International Financial Markets 2. Major Markets and Their Assets

Transcription

1 International Financial Markets Capital Markets Credit Markets Stock Markets Spot Markets Forward Markets 2.3. Derivatives Forwards and Futures Options Literature: 1) Chapter 4, 5, 6, 7, 8 Fell, Lindsay (2000): Financial Products and Markets, Continuum, London. Chapter 17, 18, 19, 21 Kohn, Meir (1994): Financial Institutions and Markets, McGraw-Hill, New York. 1) The recommended literature typically includes more content than necessary for an understanding of this chapter. Relevant for the examination is the content of this chapter as presented in the lectures

2 Financial Markets Capital Markets Foreign Exchange Markets Stock Market Credit Markets Spot Market Forward Market Money Market Governm. Securities Corporate Debt Mortgage Debt Derivatives Forwards Futures Options Swaps Credit Markets 2.1. Capital Markets Credit Markets Stock Markets Spot Markets Forward Markets 2.3. Derivatives Forwards and Futures Options - 4-2

3 Credit Markets Different types of securities are traded on credit markets: Securities with fixed interest rates 1) bear a fixed rate interest coupon, which guarantees a fixed annual payment of interest over the maturity of the security. Securities with floating rates pay interest rates which vary during the life of the security according to short-term reference rates. Equity-related securities carry an equity element in the form of a conversion clause or warrants to acquire stocks of a certain stock company. Securities with money market instruments are securities with maturities up to one year. 1) Synonyms for fixed rate securities: notes with fixed rates (if issued by companies), bonds with fixed rates (if issued by governments), straight bonds, plain vanilla bonds, gilts (= bonds; British) Credit Markets Securities with fixed interest rates (bonds in the following): are contracts that guarantee their owner a payment of a fixed annual rate of money plus the payment of the face value at the end of maturity. are typically issued by governments and (to a smaller part) by large firms. Before the day of issue the issuer publishes for example the following kind of information: Fixed annual interest rate: 5 % of face value Face Value (=redemption price): 100 Periods to maturity: 4 years - 6-3

4 Credit Markets If the market interest rate is lower than the fixed interest rate, the market price of the bond is higher than its face value (=Agio). For example: Market interest rate at day of issue = 4% The higher market price (= Agio) causes the internal rate of return of this bond to fall below its fixed rate and to equal the market interest rate! Credit Markets At the day of issue the market price of the bond is then determined by the prevailing market interest for a bond with the same risk rate following the discounted cash-flow method. For example: Market interest rate at day of issue = 6 % Consequently, if the market interest rate is higher than the fixed interest rate of the bond, the market price of the bond is lower than its face value (=Disagio). The lower market price causes the internal rate of return of this bond to rise above its fixed rate and to equal the market interest rate! - 8-4

5 Credit Markets Only if the market interest rate equals the fixed interest rate, the market price of the bond equals its face value (= Pari) For example: Market interest rate at day of issue = 5% At this market price, the internal rate of return of this bond exactly equals the market interest rate (=Pari)! Credit Markets Why does the price of a bond always adjust so that its internal rate of return equals the market interest rate? This adjustment is made by market forces, i.e. movements of supply and demand: If the internal rate of return of a bond were higher than the market interest rate, people would buy this bond only. As a consequence, this increase in demand causes the market price of the bond to grow until it reaches a level where its internal rate of return equals the market interest rate. If the internal rate of return of a bond were lower than the market interest rate, people would not like to buy this bond. As a consequence, this lack of demand causes the market price of the bond to fall until it reaches a level where its internal rate of return equals the market interest rate

6 Credit Markets The risk profile of bonds with fixed rates: If you buy a fixed rate bond and keep it to the end of maturity, you will receive an ex ante fixed return plus the face value. Consequently, the internal rate of return is fix. If you keep your fixed rate bond to the end of maturity, the only risk involved in a bond is the default risk of the issuer. Therefore fixed rate securities of different issuers, are bonds of different default risk: Government Bonds Corporate Bonds Therefore, fixed rate bonds of different issuers typically bear different yields to maturity i.e. a risk premium Source: Deutsche Bundesbank = Corporate Bonds = Government Bonds

7 Credit Markets The risk profile of bonds with fixed rates: However, if you sell your fixed rate bond before the end of maturity, you may receive a market price for your fixed rate bond significantly lower than its face value. Consequently, selling a fixed rate bond before maturity involves price risk. Why is it possible that the market price of a fixed rate bond decreases? Demand and supply on the market for fixed rate securities may have changed since you have bought your fixed rate bond. For example: Supply of fixed rate bonds (with the same maturity as yours) may have grown faster than demand, so that prices may have declined Summary: Price Risk of Fixed Rate Securities i o i Market for fixed rate securites with a maturity D(i) of 4 years =Credit Supply Date of issue: t Market interest rate for fixed rate bonds with a maturity of 4 years: i o = 5% B o S(i) =Credit Demand ( ) => As already seen above, if the fixed rate of a bond equals exactly 5%, its market price will equal its face value (100 ):

8 i 1 i o i Summary: Price Risk of Fixed Rate Securities Market for fixed rate securites with a maturity of 3 years B o B 1 ( ) D(i) S(i) 2 S(i) 1 One year later: t+1 Market supply (=credit demand) has grown so that interest rate for fixed rate securities with a maturity of 3 years equals: i o = 6% => As already seen above, the price of the bond has to decrease to adjust its internal rate of return to the market interest rate Credit Markets The risk profile of securities with fixed rates: Of course, this decrease in market price is only a disadvantage, if you need to sell your bond before its maturity. Only in this case you will suffer from price risk. If you hold your bond until the end of maturity, you will get back all your money plus a fixed rate of return. Consequently, if you cannot be sure, whether you need your money back before the end of maturity or not, don t buy a bond with a fixed rate of return. Else you will suffer from price risk. If you cannot be sure, whether you need your money back before the end of maturity or not, you better buy a security with a floating rate or a similar instrument (e.g. giro account)

