# Chapter 15 - Options Markets

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1 Chapter 15 - Options Markets Option contract Option trading Values of options at expiration Options vs. stock investments Option strategies Option-like securities Option contract Options are rights to buy or sell something at a predetermined price on or before a specified date American options vs. European options American options can be exercised at any time on or before the expiration date European options can only be exercised on the expiration date Assuming everything else is the same, which option should be worth more? remium: the purchase price of an option Call option gives its holder the right to buy an asset for a specified price, call the exercise price (strike price) on or before the a specified date (expiration date) Example: buy an IBM October call option with an exercise price of \$200 for \$5.00 (the premium is \$500). IBM is currently trading at \$191 per share. Details: this is a call option that gives the right to buy 100 share of IBM stock at \$200 per share on or before the third Friday in October rofits or losses on the expiration date If IBM stock price remains below \$200 until the option expires, the option will be worthless. The option-holder will lose \$500 premium. If IBM stock price rises to \$204 on the expiration date, the value of the option will be worth ( ) = \$4.00. The option-holder will lose \$100. If IBM stock price rises to \$210 on the expiration date, the value of the option will be worth ( ) = \$ The option-holder will make \$500 net profit. At what stock price, will the option-holder be break-even? Answer: at \$205 Rationale: if you expect that the stock price is going to move higher, you should buy call options 44

2 ut option gives its holder the right to sell an asset for a specified price, call the exercise price (strike price) on or before the a specified date (expiration date) Example: Buy an IBM October put option with an exercise price of \$185 for \$3.00. IBM is currently trading at \$191 per share. Details: this is a put option that gives the right to sell 100 shares of IBM stock at \$185 per share on or before the third Friday in October rofits or losses on the expiration date If IBM stock price falls to \$170 on the expiration date, the option will be worth ( ) = \$15. The option-holder will make \$1,200 net profit. If IBM stock price drops to \$183 on the expiration date, the value of the option will be worth ( ) = \$2.00. The option-holder will lose \$100. If IBM stock price remains above \$185 until the expiration date, the value of the option will be worthless. The option-holder will lose \$300 premium. At what stock price, will the option-holder be break-even? Answer: at \$182 Rationale: if you expect that the stock price is going to move lower, you should buy put options In-the-money option: an option where exercise would generate a positive cash flow Out-of-the-money option: an option where, if exercised, would generate a negative cash flow. Out of the money options should never be exercised. At-the-money option: an option where the exercise price is equal to the asset price Option trading OTC markets vs. organized exchanges Over-the-counter markets: tailor the needs of the traders, such as the exercise price, expiration date, and number of shares Organized exchanges: for example, the Chicago Board of Option Exchange (CBOE), standardized contracts Option clearing corporation (OCC): the clearinghouse between option traders to guarantees option contract performance 45

3 Other listed options Index options: the underlying asset is a stock index Futures options: the underlying asset is a futures contract Foreign currency options: the underlying asset is a foreign currency Interest rate options: the underlying assets are T-bonds, T-notes, or T-bills Values of options at expiration Two types of options: call options vs. put options Four positions: buy a call, sell (write) a call, buy a put, sell (write) a put Notations S 0 : the current price of the underlying asset X: the exercise (strike) price T: the time to expiration of option S T : the price of the underlying asset at time T C: the call price (premium) of an American option : the put price (premium) of an American option r: the risk-free interest rate : the volatility (standard deviation) of the underlying asset price In general, the payoff at time T, the expiration date is (1) ayoff to a call option holder is = max (S T - X, 0) or = S T - X if S T > X 0 if S T X For example, if S T = 100 and X = 95, then the payoff to the call option holder is 5; If S T = 90 and X = 95, then the payoff to the call option holder is 0. (2) ayoff to a call option writer is = min (X - S T, 0) = -max (S T - X, 0) or = -(S T - X) if S T > X 0 if S T X For example, if S T = 100 and X = 95, then the payoff to the call writer is -5; If S T = 90 and X = 95, then the payoff to the call option writer is 0. (1) is the mirror of (2) across of the x-axis (3) ayoff to a put option holder is = max (X - S T, 0) or = X - S T if S T < X 0 if S T X For example, if S T = 100 and X = 95, then the payoff to the put option holder is 0; If S T = 90 and X = 95, then the payoff to the put option holder is 5. 46

