Multinational Business Finance
Multinational Business Finance FINANCE 745
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This 92 page Class Notes was uploaded by Meagan Stroman on Thursday September 17, 2015. The Class Notes belongs to FINANCE 745 at University of Wisconsin - Madison taught by Charles Engel in Fall. Since its upload, it has received 44 views. For similar materials see /class/205265/finance-745-university-of-wisconsin-madison in Finance at University of Wisconsin - Madison.
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Date Created: 09/17/15
c To evaluate projects we will calculate a present value of returns from that project 0 But what rate do we discount at o Risky projects sometimes have a higher average return but how do we take into account the risk oWe will use a larger riskadjusted discount rate 0 But how do we evaluate the riskiness of a project o Is it the volatility of returns 0 No we want to use a measure of how the market measures the riskiness of a project oWhat matters is whether adding an investment to our portfolio increases the volatility of our portfolio 0 For example and investment that has volatile returns but which are uncorrelated with our portfolio are not considered risky Sources of risk on an international investment Volatility of the return in foreign currency Volatility of the foreign exchange rate Comovement of foreign return and foreign exchange rate Recall 1rt1 gtlt1rt1FC SUM 1st1 where st1 2w St St St1 S t Write Then rt1 st 1 rt1FC st 1 x rt 1FC z st1rt1FC The dollar rate of return is the sum of the foreign currency rate of return and the rate of appreciation of the foreign currency We will use Var to denote variance and Vol to denote volatility as measured by the standard deviation which is the square root of the variance Cov is the covariance p is the correlation Var rt 1 Var st 1 rt 1 FC 2 Var st 1 Var rt 1FC ZCov st 1 rt 1 FC Var rt 1 Var st 1 Var rt 1 FC 2 pVO st 1 Vol rt 1 FC Means Volatilities Market Currency Dollar Market Currency Dollar Return Return Return Return Return Return US 1338 000 1338 1501 000 1501 Canada 1151 032 1218 1686 531 1934 Japan 792 343 1159 1883 1153 2317 UK 1454 017 1415 1633 1054 1837 France 1479 025 1409 2017 1093 2123 Germany 1228 115 1309 2104 1104 2222 Italy 1762 173 1536 2458 1066 2510 Country Correlation Canada 035 Japan 008 UK 0 13 France 0 16 Germany 0 17 Italy 0 15 Sharpe ratio Volr Investors want higher Sharpe ratios on their portfolios That is intuitive It is the assumption underlying CAPM But it is incorrect to conclude that to achieve the highest possible Sharpe ratio on our portfolio we want to acquire investments with high Sharpe ratios Acquiring an asset with a lower Sharpe ratio than our current portfolio may increase the Sharpe ratio of our portfoliol Let the return on some foreign investment in dollars be r r is the return on our risky portfolio of domestic assets Will adding the foreign asset to our portfolio increase the Sharpe ratio of our portfolio The appendix of Chapter 13 shows it will as long as Er rf Er rf gt 0 Volr Volr p is the correlation of rand r As long as p lt 1 the foreign asset can increase the Sharpe ratio of our portfolio even if its Sharpe ratio is less than the Sharpe ratio of our domestic portfolio We can rewrite this a formula for determining a hurdle rate for whether we should add the asset to our portfolio We add the asset to our portfolio if Er rf Er rf gt p Volr Volr or Er gt p Vow rf Volr Exhibit 136 Correlations Between Foreign and US Equity Market Returns 19802006 Country Correlation Canada 073 Japan 031 UK 061 France 054 Germany 052 Italy 033 Copyright 2009 Pearson Education Inc Publishing as Prentice Hall Exhibit 137 Hurdle Rates for Foreign Investments Country Er 10 Er 12 Canada 974 1162 Japan 791 888 UK 897 1045 France 908 1062 Germany 908 1062 Italy 822 933 Copyright 2009 Pearson Education Inc Publishing as Prentice Hall How does an investor find hisher optimal portfolio of assets We have in mind that the investor can buy the risk free asset that pays r with certainty Or they can buy any of a large number of risky assets A portfolio of risky assets will generally offer a higher Sharpe ratio than any single asset We can derive the efficient portfolios of risky assets These are the portfolios that offer the highest expected return for any given volatility EU Efficient Frontier Vor But we can obtain an even better tradeoff between expected return and risk by holding a portfolio that is a mix of the riskless asset and a risky portfolio that is on the efficient frontier We find that the optimal portfolio is a mix between the riskless asset and the meanvariant efficient MVE portfolio We choose the portfolio we prefer on the Capital Allocation Line depending on our preferences for expected return vs risk EU Vor EU rf Capital Allocation Line Efficient Frontier MVE Portfolio Vor We can draw in indifference curves that show a person s preferred tradeoff between expected return and