9 Credit Markets The bond market listings of newspapers present both, the market price of a bond and the calculated internal rate of return To sum up: Credit Markets The market price of a fixed rate bond does always adjust so that its internal rate of return equals the market interest rate. If the market interest rate increases, the price of the bond decreases. If the market interest rate decreases, the price of the bond increases. As a consequence of this behavior the market price of a fixed rate bond can display a high variance and hence a high price risk. However, the holder of a bond suffers from this price risk only, if he sells the bond before its maturity. If she keeps the bond until its maturity he gets the promised face value as well as all the promised interest payments back

10 Credit Markets Stock Markets 2.1. Capital Markets Credit Markets Stock Markets Spot Markets Forward Markets 2.3. Derivatives Forwards and Futures Options

11 Source: Bank for International Settlements Source: Bank for International Settlements

12 Stocks 1) Stock Markets are a right to part ownership of a joint stock company entitle their owner to the residual profit of the company, i.e. any extra wealth that the company might generate, after all other claimants (suppliers, employees, providers of debt capital, the taxman) have received their money. do not obligate their owner to cover the debts of the company beyond the amount actually subscribed for the stock ( limited liability ). 2) What does residual profit mean? Take a look at the next graph: 1) Synonyms for stocks: shares (Brit.), equities (general term for stocks + other own capital) 2) In most countries stocks can only be issued by joint stock companies (or corporations ), i.e. companies which are set up in accordance with a particular body of law in the country Money received from sales./. Payments for costs to suppliers of goods and services and to labor./. Payment of interest on outside capital (to holders of securities and to banks)./. Payment of tax on profit = Profit after tax = Money available for stockholders = Residual Profit Dividend payments Retained Earnings

13 Stock Markets The determination of the residual profit shows: The payment to the owner of a stock is very uncertain. Many factors affect dividend payments: Sales success (strength of demand: business cycles as well as quality of products and success of marketing activities) Development of production costs (energy prices, raw materials, labor etc.) Development of the costs for outside capital Development of tax laws Decision about retained earnings by the directors of the company Therefore the yield on stocks is uncertain. It depends on the expected values of all these factors Stock Markets Stocks are daily auctioned on stock markets. Stock brokers and/or computer chose the market equilibrium price of a stock several times a day so that demand and supply are equilibrated

14 Stock Markets List of quotations of a stock market broker for a specific stock Supply Curve Number of stocks 14

15 Supply Curve Number of stocks Stock Markets List of quotations of a stock market broker for a specific stock 15

16 Demand Curve Menge (kg) Number of stocks Demand Curve Menge (kg) Number of stocks 16

17 Market Diagram Supply Supply=350 Demand=350 Demand Number of stocks Stock Markets List of quotations of a stock market broker for a specific stock 17

18 Market Diagram Supply Supply=450 Demand=350 Excess Supply Percentage allotement of demand to supply: 350/450 = 77,7% Demand Number of stocks Market Diagram Supply Demand Number of stocks 18

19 Stock Markets Consequently, the market price of a stock is known every day. Contrary to fixed rate bonds, the return of a stock, its dividend payment, is not known in advance. Hence the evaluation of the profitability of a stock must be based on a forecast of future dividend payments. Such a forecast must use firm specific information on all the factors displayed by the above graph. It is clear that such a forecast is highly insecure Stock Markets Another problem with dividend forecasts is the infinite maturity of stocks: While fixed rate bonds typically have finite maturities between 1 and 30 years, stocks have no redemption date. One procedure to tackle this problem is the fair value approach: 1. Forecast based on firm specific data dividend payments over a certain span of time. 2. Use the average or last dividend payment (e.g. D T = 5) as a forecast for a perpetuity. 3. Choose an appropriate discount rate (e.g. i=0,06) and apply the formula for the present value of a perpetuity (P=D/i) to determine the price of the stock after the last year (P T =5/0,06 = 83,3)

20 Stock Markets The resulting flow of payments can then be evaluated either with the internal rate of return method or with the discounted cash flow method. The more usual method for the evaluation of stock is the discounted cash flow method, for example: The resulting fair value is than used for comparison with the market price of the stock: Market Price > Fair Value => Stock is overvalued => Sell! Market Price < Fair Value => Stock is undervalued => Buy! Stock Markets Problems of the fair value approach: 1. The calculation forecast of each single dividend is not only very insecure but also very cumbersome, given all the factors that influence a dividend payment. 2. The forecast of the resale price has a large weight on the fair value (see the above example): Small changes of the dividend value taken to estimate the resale price have a large impact on the fair value. 3. The discount rate has also a large impact on the fair value. 4. The discount rate is unknown and must also be estimated under consideration of the specific risk of the stock!

21 Stock Markets One often used orientation for the appropriate risk specific discount factor of a stock is the Capital Asset Pricing Model (CAPM): i j = yield of a risk-free security + specific risk premium for stock j i j = yield of a risk-free security + market return for one unit of risk * units of risk attached to stock j i j = + * i j = discount rate of stock j, r j = rate of return of stock j, r M = rate of return of the market portfolio, r o = yield of a risk-free security Stock Markets i j = + * i j = + * Market Beta (chapter 1.2.2) Interpretation: (1) If the yield of stock j displays no correlation with the return of the market portfolio (cov(i j,r M )= 0) the risk equivalent yield of security j equals the yield of the risk-free security (r o ). (2) If the yield of stock j displays perfect correlation with the return of the market portfolio M (cov(i j,r M )/var(r M ) = 1) the risk equivalent yield of security j equals the yield of the market portfolio ( i j = r 0 + 1* (r M r 0 ) = r M )

22 Stock Markets Problems of the discount factor calculation based on the CAPM: To use the formula, it is necessary to know the future covariance between the yield of the market portfolio and the yield of stock j, cov(i j,r M ) and the future variance of yield of the market portfolio var(r M ). Both numbers, however, can only be calculated on the basis of the historic values of these yields. The present and the future covariance and variance may however be different from the covariance calculated on the basis of past values, since all the factors that influence i j and r M may change. Consequently, the CAPM is a good theoretical orientation for the determination of an appropriate discount factor. However, one has to bear in mind that it is also based on a forecast only Stock Markets To sum up: The evaluation of stock is based on a lot of incertitudes: Forecast of dividends, resale price, discount factor This shows that investing in stock is a highly risky way of investment. Because of all the difficulties in evaluating stocks, a lot of key figures and technical methods are in usage in stock market analysis. Two of them are discussed in the following