4 (4) ayoff to a put option writer is = min (S T - X, 0) = -max (X - S T, 0) or = -(X - S T ) if S T < X 0 if S T X For example, if S T = 100 and X = 95, then the payoff to the put option writer is 0; If S T = 90 and X = 95, then the payoff to the put option writer is -5. (3) is the mirror of (4) across of the x-axis ayoff ayoff ayoff ayoff 0 S T 0 S T 0 S T X X X S T 0 X (1) (2) (3) (4) rofit/loss diagrams (including the premium) for four option positions Buy a call Sell (write) a call Buy a put Sell (write) a put (1) Buy a call option: buy an October 90 call option at \$2.50 Stock price at expiration Buy October 90 \$ Net cost \$ rofit / loss Maximum Gain Unlimited Max loss Stock price (2) Write a call option: write an October 90 call at \$2.50 (exercise for students, the mirror of (1) across of the x-axis) 47

5 (3) Buy a put option: buy an October 85 put at \$2.00 Stock price at expiration Buy October 85 \$ Net cost \$ Max gain rofit / loss Max loss Stock price (4) Write a put option: write an October 85 put at \$2.00 (exercise for students, the mirror of (3) across of the x-axis) Options vs. stock investments Suppose you have \$9,000 to invest. You have three choices: (1) Invest entirely in stock by buying 100 shares, selling at \$90 per share (2) Invest entirely in at-the-money call option by buying 900 calls, each selling for \$10. (This would require buying 9 contracts, each would cost \$1,000. Each contract covers 100 shares.) The exercise price is \$90 and the options mature in 6 months. (3) Buy 1 call options for \$1,000 and invest the rest of \$8,000 in 6-month T-bill to earn a semiannual interest rate of 2%. Outcome: it depends on the underlying stock price on the expiration date Untab1504 excel outcome when the underlying stock price on the expiration data is \$85, \$90, \$95, \$100, \$105, and \$110 respectively Risk-return tradeoff: option investing is considered very risky since an investor may lose the entire premium. However, the potential return is high if the investor is right in betting the movements of the underlying stock price. Stock investing is less risky compared with option investing. 48

8 Chapter 17 - Futures Markets and Risk Management Futures contract Trading mechanics Futures market strategies Futures prices Financial futures Swaps Futures contract Forward contract vs. futures contract A forward contract is an agreement between two parties to either buy or sell an asset at a certain time in the future for a certain price. A forward contract, usually, is less formal, traded only in OTC markets, and contract size is not standardized. A futures contract is an agreement between two parties to either buy or sell an asset at a certain time in the future for a certain price. It is more formal, traded in organized exchanges, and contract size is standardized (focus). Comparison of futures and forward contracts Exchange trading Standardized contract size Marking to market Forward No No No Futures Yes Yes Yes Delivery Yes or cash settlement Usually closed out Delivery time One date Range of dates Default risk Some credit risk Virtually no risk Characteristics of futures contracts Opening a futures position vs. closing a futures position Opening a futures position can be either a long (buy) position or a short (sell) position (i.e., the opening position can be either to buy or to sell a futures contract) Closing a futures position involves entering an opposite trade to the original one The underlying asset or commodity: must be clearly specified 51