risk The best portfolio for the person is the one that achieves the highest indifference curve It is found at the indifference curve that is just tangent to the Capital Allocation Line EU Vor Capital Asset Pricing Model CAPM The CAPM is a theory or model of how the market determines the expected rate of return on a risky asset It is based on the underlying assumption that all investors act like investors who choose the optimal expected returnvolatility tradeoff just like we have been talking about CAPM also assumes c There is a singleperiod investment horizon 0 Individual investors are pricetakers their wealth is too small to individually influence the price 0 All potential investments are traded c There are no taxes or transactions costs 0 Information is costless and available to all investors o Investors all agree on their expectations expected returns volatility and covariances among returns Why are we looking at CAPM c We want to understand how assets are priced 0 But also we want to learn the appropriate way to discount future returns from a project We use the adjusted net present value approach to determine the value international projects We begin by looking at the present discounted value of cash flows But we make some adjustments Step 1 Calculate the net present value of the project s cash flow under the scenario that all projects are financed through equ y This is the sum of all discounted expected future revenues minus the sum of current and discounted expected future costs Revenues and costs are measured on an aftertax cash flow basis They are measured in the same currency They are discounted by a rate that reflects the time value of money the riskless interest rate and the risk premium demanded by the firm s equity holders Step 2 Add the value of financial side effects Costs of issuing securities Taxes or tax deductions associated with different types of financing Costs of financial distress Subsidized financing from government Step 3 Value the growth options Undertaking a project may open an option to do further profitable projects Could be included in Net Present Value but we separate itbecause 1 It is hard to value 2 It is always positive so if the project is valuable just based on steps 1 and 2 it is also worthwhile once we add in the value of the growth options Deriving the NPV of Free Cash Flow There are several steps in this derivation One of the trickier steps involves properly valuing the present value of taxes on the project We want to measure the present value of incremental profits from the project The point here is that we want to count the incremental increase in the firm s revenue from undertaking a project A new project might cannibalize a previous operation of the firm We care about the net addition to the firm s profit Again we are valuing the project first as if it were completely financed with equity So we don t want to consider at this stage any tax benefits or costs from financing by borrowing Revenues Estimate the future revenues from a project Include projections of the exchange rate so that we get the revenues in dollar terms Subtract costs These costs include the costs of the raw materials and the labor costs These are called costs of goods sold CGS Also we need to subtract off managerial expenses advertising and fixed costs of the project These are called selling and administrative expenses SGA Finally we subtract off the accounting cost of depreciation expense This is not a true cost but we are doing this to get our measure of expected earnings before interest and taxes EBIT which will form the basis upon which taxes are levied So EBIT Revenue CGS SGA Accounting depreciation Then we calculate taxes and subtract them from EBIT to get net operating profit less adjusted taxes NOPLAT So NOPLAT EBIT Taxes on EBIT But then we add back in the accounting depreciation which wasn t a true cost to get Gross Cash Flow GCF So GCF NOPLAT Accounting depreciation Then to get Free Cash Flow FCF we need to subtract off actual investment expenses These are capital expenditure CAPX and the change in net working capital ANWC CAPX includes the firm s purchases of additional property plant or equipment that is required for the project FCF GCF CAPX ANWC We then use the Net Present Value NPV formula 00 E FCFtk NPVt 1H This formula assumes a constant discount rate but in general we may want to let the discount rate vary from period to period The present value formula goes on to infinity but obviously we are not going to calculate FCF for an infinite number of periods Instead we will calculate a Terminal Value for the project Suppose year T is the last year that we calculate an expected FCF We can then calculate the terminal value in year T using the perpetual cash flow formula EFCFT1 g r g 39 Terminal value in year T Then to get the expected terminal value at time t we need to discount the terminal value at time T back to time t EFCFT1g 1 Terminal value at time t H r g 1r Financial Side Effects We