23 Key figures for stocks: The Dividend Yield : Stock Markets Details Market price per stock = market value of the stock at period t = P t Example: Profit after tax = 30 million Retained earnings = 10 million Number of stocks = 10 million Market price of stock = 60 => Dividend Yield = ((30-10) /10) / 60 = 3,33% Key figures for stocks: The Dividend Yield : Stock Markets Details Interpretation: The dividend yield is the yield per period an investor will have, if dividend payments in all future periods stay the same. This number is of particular interest for investors that need a regular income but don t want to sell their stock in order to realize price gains (e.g. pension funds, investors borrowing to invest)

24 The dividend yield, D t /P t, has reached a historic low since the 80s. This indicates that, since the beginning of the 80s, investors are less interested in dividend payments from stock but price gains Stock Markets Key figures for stocks: The Price Yield : Details Market price per stock = market value of the stock at period t = P t Example: Market Price t = 120 Market Price t-1 = 100 => Price Yield = ( ) /100 = 20 %

25 Stock Markets Key figures for stocks: The Price Yield : Details Interpretation: The price yield is the yield per period an investor will have, if he buys the share at the beginning of a period and sells it at the end, neglecting the dividend payment. This number is of particular interest for speculationoriented investors This diagram reveals that since the beginning of the 1980s the total return from stock investments is driven by price increases: The motive for stock investment is no longer the dividend payment but the potential price gain

26 Stock Markets Key figures for stocks: The Total Yield : Details Dividend Yield t = 3,3% Price Yield t = 20 % => Total Yield = 23,3%

27 This diagram shows that in most of the 10-years averages a stock investment performed much better than an investment in a government bond. This higher average return of a stock investment is called the "stock premium". It is very often interpreted as the "risk premium" of a stock investment This diagram shows that even though the 10-years average returns of a stock investment are significantly larger, the yearly returns of a stock investment fluctuate significantly more. The higher long-run return of a stock investment is therefore interpreted as a "risk premium". 27

28 As a consequence of the stock premium, an investment of 1$ in the S&P-500 Portfolio in the year 1871 reaches an inflation adjusted value of 7044,3 $ in the Year 2007 (yearly average: 6,73 %). An investment of 1$ in US government bond in the year 1871 reaches an inflation adjusted value of 30,5 $ in the Year 2007 (yearly average: 2,54 %) Key figures for stocks: Stock Markets Details The price earnings ratio (P/E ratio): Market price per stock = market value of the stock at period t = P t Earnings per stock from the recent set of accounts = [(Profit after tax / number of stocks)] = [(Dividend payments + retained earnings) / number of stocks] (s. figure on slide 46 ) Example: Profit after tax = 30 million Number of stocks = 10 million Market price of stock = 60 => Price earnings ratio = 60 / (30/10) =

29 Key figures for stocks: Stock Markets Details The price earnings ratio (P/E ratio): Interpretation: (1) If retained earnings pay off either in form of future dividend payments or future price gains, the P/E ratio is equivalent to the number of years a stock has to be hold in order to regain the money invested if the earnings stay the same in all future periods. (2) The inverse of the P/E ratio is equivalent to the Earnings yield, i.e. to the long run yield per period that can be expected if the earnings in all future periods will be the same as the present earnings. Example: a P/E ratio of 20 is equivalent to an earnings yield of 1/20 = 5% Standard&Poors Cyclically Adjusted Price/Earnings Ratio January 1880 November The all time average of the S&P 500 P/E-ratio is 16,5 (what corresponds to an average earnings yield of 6,0%). As the development of the S&P 500 P/E-ratio shows, the bubbles which led to the world economic crises of 1929 and the dot.com-crisis of 2000 had been periods with very strong growth of the P/Eratio. Such an increase is justified, if the future earnings of a stock grow

30 Standard&Poors 500 Price and Earnings January 1870 November As this chart shows, the decrease in the P/E-ratio after these bubbles had not been caused by a strong increase in earnings, but by a strong decrease in prices. Hence expectations of a strong growth of earnings that might have led to these very high P/E-ratios were not met by the actual development. As the next chart shows the contrary is true: On average low P/E-ratios are followed by high return rates measured as price gains plus dividend payments (forward looking) Shiller (2005), Irrational Exuberance (backward looking) This cloud shows a clear downward slope, indicating that a low P/E-ratio is in the long-run (=over a period of 20 years) on average followed by a high return, measured as price gains plus dividend payments, and vice versa. This indicates that a long-term investor is on average best advised to choose stocks with a low P/E-ratio = value investor (Benjamin Graham, Security Analysis, 1934)

31 (forward looking) Are these empirical observations compatible with market efficiency? Shiller (2005), Irrational Exuberance Efficient Market Hypothesis (Eugene Fama,1965): (backward looking) Prices on traded assets already reflect all past publicly available information. (Weak-form EMH) (forward looking) Are these empirical observations compatible with market efficiency? Shiller (2005), Irrational Exuberance How Fama made observations compatible: Returns might well still be predictable at long horizons, if investors fear of risk varies over time. For example, in a recession few people may want to hold risky assets, as they are worried about their jobs or the larger economic risks at these times. This quite rational fear lowers the demand for risky assets, pushing down their prices and pushing up subsequent returns. (John Cochrane (2013): ) (backward looking)

32 (forward looking) Are these empirical observations compatible with market efficiency? Shiller (2005), Irrational Exuberance Problem with Fama s changing risk aversion : According to standard neoclassical theory risk aversion (= the slope of the utility function) is a parameter of preference and preferences does not change. If preferences change, we need a meta-theory why preferences change. Contrary to non-rational behavioral theories, neoclassical theory does not provide such a theory, Fama s changing risk aversion is an ad-hoc-assumption introduced to immunize the EMH against empirical observations (backward looking)

