0] profit ST E-p E loss Source: McGraw/Hill 47
  48. 48. Basic Option Profit Profiles: Short Put PaT = PeT = Max[E - ST, 0] profit ST E-p E loss Source: McGraw/Hill 48
  49. 49. Currency Futures Options The #s in the ‗call‘ and ‗put‘ columns denote the premium for a call or put expiring in the specified months. So a call expiring in March with a strike price of 8500 hundredths of a cent (or $0.85 per ¥100) sells for a premium of 0.83 but the premium is substantially higher for the April and May expiry dates. 49 Source: WSJ
  50. 50. Test Theory: Expiration Value of an American Call Option (~Ex 9.4) • CaT = CeT = Max[ST - E, 0] • Given that the strike price = 8500, we have locked in a rate of $0.85/100 yen  $10.625 mn. • Suppose the exercise price = 8400. – CaT = Max [8500-8400, 0] = 100. – This means we have the option to buy 12.5mn yen at the current price of $0.84 per 100 yen  profit of $125,000!  • Suppose the exercise price = 8600. – CaT = Max [8500-8600, 0] = 0. – Now, we‘d choose not to exercise the call because the exercise value is negative. 50
  51. 51. Currency Futures Options The #s in the ‗call‘ and ‗put‘ columns denote the premium for a call or put expiring in the specified months. So a put expiring in March with a strike price of 8500 hundredths of a cent (or $0.85 per ¥100) sells for a premium of 0.45 but the premium is substantially higher for the April and May expiry dates. 51 Source: WSJ
  52. 52. Test Theory: Expiration Value of an American Put Option (~Ex 9.5) • PaT = PeT = Max[E - ST, 0] • Given that the strike price = 8500, we have locked in a rate of $0.85/100 yen  $10.625 mn. • Suppose the exercise price = 8400. – PaT = Max [8400-8500, 0] = 0. – This means we have the option to sell 12.5mn yen at the current price of $0.84 per 100 yen (when we paid $0.85!). Now, we‘d choose not to exercise the call because the exercise value is negative. • Suppose the exercise price = 8600. – PaT = Max [8600-8500, 0] = 100. – This means we have the option to sell 12.5mn yen at the current price of $0.86 per 100 yen  profit of $125,000!  52
  53. 53. Market Value, Time Value and Intrinsic Value for an American Call CaT > Max[ST - E, 0] Profit Market Value Time value Intrinsic value E ST Out-of-the-money In-the-money loss We can draw similar pictures for puts. This is just 53 Source: McGraw/Hill an example to illustrate the existence of a premium.
  54. 54. Interpretation of Graph • Intrinsic Value – you only care about it when you make a profit. Hence, this line was truncated at ―zero‖. • Time Value – reflects a gamble that the option might be more profitable (more in- the-money) as time passes (i.e. before time of expiry). 54
  55. 55. How is a call (or put) priced? • Given that CaT > Max[ST - E, 0], the market value of this call will be greater or equal to this amount. Why? 1. CaT = intrinsic value of the call. Translation: when you actually make a profit, this is positive. Otherwise you don‘t care. 2. Premium = time-value of money. You expect that the call will be worth more at date of expiry. This reflects private information or beliefs. This will be largest when date of collection is most distant. 3. Market value = Time value + Intrinsic Value 55
  56. 56. One Very Important Caveat • When we discuss whether to exercise a call or put at expiration we examine only the marginal value of exercising the option at that date. • When we discuss profit we look at the relative values of strike and exercise price. • But what happened to the initial premium we paid to purchase the option? That is an up-front cost that we have already absorbed in its entirety. • Therefore we should really look at profits realized at time of option expiration net of initial costs. 56
  57. 57. Sailing in Uncharted Waters? • How do you decide to go long/short a call/put or to buy a contract vs. an option? 1. Hire PhD economists!  2. Purchase research reports and follow their recommendations (e.g. each bank publishes forecasts).* 3. Take a guess and pray your intuition is good. 4. Use 2 or 3 of these methods simultaneously. Most common is 1 & 2 together. • Which method is best? Depends! * Note the banks hire PhD economists too but the marginal cost to an individual company is lower. 57