need to consider the effects that arise from the costs of issuing securities from tax deductions that financing might provide the costs of financial distress associated with issuing debt and the value from governmentsubsidized financing Cost of issuing securities typically firms pay a fee and an undenNriting discount The latter refers to the difference between what the corporation receives from issuing securities and what the public pays for the securities which goes to the investment bank undenNriting the security issuance Tax Shields for certain securities if firms issue debt interest paid is tax deductible If T is the corporate income tax rate and rD is the interest rate on the loan and D is the amount borrowed then the tax deduction is erD The value of the tax shield is the discounted stream of tax deductions discounting at the market rate Why are we discounting at the market rate and not the riskadjusted rate we used to discount free cash flow Because we want to discount by the rate that reflects the riskiness of the cash flows In this case there is no covariance risk so we use rD rD might incorporate default risk but the textbook shows why it is equivalent to discount erD using rD and to discount expected erD using the risk free rate Costs of financial distress If a firm takes on too much debt it runs the risk of going bankrupt Bankruptcy proceedings are costly and even the threat of bankruptcy can be costly So if the firm takes on too much additional debt we need to value the potential costs Interest subsidies Some governments will offer loans at a subsidized rate rs There is a subsidy to the firm of rD rsD In addition the firm still gets a tax break on interest payments worth rrsD We want to add the present discounted value of these subsidies What rate do we use to discount The subsidized rate No the appropriate rate of return is the market s required rate of return on the debt of the corporation which determines the market value of the subsidy Growth option Finally we need to value the option to do another project that arises when a firm undertakes a new project The key thing here is that this is an option For example if a movie is a hit there is a positive value to the option because we can make a sequel But if the movie is a flop we can simply not make a sequel So the growth option cannot have negative value Foreign Exchange Futures In many ways like forward contracts but some important differences 0 Futures contracts can be traded in smaller amounts than forward contracts 0 Futures contracts are traded on exchanges such as the Chicago Mercantile Exchange Forward contracts are over the counter o Futures contracts are traded in fixed contract sizes Standards are JPY12500000 EUR125000 CAD100000 GBP62500 CHF125000 AUD100000 and MXN500000 o Futures contracts have fixed maturity dates eg the third Wednesday of March June September and December Forward contracts have standard maturities of 30 60 90 180 and 360 days o Parties on forward contracts must assess each other s riskiness Licensed brokers make contracts with customers in futures market c There are margin requirements in futures markets but not in forward market oThese margins pay interest oThere is an initial margin oThe contract is marked to market If the margin falls below the maintenance marginquot there is a margin call and the account must be brought up to the original margin Exhibit 201 Futures Change in Futures Gain or Cumulative Margin Day Price Price Loss Gain or Loss Account I 13321 0 0 200000 l 1 13315 00006 7500 7500 192500 l 2 13304 00011 13750 21250 178750 t 3 13288 00016 20000 41250 158750 l 4 13264 00024 30000 71250 200000 t 5 13296 00032 40000 31250 240000 t 6 13301 00005 6250 25000 246250 Note that because futures contracts are only traded at a very limited number of maturity dates there is a greater possibility of misalignment of the maturity date and the date at which you need to hedge FX risk Also note that because futures are traded in fixed amounts there is risk of mismatch between the size of the contract and what you need Basics of foreign exchange options o Foreign exchange options are both exchange traded and over the counter o A call option gives the buyer the right but not the obligation to buy foreign exchange at an exchange rate stated in the contract 0 A put option gives the buyer the right but not the obligation to sell foreign exchange at the exchange rate stated in the contract o A European option can only be exercised at the maturity date An American option can be exercised early o The exchange rate in an option contract is the option s strike price or exercise price o If the option holder could make money by exercising the option immediately the option is in the moneyquot o If the option holder cannot make money by exercising the option immediately the option is out of the moneyquot 0 If the option holder would break even by exercising the option immediately that is if the strike price equals the current spot price