33 2.1. Capital Markets Credit Markets Stock Markets Spot Markets Forward Markets 2.3. Derivatives Forwards and Futures Options Spot Markets Why do people demand foreign currencies? Lower prices of goods sold for foreign currencies. => Domestic consumers (or their retailers and intermediaries) want to buy foreign goods and need foreign currencies to do so. Higher interest rates and expected return of securities denominated in foreign currencies. => Domestic savers (or their banks and investment funds) want to buy foreign securities and need foreign currencies to do so

34 Spot Markets Spot Markets These considerations show, demand and supply on foreign exchange markets are influenced by two factors: The relation between domestic and foreign prices for goods: P versus P $ The relation between domestic and foreign interest rates: i versus i $ In the following we will study these relationships in some more detail

35 Spot Markets We can find the accurate relation between the exchange rate and prices for domestic and foreign goods with the help of a numerical experiment: Where would you buy your cookies at the following exchange rate and prices: 1. Example: Price per kg domestic cookies = 1 = P Price per kg foreign cookies = 2 $ = P $ Exchange rate = 4 $ How would this affect the demand for Euro? 2. Example: Price per kg domestic cookies = 1 = P Price per kg foreign cookies = 2 $ = P $ Exchange rate = 1 $ How would this affect the demand for Euro? Spot Markets At what exchange rate would you be indifferent between buying cookies in Europe or in the USA given the following prices: Example: price per kg domestic cookies = 1 = P price per kg foreign cookies = 2 $ = P $ exchange rate = How would this affect the demand for Euro? Consequently, a necessary condition for an equilibrium on the exchange market is that all goods, which can be traded between the two currency areas, have the same price, whether measured in or measured in $. This relation is called the purchasing power parity

36 Spot Markets The purchasing power parity formula: P = P $ / e $ prices measured in <=> e $ * P = P $ prices measured in $ <=> e $ = P $ / P the PPP-exchange rate However, the simple purchasing power formula does only hold for goods whose transportation costs are close to zero. For most goods this assumption is not justified. In this case the formula must take care of transportation costs. As a result there is a band around the PPP-exchange rate, in which the exchange rate is not affected by goods prices

37 Spot Markets If there are transport costs, the formula for the PPPexchange (e $ ) rate has to be modified: Lower border of the transport costs band Upper border of the transport costs band => The higher transport costs per piece (C $ ) the lower is the effect of international trade on the exchange rate: If transport costs are infinitely high (C $ ), there will be no trade and the exchange rate will not be affected by trade. If transport costs are zero (C $ = 0), the exchange rate will be completely determined by the prices for tradable goods. In reality, where transport costs for most goods lies somewhere between zero and infinity, there will be an exchange rate band around the PPP-exchange rate, in which the actual exchange rate is not affected by trade

38 Spot Markets In reality transport cost for most goods are between zero and infinte. Beside transport costs, there are also other factors preventing strict empirical validity of the purchasing power theorem: Tariffs and quantitative restrictions act like transport costs. Monopolies & oligopolies allow companies to apply profit maximizing price differentiation strategies between different currency areas. => Consequently, there exists a kind of band width around the PPP-exchange rate, within which the actual exchange rate cannot be affected by international trade. Prof. Dr. Rainer Maure Spot Markets 39,99 $ / 1,216 $ = 32,88 e $ = P $ / P <=> 0,640 $ =39,99 $ / 62,49 => At an exchange rate of 1,216 $ the Euro is overvalued against the Dollar Prof. Dr. Rainer Maure

39 3. Währungstheorie und Währungspolitik Kaufkraft- und Zinsparität Prof. Dr. Rainer Maure => Given this trade restriction by Levi s ( monopolistic competition ), no extra supply of Euro for Dollar is triggered and hence the Euro will not depreciate against the Dollar e $ Spot Markets The more $ is paid for one, the more US-goods are cheaper than Euro-goods and the more is hence supplied in exchange for $. -Supply e o Equilibrium on the exchange market in terms of -Supply and -Demand The less $ has to be paid for one, the more Euro-goods are cheaper than $-goods and the more is demanded in exchange for $. o -Demand

40 e $ Spot Markets What happens to the equilibrium exchange rate if inflation in the USA is higher than inflation in the -Area? P $ 1 < P $ 2 -Supply(P $,1 ) e o -Demand(P $,1 ) o Spot Markets e $ What happens to the equilibrium exchange rate if inflation in the -Area is higher than inflation in the USA? P 1 < P 2 -Supply(P,1 ) e o -Demand(P,1 ) o

41 Spot Markets International trade causes the exchange rate to adjust for inflation differentials between to countries (at least in the long run): If inflation in the USA is higher than inflation in the -area the -exchange rate (e $ ) will appreciate. If inflation in the USA is lower than inflation in the -area the -exchange rate (e $ ) will depreciate Spot Markets The purchasing power parity theory shows that goods prices and hence trade with goods does affect the exchange rate. However, differences in interest rates and expected returns on capital markets can display a strong influence on exchange rates too. To analyze the relationship between exchange rates and interest rates we need to understand the difference between the spot and the forward exchange rate:

42 Spot Markets On the spot exchange market Euro today t=0 is traded gainst Dollar today t=0 at the exchange rate today. Purchase agreement and exchange of currencies take place at the same point in time. t=0 t+1 t+2 t+3 Agreement between buyer and seller today t Currency delivered by seller to buyer today Spot Markets On the forward exchange market, Euro at e.g. day t+3 is traded against Dollar at day t+3 at an exchange rate fixed today t for day t+3. Purchase agreement inclusive fixation of exchange rate takes place today t, while the exchange of currencies takes place at day t+3. t=0 t+1 t+2 t+3 Agreement between buyer and seller today t Currency delivered by seller to buyer at t

43 Spot Markets Again, we can find the accurate relation between the exchange rate and prices for domestic and foreign goods with the help of a numerical experiment: Where would you invest your money at the following exchange and interest rates? 1. Example: Interest rate for a fixed rate bond denominated in with maturity of one year is: i = 10 % Interest rate for a fixed rate bond denominated in $ with maturity of one year is: i $ = 6 % Spot market exchange rate: e $ = 1 Forward market exchange rate for paid in one year: f $ = 0,92 How would this affect the demand for Euro? Spot Markets Where would you invest your money at the following exchange and interest rates? 2. Example: Interest rate for a fixed rate bond denominated in with maturity of one year is: i = 10% Interest rate for a fixed rate bond denominated in $ with maturity of one year is: i $ = 6% Spot market exchange rate: e $ = 0,94 Forward market exchange rate for paid in one year: f $ = 0,92 How would this affect the demand for Euro?