9 The contract size: standardized Corn and wheat: 5,000 bushels per contract Live cattle: 40,000 pounds per contract Cotton: 50,000 pounds per contract Gold: 100 troy ounces per contract DJIA: \$10*index Mini DJIA: \$5*index S& 500: \$250*index Mini S& 500: \$50*index Delivery month: set by the exchange Delivery place: specified by the exchange For example, a trader in June buys a December futures contract on corn at 500 cents (or \$5) per bushel Corn: underlying asset - commodity (commodity futures contract) Buy a futures contract: long position (promise to buy) 500 cents/bushel: futures price/delivery price 5,000 bushels: contract size - standardized December: delivery month Spot price: actual price in the market for immediate delivery If S T > \$5 (+) June: a trader buys a Dec.: the trader must Dec. futures contract on buy 5,000 bushels of If S T = \$5 (0) corn at 500 cents/bushel corn for \$25,000 If S T < \$5 ( ) rofit rofit 0 S T 0 S T X=\$5 X=\$5 Long position (buy futures) Short position (sell futures) X = delivery price = \$5/bushel and S T = the spot price at maturity (can be greater than, equal to, or less than \$5/bushel) 52

11 Marking to market and margin account Marking to market: the procedure that the margin account is adjusted to reflect the gain or loss at the end of each trading day Example: suppose an investor buys two gold futures contracts. The initial margin is \$2,000 per contract (or \$4,000 for two contracts) and the maintenance margin is \$1,500 per contract (or \$3,000 for two contracts). The contract was entered into on June 5 at \$850 and closed out on June 18 at \$ (Gold is trading around \$1,300 per ounce now.) Day Futures price (settlement) Daily gain (loss) Cumulative gain (loss) Margin balance Margin call (variation margin) ,000 June (400) (400) 3,600 June (100) (500) 3,500 June (300) 3,700 June (500) (800) 3,200 June (300) (1,100) 2,900 Yes (1,100) June (1,000) 4,100 June (700) 4,400 June (800) (1,500) 3,600 June (900) (2,400) 2,700 Yes (1,300) June (1,900) 4,500 Note: the investor earns interest on the balance in the margin account. The investor can also use other assets, such as T-bills to serve as collateral (at a discount) Margin account: an account maintained by an investor with a brokerage firm in which borrowing is allowed Initial margin: minimum initial deposit Maintenance margin: the minimum actual margin that a brokerage firm will permit investors to keep their margin accounts Margin call: a demand on an investor by a brokerage firm to increase the equity in the margin account Variation margin: the extra fund needs to be deposited by an investor 54

12 Convergence of futures price to spot price As the delivery period approaches, the futures price converges to the spot price of the underlying asset. Why? Because the arbitrage opportunity exists if it doesn t happen If the futures price is above the spot price as the delivery period is reached (1) Short a futures contract (2) Buy the asset at the spot price (3) Make the delivery If the futures price is below the spot price as the delivery period is reached (1) Buy a futures contract (2) Short sell the asset and deposit the proceeds (3) Take the delivery and return the asset Cash settlement vs. actual delivery Some futures contracts are settled in cash cash settlement, for example, most financial futures contracts Most commodity futures contracts are offset before the delivery month arrives For agricultural commodities, where the quality of the delivered good may vary, the exchange sets the standard as part of the futures contract. In some cases, contracts Regulations: federal Commodity Futures Trading Commission (CFTC) regulates futures markets The futures exchanges may set position limits and price limits. Taxation: because of the marking-to-market procedure, investors do not have control over tax year in which they realize gains or losses. Therefore, taxes are paid at year-end on cumulated gains or losses. In general, 60% of futures gains or losses are treated as long term while 40% as short term. 55