the option is at the moneyquot 0 Would you necessarily exercise an American option that is in the moneyquot o The immediate revenue that could be obtained by exercising an option is called the option s intrinsic valuequot 050 let S be the current spot rate and K be the strike price oThe intrinsic value of a call option is maxS KO oThe intrinsic value of a put option is maXKSO o Maturity dates of options contracts on the Chicago Mercantile Exchange correspond to those of futures contracts o Banks and other financial institutions sell options over the counter o Longermaturity currency options are called currency warrants Example 202 Buy a European call option that allows us to buy 1000000 at the price of 120 Suppose at the maturity date the spot exchange rate is 125 Then exercising the option gains 125 120 x 1000000 50000 The right to buy 1000000 for 120 is the same as the right to sell 1200000 for 83333 So the call option above that allows the buyer of the option to buy euros is equivalent to a put option that allows the buyer of the option to sell dollars Suppose a firm expects to receive payment in a foreign currency Buying a put option a contract that allows it to sell the foreign currency at the strike price buys insurance against a big weakening of that currency A put option puts a floor on the losses that the firm can suffer from an adverse foreign exchange movement It allows the firm to reap the benefits of a strengthening of the foreign currency In contrast hedging with a forward or futures contract eliminates both the up side and down side risk Example 207 Pfimerc will receive 500000 in 1 month 32 days There are several put options it can buy We focus on one that gives the firm the option to sell pounds at 15250 The cost of such a put is 0228 For 500000 the cost is 500000 X 0228 11400 The interest rate is 375 on an annualized basis which is 035 for the one month Since the put contract must be bought now the cost including foregone interest in one month is 11400 X 10035 1143990 What does Pfimerc get for this put contract If the pound depreciates to an exchange rate lower than 15250 Pfimerc can sell its pounds for 500000 x 15250 762500 If the exchange rate is above 15250 it does not exercise its option and instead sells its pounds at the spot rate But in either case it has the 1143990 cost of the option So its net revenue has a floor of 762500 1143990 75106010 Per pound that it is due the floor in is 75106010 500000 15021 If the exchange rate rises above 1525 Pfimerc s revenue per pound rises 1 for 1 with the exchange rate If it does not hedge at all there is no cost of the put contract but its revenue rises 1for1 with the spot rate for all exchange rates Finally a third alternative is to sell all of its revenues forward at 15292 the 1month forward rate Then no matter what the spot exchange rate its revenue per pound is 15292 Exhibit 205 shows the payoffs per pound from each of these three strategies Note that when the exchange rate equals 15521 the payoff is exactly the same when buying the put option or hedging on the forward market The put option allows the firm to have the up side of a pound appreciation but puts a floor on its losses in the event of a pound depreciation It is like an insurance contract However the put option costs money to buy It is better than a forward contract the more likely it is that the actual spot rate will be more than 15521 156 154 15292 152 150 bcsoa Ea wEwo mscwgtwm 148 152 154 156 October US cents per pound 150 148 Example 208 Now suppose a firm will be buying a product from Switzerland and must pay CHF750000 It can buy a call option that allows it to buy Swiss francs at the strike price Suppose it buys a call option that allow it to buy Swiss francs at 072CHF The cost of such a contract is 00155CHF The interest cost is 94 The ceiling on the firm s costs are 750000x072CHF 00155CHFX1OO94 55173428 The per CHF cost is capped at 55173428CHF750000 7356 CHF If the Swiss franc spot rate turns out to be less than the strike price of 072CHF the firm does not exercise the option It just buys Swiss francs on the spot market But of course it still has to bear the cost of having bought the option So its costs per Swiss franc are capped at 7356 CHF and fall 1 for 1 as the Swiss franc falls below 072CHF Alternatively it could buy Swiss francs on the forward market at 7114 CHF Or it could not hedge at all Exhibit 206 displays the payoffs from the three strategies 74 7356 2 7 chon an mEmo mj moo 72 74 us cents per Swiss franc 70 The forward contract and the option leave the firm with the same cost if the spot exchange rate turns out to be 695 CHF For lower values of the exchange rate the option will turn out to be a better deal The firm may buy the option instead of buying Swiss francs forward if it believes there is a high probability that the exchange rate will be less than 695 CHF What if instead the firm bought options that had a strike price of 70 CHF Those give the firm more protection