44 Spot Markets At what spot market exchange rate would you be indifferent between an investment in and $ bonds? 3. Example: Interest rate for a fixed rate bond denominated in with maturity of one year is: i = 10% Interest rate for a fixed rate bond denominated in $ with maturity of one year is: i $ = 6% Spot market exchange rate: e $ =??? Forward market exchange rate for paid in one year : f $ = 0,92 How would this affect the demand for Euro? Spot Markets Return on investment of 1 in a -bond Exchange of 1 in $ Return on investment of 1$ in a $-bond Exchange of $-return in

45 Spot Markets The interest rate parity formula shows the potential effect of interest rates on the exchange rate: If the domestic interest rate i increases (and the foreign interest rate and the forward exchange rate stay constant!) the Euro appreciates against the Dollar e $. Economic interpretation: If the domestic interest rate increases and everything else stays constant, Euro-bonds offer a higher return than Dollar-bonds. Consequently, investors will want to buy Euro-bonds and sell Dollarbonds. To do so, they have to exchange Dollar against Euro so that the demand for Euro grows and the supply of Dollar increases and the Euro appreciates against the Dollar Spot Markets The interest rate parity formula shows the potential effect of interest rates on the exchange rate: If the foreign interest rate i $ increases (and the domestic interest rate and the forward exchange rate stay constant!) the Dollar appreciates against the Euro e $. Economic interpretation: If the foreign interest rate increases and everything else stays constant, Dollar-bonds offer a higher return than Euro-bonds. Consequently, investors will want to buy Dollar-bonds and sell Eurosecurities. To do so, they have to exchange Euro against Dollar so that the demand for Dollar grows and the supply of Euro increases and the Euro depreciates against the Dollar

46 Spot Markets The interest rate parity theory helps us to understand for example why the Euro appreciates against the Dollar, when the European Central Bank keeps its interest rate (the main refinancing rate) constant, while the Fed (=the US central bank) lowers its interest rate (the Fed funds rate). the Euro depreciates against the Dollar, when the US-economy displays strong growth, which increases profits of US firms and hence expected stock dividends. The interest rate parity theory is an important mechanism that helps us understand the interrelationships between the exchange market and domestic and foreign capital markets. How well does the interest parity theory perform empirically? Spot Markets

47 Spot Markets Source: Dt. Bundesb. (Juli, 2005), Daily data Spot exchange rate of the Euro is undervalued given the interest rates! Empirical Evidence: Strict validity of the interest parity theory would imply that all points lie on the 45 -line. This is obviously not the case. The standard explanation for these deviations are transaction costs in buying assets and exchanging currencies. Nevertheless the diagram shows that the correlation between both factors does to a large extent correspond to the prediction of the interest parity theory. e $ Spot Markets The more $ is paid for one the cheaper USassets get so that the return on investment in US-assets grows => The more is supplied to the spot market. -Supply e $,1 The more is paid for one $ the cheaper Euroassets get so that the return on an investment in Euro-assets grows. => The more is asked for on the spot market. o -Demand

48 e $ Spot Markets What happens to the equilibrium exchange rate if the Fed increases th the Dollar interest rate from i $ 1 to i $ 2? i $ 1 < i $ 2 -Supply(i $ 1) e $,1 -Demand(i $ 1) o Capital Markets Credit Markets Stock Markets Spot Markets Forward Markets 2.3. Derivatives Forwards and Futures Options

49 Forward Markets On the spot exchange market Euro today t=0 is traded against Dollar today t=0 at the exchange rate today. Purchase agreement and exchange of currencies take place at the same point in time. t=0 t=1 t=2 t=3 Agreement between Buyer and Seller today t Currency delivered by Seller to Buyer today Forward Markets On the forward exchange market, e.g. Euro at day t+3 is traded against Dollar at day t+3 at an exchange rate fixed today for day t+3. Purchase agreement inclusive fixation of exchange rate takes place today t, while the exchange of currencies takes place at day t+3. t=0 t=1 t=2 t=3 Agreement between Buyer and Seller today t Currency Delivered by Seller to Buyer at t

50 Forward Markets Standard forward exchange contracts are written for one, three, six and 12 month Forward Markets Why do people demand on the forward exchange markets? How could the following companies reduce their sales risk caused by potential changes of the exchange rate? An European car manufacturer sells one car to an American dealer one month forward at a price of $ payable at the date of delivery. The production costs for this car are At the current spot market exchange rate of 2 $ the company could cover its costs (total sales = $ / 2 $ = ). If the would appreciate to an exchange rate of 4 $, the company made a loss of $ / 4 $ =

51 Forward Markets An American manufacturer of refrigerators sells 100 refrigerators to an European dealer one month forward at a price of payable at the date of delivery. The production costs for 100 refrigerators are $. At the current spot market exchange rate of 2 $ the company could cover its costs (total sales = * 2 $ = $). If the would depreciate to an exchange rate of 1 $, the company made a loss of * 1 $ $ = 8000 $ Forward Markets What kind of deal would reduce the sales risk of both manufacturers? The manufacturers could sign the following forward contract: The European manufacturer sells the American manufacturer $ in exchange for payable in one month. This implies an agreement on a forward exchange rate of f $ t, t+1 = 2. This forward contract would eliminate the exchange rate risk of both manufacturers to zero. Consequently, given a forward market that allows such kind of deals, manufacturers can sell their products to different currency areas without exchange rate risk

52 f $, t, t Forward Markets The more forward-$ are paid for one, the more sales to European goods markets are profitable for American producers. => The more is supplied to the forward market. Forward -Supply The less forward-$ have to be paid for one, the more sales to American goods markets are profitable for European producers. => The more is demanded on the forward market. Forward -Demand Forward Markets So far we have motivated transactions on the forward exchange market by trade with goods. However, another important motivation for transactions on the forward exchange market comes from the capital markets. As we have already seen, the forward exchange rate appears in the interest rate parity equation. Hence all changes that effect the other variables in this equation may also affect the foreign exchange rate. This is shown by the following considerations:

53 Forward Markets Not only trading transaction give rise to demand or supply to forward exchange markets: Capital market transactions play an important role too: Return on -bond < Return on $-bond => => Supply of forward-$ grows = Demand for forward- grows f Forward Markets Not only trading transaction give rise to demand or supply to forward exchange markets: Capital market transactions play an important role too: Return on -bond > Return on $-bond => => Demand for forward-$ grows = Supply of forward- grows f

54 Forward Markets Consequently, the forward exchange market is hit by interest rate changes in the opposite way as the spot exchange market! Derivatives 2.1. Capital Markets Credit Markets Stock Markets Spot Markets Forward Markets 2.3. Derivatives Forwards and Futures Options

55 What are forwards? A forward contract is an agreement between two parties at date t, to sell respectively buy a particular asset at a particular price at date t+x Derivatives Forwards and Futures The two parties may be private companies, private investors as well as financial institutions. The particular asset is also called underlying asset and may be a financial asset (fixed rate bonds, stocks ) as well as standardized goods (raw materials, intermediate products, precious metals, grain, lean hog ). The particular price is also called delivery price or contract price. It does not change over the whole period form date t to date t+x. Date t+x is also called maturity date. =>A forward exchange contract is a forward with a currency as underlying asset! Derivatives Forwards and Futures What are forwards? Example: Two parties agree that one party sells and the other party buys a stock of corporation XYZ in 6 months at a delivery price of 100. What will the value of this forward contract be when the market price of the stock at six months date will be 80? For the selling party: For the buying party: What will the value of this forward contract be when the market price of the stock at six months date will be 150? For the selling party: - 50 For the buying party:

56 Value of the forward contract to the buyer at maturity date Value of forward contract ( ) Value of the forward contract to the seller at maturity date Value of forward contract ( ) Delivery Price Market value of stock ( ) Delivery Price Market value of stock ( ) Derivatives Forwards and Futures Example: Complete risk elimination for the selling party What will the be value of this stock plus the forward contract (with K =100 ) for the selling party after 6 months when the market price of the stock today is 100 and at 6 months date will be 80? For the selling party: + 80 (selling the stock) + 20 (selling the forward contract) =F t+x = K - P t+1 = = 100 What will be the value of this stock plus the forward contract for the selling party after 6 months when the market price of the stock today is 100 and at six months date will be 150? For the selling party : (selling the stock) - 50 (selling the forward contract) =F t+x = K - P t+1 = = 100 => Held together with the corresponding stock, the forward contract completely eliminates risk for the selling party

57 Example: Complete risk elimination for the buying party 2.3. Derivatives Forwards and Futures What will the be value of selling short the stock plus the forward contract for the buying party when the market price of the stock today is 100 and at six months date will be 80? For the buying party: (selling short the stock) - 80 (buying back the stock) - 20 (selling the forward contract) = 0 What will be the value of selling short the stock plus the forward contract for the buying party when the market price of the stock today is 100 and at six months date will 150? For the buying party: (selling short the stock) (buying back the stock) + 50 (selling the forward contract) = 0 Held in conjunction with the corresponding short position, the forward contract completely eliminates risk for the buying party Derivatives Forwards and Futures Example: Higher risk for the buying party Held together with the corresponding stock, the forward contract completely eliminates risk for the buying party. Held on its own, the forward contract implies a higher risk than holding the stock for the buying party: Assumption: stock price shortly before maturity date: 110 => value of forward contract for buying party = 10 = P t+1 - K = Assumption: stock price decreases to: 90 => price of forward contract for buying party = 10 = P t+1 - K = Percentage decrease in stock price: 18 % (=( ) / 110 ) Percentage decrease in forward price: 200% (=(10 -(-10 ))/10 )

58 2.3. Derivatives Forwards and Futures Example: Higher risk for the buying party This is of course also true for a increase in the stock price: Assumption: stock price shortly before maturity date: 110 => value of forward contract (with a delivery price equal to 100 ) for buying party = 10 = P t+1 - K = Assumption: stock price rises to: 120 => value of forward contract for buying party = 20 = P t+1 - K = Percentage increase in stock price: + 9 % (= ( )/110 ) Percentage increase in forward price: + 100% (= (20-10 )/10 ) These large percentage gains or losses as a result of smaller percentage movements of the underlying assets is characteristic of many types of derivatives. It is called leverage-effect or gearing-effect Example for Higher Risk: The leverage effect Value of forward contract ( ) Value of forward contract ( ) +200 % = (30-10)/ % = ( )/ % = (-10-10)/10 Market value of stock ( ) Market value of stock ( ) -18 % = (90-110)/

59 2.3. Derivatives Forwards and Futures The pricing of forwards / futures: 3.3. Derivatives Forwards and Futures Details As shown by the above diagrams, the value (or price ) of a forward contract (F) to the buyer (= the one who must buy the underlying asset at the delivery price) at maturity date (t+x) is equal to the difference between the delivery price (=K) and the market price of the underlying asset at maturity date P t+x : The price before maturity date (t+n, 0<n<x) is given by the following formula: where r is the interest rate of a risk-free security and x-n is the number of periods to maturity date. 59

60 The pricing of forwards / futures: 3.3. Derivatives Forwards and Futures Details This forward pricing formula F t+n = P t+n K /(1+r) (x-n) will be only valid if the underlying asset pays no income (=interest, dividends, ) until maturity date of the forward contract (see our first example). If there are income payments before maturity to the holder of the instrument, they affect of course the above arbitrage mechanisms. Therefore the formula has to modified in the following way: where I t+n is the present value of all the income payments that the underlying asset generates Derivatives Forwards and Futures Details The settlement of forwards / futures - e.g. a commodity forward: Selling position: A Bavarian farmer, who wants to hedge the profit of the cultivation of hop on marginal agricultural land at a delivery price of K at point t (springtime) with maturity date t+x (autumn). Buying position: A Hamburg brewery, who wants to hedge the production costs of beer for an export contract with delivery time t+x+1. Value of the buyer position (hold by the brewery) in the forward at maturity date t+x: F t,t+x = P t+x - K 60