  58. 58. Hedging Your Bets • Suppose you aren‘t sure which way an exchange rate will move. Could go up or down. If you guess wrong, you could lose big. • So, try to protect yourself by using a complicated scheme. • Instead of counting only on the future income generated by the futures contract (1), • you borrow and lend the present value of the expected value at time of expiration (2). • If your expectations are not fulfilled, you will have protected yourself via this hedge. 58
  59. 59. European Option Pricing Relationships Consider two investments: 1 Buy a call option on the British pound futures contract. The cash flow today is -Ce 2 Replicate the potential upside payoff of the call: a. Borrowing the present value of the exercise price of the call in the U.S. at i$ The cash flow today is E /(1 + i$) b. Lending the present value of ST at i£ The cash flow is - ST /(1 + i£) Source: McGraw/Hill 59
  60. 60. European Option Pricing Relationships • When the option is in-the-money both strategies have the same payoff. • When the option is out-of-the-money the borrowing and lending strategy has a higher payoff. Thus: S E T Ce max ,0 (1 i£ ) (1 i$ ) Source: McGraw/Hill 60
  61. 61. European Option Pricing Relationships • Using a similar portfolio to replicate the upside potential of a put, we can show that: E ST Pe max ,0 (1 i$ ) (1 i£ ) Source: McGraw/Hill 61
  62. 62. Option Value Determinants Call Put 1. Exchange rate (S) + – 2. Exercise price (E) – + 3. Interest rate in U.S. (i$) + – 4. Interest rate in other country (i£) – + 5. Variability in exchange rate + + 6. Expiration date + + 7. Interest rate spread (i$ - i£) + – The value of a call option C0 must fall within max (S0 – E, 0) < C0 < S0. The precise position will depend on the above factors. 62
  63. 63. Portfolio Evaluation (1) • Imagine a simple world where the dollar-euro exchange rate is S0($/ ) = $1 today and in the next year, S1($/ ) is either $1.10 or $.90. S0($/ ) S1($/ ) $1.10 $1 $.90 63 Source: McGraw/Hill
  64. 64. Portfolio Evaluation (2) • A call option on the euro with exercise price S0($/ ) = $1 will have the following payoffs. • We can replicate the payoffs of the call option with a levered position in the euro. S0($/ ) S1($/ ) C1($/ ) $1.10 $.10 $1 $.90 $0 64 Source: McGraw/Hill
  65. 65. Portfolio Evaluation (3) Borrow the present value of $.90 today and buy 1. Your net payoff in one period is either $.20 or $0. S0($/ ) S1($/ ) debt portfolio C1($/ ) $1.10 -$.90 $.20 $.10 $1 $.90 -$.90 $.00 $0 65 Source: McGraw/Hill
  66. 66. Portfolio Evaluation (4) • In this example, the portfolio has twice the option‘s payoff so the portfolio is worth twice the call option value. • The portfolio value today is today‘s value of one euro less the present value of a $.90 debt: $.90 $1 (1 i$ ) • We can value this option as half of the value of the portfolio: 1 $.90 C0 $1 2 (1 i$ ) 66
  67. 67. Portfolio Evaluation (5) • The most important lesson to draw from this is that a position can be replicated by building a portfolio. ―The replicating portfolio intuition.‖ • Many derivative securities can be valued by valuing portfolios of primitive securities when those portfolios have the same payoffs as the derivative securities. 67 Source: McGraw/Hill
  68. 68. Technical Extension • We‘ve determined the lower bounds on call & put premiums but have not figured out exact pricing. • To derive the exact pricing scheme, you‘d need to adjust for all possible scenarios: – volatility of exchange rate movements, – probabilities of appreciation and depreciation, and – the risk-free hedge ratio. • If you‘re really gung-ho about this, read pages 225-227 very carefully. Otherwise, spend just a few minutes on that section – enough time for your eyes to glaze over and you‘re done. 68
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