but are more expensive 255 CHF as compared to 155 CHF for the option that allows it to buy at 72 CHF Exhibit 208 compares payoffs 7114 72 US cents per franc 7O 74 0 735639 257 7 cm Ea mEmo mj E 500 68 5 74 6857 6958 Speculating with options Suppose you expect to receive English pounds as in our first example that you want to sell for Buying a put option that allows you to sell pounds at the strike price puts a floor on the revenues you will receive It is like insurance But you could sell a call option that allows the buyer to purchase pounds for dollars at the strike price This is speculation If you sell a call option you are obligated to sell pounds at the strike price if the buyer of the option exercises the option Selling such an option would be risky for Pfimerc It stands to lose the up side of any pound appreciation and it is not insuring against a drop in the pound Why would Pfimerc do it If the price of the call option is high it might be attractive to take such a gamble Pfimerc receives the money from selling the option contract Suppose it sells a call option with a strike price of 155 Pfimerc has 500000 to sell The most it can make is 155 X 500000 775000 which it will get if the spot rate rises above 155 20 It sells these contracts for 00150 And it earns interest of 035 So the most it can earn is 500000x155 O0150 X10035 78252625 Per pound it puts a cap on its revenue of 78252625 500000 15651 For spot rates less than 155 its revenue falls 1for1 with a fall in the exchange rate 21 Exhibit 209 compares the payoffs from this strategy with the payoffs from selling pounds forward or not hedging If the spot rate turn out to be greater than 15651 Pfimerc would have been better off not hedging at all If the spot exchange rate is less than 15141 Pfimerc would have been better off seing pounds at the forward rate of 15292 22 157 15651 Revenue in cents per pound 155 153 151 149 15292 s151 41 149 151 153 155 October US cents per pound I 157 23 Conversely a firm that has foreign exchange liabilities can speculate by selling put options That is if a firm will have to pay Swiss francs as in our second example it could sell a put option that obligates it to sell dollars for Swiss francs at the strike price This gives the firm a minimum cost it must pay for Swiss francs but put no ceiling on its costs Alternatively recall that by buying a call option to buy Swiss francs it put a ceiling on its costs but imposed no floor 24 Now return to the case of Pfimerc What would happen if it both bought a put option with a strike price of 15250 and it sold a call option with a strike price of 155 It pays 500000 x 0228 x 1039 1143990 for the put option It earns 500000 X 00150 X 10035 752625 from selling the call option So its option portfolio costs 1143990 752625 391365 It puts a floor on the value of its sale of pounds of 500000 x 15250 762500 25 If the pound spot exchange rate is less than 15250 the firm earns 762500 391365 75858635 The per pound earnings are 75858635 500000 15172 If the pound rises above 155 the firm must sell its pounds at 155 The most it can earn is 500000 x 155 775000 Its earnings less the cost of its option portfolio are then capped at 775000 391365 77108665 Per pound earnings are 77108665 500000 15422 26 So by buying a put and selling a call the firm guarantees its earnings are between 15172 and 15422 If the spot exchange rate ends up between 15250 and 155 the firm exercises neither option and sells on the spot market Its earnings per pound are the spot rate ess 391365 500000 O78 That is the cost of keeping the exchange rate within the bands of 15250 and 155 is O78 27 Options Valuation The BlackScholes formula was derived to determine the prices of European put and call options on stocks The formula and its derivation are too complicated for this class but a nice simple derivation can be found on Wikipedia httpenwikipediaorqwikiBlack scholes Here we will simply discuss the major factors that determine option prices for foreign exchange 28 Recall that the intrinsic value of a call option is maxS KO K is the strike price and S is the spot exchange rate That is the value of a call is SK if SKgtO and otherwise it is worth 0 Now consider a European call option At the time of maturity T the price of the call CT will be equal to its intrinsic value maxSTKO That is at the time of maturity the call option will have value gt 0 if STKgtO Therefore the call option is worth more today the more likely it is that STKgtO We can form a probability distribution over the various possibilities we think the spot rate will take at time T as in Exhibit 2010 29 Probability of future exchange rates Probability of Sz 90 I I I I I I I I I 100 105 110 115 120 125 130 135 140 145 150 Possible values of future USDEUR Sz 90 It is very likely for example that the exchange rate will be less than 145 If investors only cared about expected return they would be willing to pay today the expected intrinsic value of the call option at time T discounted