61 3.3. Derivatives Forwards and Futures Details The settlement of forwards / futures - e.g. a commodity forward: Possible ways of settlement if P t+x > K: (1) Settlement by delivery of hop by the Bavarian farmer to the Hamburg brewery at price K. Advantage to the farmer: Despite of the fact that he could have realized a higher profit without the forward contract (P t+x > K), he has realized a safe profit per unit hop equal to K minus his production costs. Advantage to the brewery: The brewery has a safe profit from its export contract, despite of the fact the spot price of hop is much higher at t+x, because the forward contract allows to buy at price K. Disadvantage of the settlement by delivery: One of both parties has to bear the transportation, storage and insurance cost from Bavaria to Hamburg Derivatives Forwards and Futures Details Value of the buying position in the forward contract F t,t+x = P t+x - K The settlement of forwards / futures - e.g. a commodity forward: Possible ways of settlement if P t+x > K: (2) Settlement in cash by the Bavarian farmer to the Hamburg brewery at price K: The farmer sells his hop at the spot market price of P t+x to a Bavarian brewery and pays to the Hamburg brewery the value of the forward contract at maturity date t+x: F t,t+x and keeps the difference P t+x - F t,t+x = K as his sales revenue. So the farmer has finally sold his hop at the delivery price K! The brewery buys its hop at the spot market price of P t+x from an East Frisian Farmer and uses the F t,t+x payment from the Bavarian farmer to finance this purchase in part. => Net costs of buying the hop at the spot market: P t+x - F t,t+x = K. So the brewery has finally bought its hop at the delivery price K! 61

62 3.3. Derivatives Forwards and Futures Details The settlement of forwards / futures - e.g. a commodity forward: Possible ways of settlement if P t+x > K: Advantage to the farmer: The same as in (1) Advantage to the brewery: The same as in (2) Value of the buying position in the forward contract F t,t+x = P t+x - K Advantage of settlement in cash compared to settlement by delivery: Avoidance of transportation, storage and insurance cost from Bavaria to Hamburg Derivatives Forwards and Futures Details Value of the buying position in the forward contract F t,t+x = P t+x - K The settlement of forwards / futures - e.g. a commodity forward: Possible ways of settlement: (3) Daily settlement in cash at t+n with 0<n<x: If F t,t+n > F t,t+n-1 : The farmer pays F t,t+n - F t,t+n-1 to the brewery at the end of the day. If F t,t+n < F t,t+n-1 : The brewery pays F t,t+n-1 - F t,t+n to the farmer at the end of the day. If at maturity date t+x the market price of hop is higher than the delivery price of the contract K, the market price of the forward will equal F t,t+x = P t+x K >0, what is equal to the net value of the daily payments of the farmer to the brewery (and vice versa), as the following example shows: 62

63 3.3. Derivatives Forwards and Futures Details The settlement of forwards / futures - e.g. a commodity forward: Possible ways of settlement: (3) Daily Settlement in cash at t+n with 0<n<3: Value of the buying position in the forward contract F t,t+x = P t+x - K t t+1 t+2 t+3 F t,t =P t -K/(1+i) 3= 0 F t,t+1 =P t+1 -K/(1+i) 2 >0 F t,t+2 =P t+2 -K/(1+i) 1 <0 F t,t+3 =P t+3 -K>0 F t,t =0 F t,t+1 - F t,t >0 F t,t+1 - F t,t+2 >0 F t,t+3 - F t,t+2 >0 Payment: Farmer to Brewery Payment: Brewery to Farmer Payment: Farmer to Brewery Sum of all payments from the farmer to the brewery: F t,t + (F t,t+1 - F t,t ) - (F t,t+1 - F t,t+2 )+ (F t,t+3 - F t,t+2 ) = F t,t Derivatives Forwards and Futures Details The settlement of forwards / futures - e.g. a commodity forward: Possible ways of settlement: (3) Daily Settlement in cash at t+n with 0<n<3: Value of the buying position in the forward contract F t,t+x = P t+x - K t t+1 t+2 t+3 F t,t =P t -K/(1+i) 3= 0 F t,t+1 =P t+1 -K/(1+i) 2 >0 F t,t+2 =P t+2 -K/(1+i) 1 <0 F t,t+3 =P t+3 -K>0 F t,t =0 F t,t+1 - F t,t >0 F t,t+1 - F t,t+2 >0 F t,t+3 - F t,t+2 >0 Payment: Farmer to Brewery Payment: Brewery to Farmer Payment: Farmer to Brewery Sum of all payments from the farmer to the brewery: F t,t + (F t,t+1 - F t,t ) - (F t,t+1 - F t,t+2 )+ (F t,t+3 - F t,t+2 ) = F t,t+3 63

64 3.3. Derivatives Forwards and Futures Details The settlement of forwards / futures - e.g. a commodity forward: Advantage to the farmer: The same as in (1) Advantage to the brewery: The same as in (2) Value of the buying position in the forward contract F t,t+x = P t+x - K Advantage of daily settlement in cash compared to settlement in cash at the end of maturity: Reduction of the risk that the counterparty will fail to execute an agreed transaction (fraudulence or bankruptcy) 3.3. Derivatives Forwards and Futures K = P t *(1+r) (x-n) P t+n K/(1+r) (x-n) F t+n = P t+n - K/(1+r) (x-n) 64

65 2.3. Derivatives Forwards and Futures What are futures? Forwards Contract between two private parties Custom-made (underlying assets, prices, rates, maturity ) One specified delivery date Typically delivery of underlying assets or clearing at the end of maturity Futures Contracts listed on a stock exchange Standardized contracts Several optional delivery dates Typically evening-up in cash before maturity Derivatives Forwards and Futures 2.1. Capital Markets Credit Markets Stock Markets Spot Markets Forward Markets 2.3. Derivatives Forwards and Futures Options