13 Futures market strategies Hedging and speculation Hedging: an investment strategy used to protect against price movements Short hedges: use short positions in futures contracts to reduce or eliminate risk For example, an oil producer can sell oil futures contracts to reduce oil price uncertainty in the future Long hedge: use long positions in futures contracts to reduce or eliminate risk For example, a brewer buys wheat futures contracts to reduce future price uncertainty of wheat Example: a refinery buys crude oil futures to lock in the price. This is a hedging behavior since the purpose of doing so is to reduce future price uncertainty (movements) - long hedging Speculation: an investment strategy used to profit from price movements Example: if you believe that crude oil prices are going to rise and you purchase crude oil futures. You are speculating crude oil price movements - long speculation (you don t need crude oil). If you believe that crude oil prices are going to drop and you sell crude oil futures. You are speculating crude oil price movements - short speculation (you don t have crude oil). Why not buy the underlying asset directly? Because trading futures contracts saves you transaction costs. Another important reason is the leverage (you use a limited amount of capital to play a bigger game). Basis: the difference between the futures price and the spot price Basis (b) = futures price (F) spot price () At maturity, T: F T T = 0 due to convergence property Basis risk: risk attributable to uncertain movements in the spread between a futures price and a spot price Let 1, F 1, and b 1 be the spot price, futures price, and basis at time t 1 and 2, F 2, and b 2 be the spot price, futures price, and basis at time t 2, then b 1 = F 1-1 at time t 1 and b 2 = F 2-2 at time t 2. Consider a hedger who knows that the asset will be sold at time t 2 and takes a short position at time t 1. The spot price at time t 2 is 2 and the payoff on the futures position is (F 1 - F 2 ) at time t 2. The effective price is 2 + F 1 - F 2 = F 1 - (F 2-2 ) = F 1 - b 2, where b 2 refers to the basis risk Example 17.6 on page

14 Spread: taking a long position in a futures contract of one maturity and a short position in a contract of a different maturity, both on the same commodity Futures prices Spot-futures parity Let us consider two investment strategies: (1) Buy gold now, paying the current or spot price, S 0, and hold the gold until time T, when its spot price will be S T (2) Initiate a long futures position on gold and invest enough money at the riskfree rate, r f, now in order to pay the futures price, F 0, when the contract matures Action Initial cash flow Cash flow at time T Strategy (1) Buy gold S 0 S T Strategy (2) Enter a long position 0 S T F 0 Invest F 0 / (1 + r f ) T F 0 / (1 + r f ) T F 0 Total for Strategy (2) F 0 / (1 + r f ) T S T Since the payoff for both strategies at maturity (time T) is the same (S T ), the cost, or the initial cash outflow must be the same. Therefore, General solution: F 0 = S 0 *(1 + r f ) T or F 0 / (1 + r f ) T = S 0 Example: gold currently sells for \$1,300 an ounce. If the risk free rate is 0.1% per month, then a six-month maturity futures contract should have a futures price of F 0 = S 0 *(1 + r f ) T = 1,300*( ) 6 = \$1, For a 12-month maturity, the futures price should be 7 F 0 = S 0 *(1 + r f ) T = 1,300*( ) 12 = \$1, If the spot-futures parity doesn t hold, investors can earn arbitrage profit. In the above example, if the 12-month maturity gold futures price is not \$1,315.69, instead, it is \$1,320 an investor can borrow \$1,300 at 0.1% per month for 12 months and use the money to buy one ounce of gold and sell a 12-month gold futures contract at \$1,320. After 12 months, the investor delivers the gold and corrects \$1,320. The investor repays the loan of \$1, (principal plus interest) and pockets \$4.31 in risk free profit. If the 12-month futures price is \$1,310, an investor can also make risk-free profit by reversing the steps above. That is an exercise for students. The arbitrage strategy can be represented in general on page

15 Spot-futures parity theorem or cost-of-carry relationship F 0 = S 0 *(1 + r f - d) T, where (r f - d) is the cost of carry and d can be positive or negative Example: buying a stock index futures contract, d will be the dividend yield Financial futures Stock index futures: a futures contract written on a stock index (the underlying asset is a stock index) Index arbitrage: an investment strategy that explores divergences between actual futures price on a stock index and its theoretically correct parity value. rogram trading: a coordinated buy or sell order of the entire portfolio, often to achieve index arbitrage objectives Foreign exchange futures: futures contracts written on a foreign currency (exchange rate) and mature in March, June, September, and December Interest rate futures: futures contracts written on an interest-bearing instrument, such as Eurodollars, T-bonds, T-notes, and T-bills, etc. rice value of a basis point: the change in price due to the change in 1 basis point (or 0.01% change in yield) Cross hedging: hedging a position in one asset by establishing an offsetting position in a related but different asset Example: a good example is cross hedging a crude oil futures contract with a short position in natural gas. Even though these two products are not identical, their price movements are similar enough to use for hedging purposes Swaps Interest rate swap and foreign exchange swap Interest rate swap: an instrument in which two parties agree to exchange interest rate cash flows, based on a specified notional amount from a fixed rate to a floating rate (or vice versa). Interest rate swaps are commonly used for both hedging and speculating 58