back to today s time To get a sense of this compare two call options One has a strike price of K1 and the other K2 where K1 lt K2 Which call option would investors pay more for The one with strike price of K1 That s because at time T the option will have value for all spot rates gt K1 while the other option will only have value for spot rates gt K2 If there is a high probability that the spot rate will fall between K1 and K2 the first option will have a much higher price today 31 Exhibit 2011 Probability of future exchange rates 8 CD I W 5 E E U D 2 I1 I l IK1 K2 100 110 120 130 f 140 150 Strike Prices Possible values of future USDEUR St 90 Conversely the intrinsic value of a put option is given by maXKSO At time T the option will only have value if KSTgtO Compare two put options One has a strike price of K1 and the other K2 where K1 lt K2 Which call option would investors pay more for The one with strike price of K2 That s because at time T the option will have value for all spot rates lt K2 while the other option will only have value for spot rates lt K1 If there is a high probability that the spot rate will fall between K1 and K2 the second option will have a much higher price today 33 If there is more uncertainty about the future spot rate the value of a given put or call option is higher That is suppose that we don t change the mean of our probability distribution for the spot exchange rate at time T but increase its spread Now consider in Exhibit 2012 a call option that has a strike price equal to the mean of the distribution 125 The more spread out distribution offers the possibility of higher payouts when the call option is in the money so the price of the call option would be higher 34 Probability of St 90 Probability distribution of future spo rates tranquil period Probability distribution of future spot rates turbulent period Possible values of future USDEUR St90 A similar logic applies to put options the value of the put option that has a strike price of 125 is higher for the more spread out distribution If the strike price of a call option is 130 it is more likely the call option will end up in the money for the more spread out distribution and there exist the possibility of very high payouts Note that if the strike price is 120 that the probability of being in the money is higher when there is lower volatility Nonetheless according to the Black Scholes formula the price of the option is higher when volatility is higher the possibility of high payouts outweighs the higher probability of ending up out of the money 36 What if there is greater time to maturity for the oonn An American option is always worth more the longer to maturity Why Consider the price of a call option of 125 at a 3 month and a 6 month horizon We can always exercise the 6 month call option at the end of 3 months But we have the option of holding onto it hoping for an even bigger payout 37 For a European option generally the price is higher for a longer maturity Longer maturity means more uncertainty about the possible spot rate at maturity and volatility increases the value of the option Recall that with a European option you have to wait until the maturity date to exercise the option If the option is strongly in the money now we might value the possibility of selling sooner rather than later to cash in So the shorter maturity option could have higher value 38 Put Call Parity Suppose you bought a put that allowed you to sell euros at price K dollars per euro You would exercise this put and sell euros at K as long as ST lt K Also suppose you sold a call that obligated you to sell euros at price K You would have to sell euros at price K if ST gt K If you hold both of these options you will definitely sell euros at exchange rate K Let P be the price of the put and C be the price of the call The value of your portfolio of options is C P x 1i at the time of maturity 39 Now this means that the gain from selling euros at price K is K C P 1i But another way to sell euros for a sure price is on the spot market at price F Arbitrage insures that these two methods of selling euros in advance yield the same profit so F K C P1i So we can derive a relationship between the difference of put and call rates to the forward rate the strike price and the interest rate PC KF1i 40 Or recall from covered interest parity that F s1i1i So we can rewrite the put call parity relationship as P C K1i S1i If we have calculated the price of all call options then we can use this formula to calculate the price of put options 41 We now want to look at the theory of how the risk premium or the excess return on an asset is determined The Capital Asset Pricing Model CAPM provides such a theory It builds on the model we have examined of individual s optimal portfolio choice First recall that we noted that under the following condition Er rf Erp rf Volr p Volrp adding an asset with return given by r to our portfolio of risky assets whose return is denoted rp will increase