16 For example, Intel and Microsoft agreed a swap in interest payments on a notional principal of \$100 million. Microsoft agreed to pay Intel a fixed rate of 5% per year while Intel agreed to pay Microsoft the 6-month LIBOR. Intel 5.0% (fixed) LIBOR (floating) Microsoft Cash flows to Microsoft in a \$100 million 3-year interest rate swap when a fixed rate of 5% is paid and LIBOR is received: Date 6-month LIBOR Floating cash flow Fixed cash flow Net cash flow % % million million million % million million -0.10million % million million million % million million million % million million million million million million Cash flows to Intel will be the same in amounts but opposite in signs. The floating rate in most interest rate swaps is the London Interbank Offered Rate (LIBOR). It is the rate of interest for deposits between large international banks. Why swaps? Comparative advantages What if the swap is arranged by a swap dealer (for example, a bank)? Arranging a swap to earn about 3-4 basis points ( %) Refer to the swap between Microsoft and Intel again when a financial institution is involved to earn 0.03% (the cost is shared evenly by both companies) 5.0% 4.985% 5.015% LIBOR Intel Institution Microsoft LIBOR LIBOR After swap, Intel pays LIBOR %, Microsoft pays 5.015%, and the financial institution earns 0.03% by arranging the swap. 59

17 Foreign exchange swap: an agreement to exchange a sequence of payments denominated in one currency for payments in another currency at an exchange rate agreed to today Example: let us consider two corporations, GM and Qantas Airway. Both companies are going to borrow money and are facing the following rates. Assume GM wants to borrow AUD and Qantas Airway wants to borrow USD. USD AUD GE 5.00% 7.60% Qantas 7.00% 8.00% How can a swap benefit both companies? Answer: GE borrows USD and Qantas borrows AUD and then two companies engage in a swap Since in the USD market, GM has a comparative advantage of 2.00% and in the AUD market it has 0.4% in comparative advantage, the net gain from the swap will be 1.6% (the total benefit will be shared by all the parties involved). Assuming a financial institution arranges the swap and earns 0.2% (by taking the exchange rate risk) 5.0% USD 5.0% USD 6.3% GE Institution Quntas USD AUD 6.9% AUD 8.0% AUD 8.0% Net outcome (assuming the net benefit is evenly shared by GM and Quntas): GE borrows AUD at 6.9% (0.7% better than it would be if it went directly to the AUD market) Quntas borrows USD at 6.3% (0.7% better than it would be if it went directly to the USD market) Financial institution receives 1.3% USD and pays 1.1% AUD and has a net gain of 0.2% ASSIGNMENTS 1. Concept Checks and Summary 2. Key Terms 3. Basic: Intermediate: 9-11 and CFA

18 Chapter 18 - ortfolio erformance and Evaluation Risk-adjusted returns M 2 measure T 2 measure Style analysis Morningstar s risk-adjusted rating Active and passive portfolio management Market timing Risk-adjusted returns Comparison groups: portfolios are classified into similar risk groups Basic performance-evaluation statistics Starting from the single index model R t R Mt t Where R t is the portfolio s excess return over the risk-free rate, R Mt is the excess return on the market portfolio over the risk-free rate, is the portfolio beta (sensitivity), t is the nonsystematic component, which includes the portfolio s alpha and the residual term t (the residual term t has a mean of zero) The expected return and the standard deviation of the returns on portfolio E( R ) E( R ) and t Mt M 2 Estimation procedure (1) Obtain the time series of R t and R Mt (enough observations) (2) Calculate the average of R t and R Mt ( R and R M ) (3) Calculate the standard deviation of returns for and M ( and M ) (4) Run a linear regression to estimate (5) Compute portfolio s alpha: E( R ) E( R ) R R M (6) Calculate the standard deviation of the residual: t Mt M 61

19 Risk-adjusted portfolio performance measurement (Table 18.1) (1) The Sharpe measure: measures the risk premium of a portfolio per unit of total risk, reward-to-volatility ratio Sharpe measure = S R (2) The Jensen measure (alpha): uses the portfolio s beta and CAM to calculate its excess return, which may be positive, zero, or negative. It is the difference between actual return and required return E( R ) E( R ) R t Mt (3) The Treynor measure: measures the risk premium of a portfolio per unit of systematic risk R M Treynor measure = T R M 2 measure M 2 measure: is to adjust portfolio such that its risk (volatility) matches the risk (volatility) of a benchmark index, then calculate the difference in returns between the adjusted portfolio and the market M 2 ( S S M ) M Example: Given the flowing information of a portfolio and the market, calculate M 2, assuming the risk-free rate is 6%. ortfolio () Market (M) Average return 35% 28% Beta Standard deviation 42% 30% S for = ( ) / 0.42 = 0.69 S for M = ( ) / 0.30 = 0.73 M 2 = ( )*0.30 = = -1.29% 62

20 E(r) CML r = 35% M r M = 28% r * =26.71% M 2 CAL * r f = 6% M =30% =42% Alternative way: adjust to * (to match the risk of the market) Determining the weights to match the risk of the market portfolio 30/42 = in portfolio = in risk-free asset Adjusted portfolio risk = 30% Adjusted portfolio return = *35% *6% = 26.71% < 28% M 2 = 26.7% 28% = -1.29% The portfolio underperforms the market (refer to Figure 18.2 for another example) T 2 measure T 2 measure: is similar to M 2 measure but by adjusting the market risk - beta T 2 * r p r M Example (continued) Weights: 1/1.2 = in and = in risk-free asset The adjusted portfolio has a beta of 1: 1.2* * = 1 Adjusted portfolio return = *35% *6% = 30.17% > 28% T 2 = 30.17% 28% = 2.17% 63

21 E(r) r = 35% * r * = 30.17% r M = 28% T 2 SML M r f = 6% The portfolio outperforms the market Why M 2 and T 2 are different? m =1 p =1.2 Because is not fully diversified and the standard deviation is too high Style analysis Style analysis: the process of determining what type of investment behavior an investor or money manager employs when making investment decisions Table 18.3 Morningstar s risk-adjusted rating Morningstar computes fund returns (adjusted for loads, risk measures and other characteristics) and rank the funds with 1 to 5 stars, with one star being the worst and 5 stars being the best. Active and passive portfolio management Active: attempt to improve portfolio performance either by identifying mispriced securities or by timing the market; it is an aggressive portfolio management technique assive: attempt of holding diversified portfolios; it is a buy and hold strategy 64

22 Market timing A strategy that moves funds between the risky portfolio and cash, based on forecasts of relative performance Assume an investor had \$1 to invest on December 1, The investor had three choices by then: (1) Invested \$1 in a money market security or cash equivalent (2) Invested in stocks (the S& 500 portfolio) and reinvested all dividends (3) Used market timing strategy and switched funds every month between stocks and cash, based on its forecast of which sector would do better next month (Table 18.8) If you can time the market perfectly you will be a billionaire. Can we time the market? Revisit the efficient market hypothesis When can we time the market? Forecast the market conditions, if r M > r f, move funds to stocks; if r M < r f, move funds to the risk-free asset ASSIGNMENTS 1. Concept Checks and Summary 2. Key Terms 3. Intermediate: 5-7 and CFA