the Sharpe ratio of our portfolio How much of this new asset should we add As we add more and more of the asset the correlation of the return on our portfolio with r denoted 0 increases We should keep adding more of the asset until Err rf Erp rf Volr Volrp This can be rewritten Remember that Covrrp p vOnworpy So we can rewrite the condition above as E Covrrp r r Er r f Varrp p f The next important result to remember from that theory is that all individuals should have the same portfolio of risky assets They all hold the meanvariant efficient MVE portfolio of risky assets Investors may differ in their distaste for risk But that gets reflected only in the balance in their holdings of the riskless asset and the MVE portfolio EU rf Capital Allocation Line I I Efficient Frontier MVE Portfolio Vor We can draw in indifference curves that show a person s preferred tradeoff between expected return and risk The best portfolio for the person is the one that achieves the highest indifference curve It is found at the indifference curve that is just tangent to the Capital Allocation Line EU Vor Now let s model the entire market for risky assets If all investors hold the same portfolio of risky assets what is that portfolio It must be the market portfolio The market portfolio contains all securities and the proportion of each security is the market value as a percentage of total market value If everyone is holding the MVE portfolio of risky assets then the MVE portfolio must be the market portfolio that is the only way there can be no excess demand or supply for any security Let rm denote the return on the market portfolio Putting things together we have that the equilibrium excess return on an asset is given by Er n COV rmErm n Varrm The beta of the return on an asset is defined as Cov rrm 3 E lt Varrm We can write the CAPM theory of excess returns as Er amp MEG n The risk premium of an asset is determined by the risk premium on the market and the asset s beta 0 Should we use nominal or real returns Real returns though in practice there is little difference 0 Should we use real returns for US investors or for some other investor In principle the theory needs to be modified if US investors and Foreign investors earn different real returns Real returns are only equal for US and Foreign investors if relative PPP holds Also the riskless real returns are only equal for US and Foreign investors if relative PPP and UIP hold 0 The International CAPM modifies the world CAPM to allow for deviations from the parities In practice little is changed if we simply use US returns A Recipe for the Cost of Equity Capital Er n mErm ngt Step 1 Get data on the market portfolio returns the equity returns on security i and the Tbill interest rate Step 2 Determine the market risk premium the expected excess return on a portfolio that approximates the market portfolio Step 3 Obtain an estimate of 3 Step 4 Compute the expected return on investment ias Er rf 3ltErm ngt What is the market portfolio Since it is fairly costless to diversify our portfolio among assets from many countries we want to use a measure of returns from a world portfolio of assets Really the measure of the market portfolio should include returns from all assets that we can invest in not only equities but also bonds real estate gold etc In practice the MSCI Morgan Stanley Capital International Index is typically used The book gives an example of how risk could be mismeasured if we measure the market index incorrectly How do we estimate the beta for asset i We collect data on r r and rm r An estimate of 3 comes from a regression of r r on rm r If we don t have enough data or if our data only comes from special periods of time for instance times when returns are not very volatile we might mismeasure In many emerging markets there are barriers to free movement of capital across borders Therefore the risk premium on an asset may be more closely related to the excess return on the domestic market portfolio rather than the world market portfolio However a multinational considering investment in an emerging market may still want to use the world market portfolio as the benchmark The Arbitrage Pricing Theory APT is an alternative model used for assessing the expected excess return or risk premium on an asset According to the APT the excess return is related to several different risk factors Err rf i1rp1 i2rp2 quot39 ikrpk CAPM is the special case with one risk factor with rp1 Erm rf There is not widespread agreement on how to measure the risk factors in the APT The main takeaways from our study of exchange rate models 1 The average real exchange rate for the US and other advanced countries is related to the difference between foreign and US real interest rates a This relationship is weaker on a currencybycurrency basis 2 It is nearly impossible to forecast exchange rate changes using this model or any other model 3 Technical analysis is of dubious value 4 Currency crises might be predictable