23 Example: Intermediate 6 (Figure - Digital Image) We first distinguish between timing ability and selection ability. The intercept of the scatter diagram is a measure of stock selection ability. If the manager tends to have a positive excess return even when the market s performance is merely neutral (i.e., the market has zero excess return) then we conclude that the manager has, on average, made good stock picks. In other words, stock selection must be the source of the positive excess returns. Timing ability is indicated by the curvature of the plotted line. Lines that become steeper as you move to the right of the graph show good timing ability. The steeper slope shows that the manager maintained higher portfolio sensitivity to market swings (i.e., a higher beta) in periods when the market performed well. This ability to choose more market-sensitive securities in anticipation of market upturns is the essence of good timing. In contrast, a declining slope as you move to the right indicates that the portfolio was more sensitive to the market when the market performed poorly and less sensitive to the market when the market performed well. This indicates poor timing. We can therefore classify performance ability for the four managers as follows: Selection Ability Timing Ability A Bad Good B Good Good C Good Bad D Bad Bad 66

24 Chapter 19 - International Investing Global equity markets Risk factors in international investing International diversification Exchange rate risk and political risk Global equity markets Developed markets vs. emerging markets (Tables 19.1 and 19.2) Market capitalization and GD: positive relationship, the slope is 0.64 and R 2 is 0.52, using 2000 data, suggesting that an increase of 1% in the ratio of market capitalization to GD is associated with an increase in per capita GD by 0.64%. However, the relationship is getting weaker, using 2010 data. The slope fell to 0.35 and R 2 drops to 0.10 Figures 19.1 and 19.2 Home-country bias: investors prefer to invest in home-country stocks Risk factors in international investing Exchange rate risk: the risk form exchange rate fluctuations Direct quote vs. indirect quote Direct quote: \$ for one unit of foreign currency, for example, \$1.5 for one pound Indirect quote: foreign currency for \$1, for example, 0.67 pound for \$1 Example: 19.1 Given: you have \$20,000 to invest, r Uk = 10%, current exchange rate E 0 = \$2 per pound, the exchange rate after one year is E 1 = \$1.80 per pound, what is your rate of return in \$? The dollar-dominated return is 1 r f ( US) [1 r f E ( UK)]* E \$20,000 = 10,000 pounds, invested at 10% for one year, to get 11,000 pounds Exchange 11,000 pounds at \$1.80 per pound, to get \$19800, a loss of \$200 So your rate of return for the year in \$ is = (19,800-20,000) / 20,000 = -1%

25 If E 1 = \$2.00 per pound, what is your return? Answer: 10% How about E 1 = \$2.20 per pound? Answer: 21% Interest rate parity: F E r 1 r f f ( US) ( UK) Where E 0 is the spot exchange rate and F 0 is the futures exchange rate now If F 0 = \$1.93 (futures exchange rate for one year delivery) per pound, what should be the risk-free rate in the U.S.? Answer: r US = 6.15%, using the interest rate parity If F 0 = \$1.90 per pound and r US = 6.15%, how can you arbitrage? Step 1: borrow 100 pounds at 10% for one year and convert it to \$200 and invest it in U.S. at 6.15% for one year (will receive 200*( ) = \$212.3) Step 2: enter a contract (one year delivery) to sell \$212.3 at F 0 Step 3: in one year, you collect \$212.3 and make the delivery to get pounds Step 4: repay the loan plus interest of 110 pounds and count for risk-free profit of 1.74 pounds Country-specific risk (political risk) Table 19.4 International diversification Adding international equities in domestic portfolios can further diversify domestic portfolios risk (Figure 19.11) ortfolio Risk With US stocks only US and international stocks Number of stocks in a portfolio 68

26 Adding international stocks expands the opportunity set which enhances portfolio performance (Figure 19.12) E(r ) US and international stocks With US stocks only (Way? Because investors with more options (choices) will not be worse off) World CML World CAM Choice of an international diversified portfolio More in Fin 430 International Financial Management ASSIGNMENTS 1. Concept Checks and Summary 2. Key Terms 3. Intermediate: 5-7 and CFA

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