66 2.3. Derivatives Options What are options? An option is an asset which gives the holder the right but not the obligation to buy (call option) or sell (put option) an underlying asset on a future date at a price (= exercise price) agreed now. The counterparty of the holder is the writer. He has to do what the holder demands. => The writer of an option has no option As a consequence, the risk is asymmetrically distributed: The writer bears a higher risk as the holder. Therefore the holder has to pay an option premium to the writer Derivatives Options The are two types of call and put options: European options American options An European option is an option which can be exercised only at a particular date. An American option is an option which can be exercised any time up to a particular date. Right to buy Particular exercise date European call option Any time up to a particular date American call option Right to sell European put option American put option In the following, we will discuss only European options

67 2.3. Derivatives Options What is the difference between options and futures? From the view point of the option holder, an option confers the right but not the obligation to buy or sell an asset at a particular price. A future implies the obligation to buy or sell an asset at a particular price. This property affects the market price of an option. Example: What is the option value (market price) at the exercise date to the holder / writer in case of a call option with an exercise price of 100, if the underlying asset is a stock? Value of a call option to the holder at exercise date (exercise price = 100 ) Value of option ( ) Market price of the holder position of the option Value of a call option to the writer at exercise date (exercise price = 100 ) Value of option ( ) Market value lower than exercise price => Call option not used! Market value of stock ( ) Market value of stock ( ) Market value lower than exercise price => Not profitable to use the call option! Market price of the writer position of the option

68 3.3. Derivatives Options Details The price of options at the exercise date: As shown by the above diagrams, the market value of a call option (C) to the holder at exercise date (t+x) is equal to the difference between the market price of the underlying asset at exercise date P t+x and the exercise price (=K): Value of a put option to the holder at exercise date (exercise price = 100 ) Value of option ( ) Market price of the holder position of the option Market value of stock ( ) Value of a put option to the writer at exercise date (exercise price = 100 ) Value of option ( ) Market value higher than exercise price => Put option not used! Market value of stock ( ) Market value higher than exercise price => Not profitable to use the put option! Market price of the writer position of the option

69 3.3. Derivatives Options Details The price of options at the exercise date: As shown by the above diagrams, the market value of a put option (C) to the holder at exercise date (t+x) is equal to the difference between the exercise price (=K) and the market price of the underlying asset at exercise date P t+x : 2.3. Derivatives Options Option terminology: When an option has a positive price it is said to be in-themoney. => A call option is in-the-money when the spot price of the underlying asset is above the exercise price. A put option is in-the-money when the spot price of the underlying asset is below the exercise price. When an option has a price of zero it is said to be out-of-themoney

70 3.3. Derivatives Options Details The price of options before the exercise date: The price of a call option before the excercise date (t+n, 0<n<x) is given by the Black & Scholes formula: where r is the interest rate of a risk-free security, σ the standard deviation of the logarithmized yearly dividend return of the underlying share, x-n is the number of periods to exercise date and Φ(y) is the cumulative probability function of the standardized variable y. The pricing of options: 3.3. Derivatives Options Details Although the B. & S. formula is somewhat more complex than the pricing formula for a forward contract, a certain analogy is recognizable. The B. & S. formula is also derived from no-arbitrage-arguments. However, it will only be valid if the following assumptions hold: (1) The stochastics of share values is lognormal with constant expected return and variance. (2) There are no transaction costs, taxes or indivisibilities. (3) There are no risk-free arbitrage opportunities. (4) There is continuous trade in all securities. (5) The risk-free rate of return is constant. (6) All agents can borrow or lent money at the same rate of return. Especially the assumption of lognormal stochastics has proven wrong for many assets, because it neglects so called tail risks. 70

71 2.4. How to Hedge Exchange Rate Risk? 2.1. Capital Markets Credit Markets Stock Markets Spot Markets Forward Markets 2.3. Derivatives Forwards and Futures Options 2.4. How to Hedge Exchange Rate Risk? How to Hedge Exchange Rate Risk? This section explores alternative ways to use derivatives to hedge the exchange rate risk of a firm engaged in international trade with goods. Consider the problem described by the following graph:

72 t=0 t=1 t=2 t=3 t Trading transaction: $ in t=3 Production costs: Incoming payment: $ Spot rate: 2 $ Spot rate: e $? Profit given the spot rate: $ / 2 $ = Prof. Dr. Rainer Maure Profit: $ / e $ =??? => If in t=3 the spot rate of t=0 were still given, a profitable trading transaction would be possible. However a depreciation of the Dollar to a level of e $ = 2,5 until t=3 is as well possible. In this case a loss of $ / 2,5 $ 9000 = would result! = Exchange Rate Risk How to Hedge Exchange Rate Risk? Three basic instruments can be used to hedge a exchange rate risk: 1. Foreign Currency Credits 2. Currency Futures 3. Foreign Currency Options Prof. Dr. Rainer Maure

73 => Certain net profit = = Prof. Dr. Rainer Maure t=0 t=1 t=2 t=3 Trading transaction: $ in t=3 Costs: Incoming payment: $ Spot rate: 2 $ Spot rate: e $? $-credit: $ Interest rate 1) : 2% Exchange in at spot rate: $ / 2 $ = Exchange of 200 * 2 $ in 400 $ for interest payment in t=3 1. Foreign Currency Credit: Incoming payment from transaction: $ used to pay back credit: $ *(1,02) $ = 400 $ t 1) Monthly interest rate = yearly rate of 8,24% = ((1,02) (1/3) ) Currency Future: t=0 t=1 t=2 t=3 t Trading transaction: $ in t=3 Costs: Incoming payment: $ Spot rate: 2 $ Spot rate: e $? Forward rate: 2,1 $ Selling $ forward t=3 at the current forward rate of 2,1 $ Incoming payment from transaction: $ used for exchange in at the agreed forward rate: $ / 2,1 $ = 523,8 => Certain net profit = 523, Prof. Dr. Rainer Maure 73

74 3. Currency Option: t=0 t=1 t=2 t=3 t Trading transaction: $ in t=3 Costs: Incoming payment: $ Spot rate: 2 $ Spot rate: 2,4 $ Exercise rate: 2 $ Purchase of a $-put option at an exercise rate of 2 $ and an option premium of 500 => Exercise of the option: $ / 2 $ = => Certain net profit = = Prof. Dr. Rainer Maure 3. Currency Option: t=0 t=1 t=2 t=3 t Trading transaction: $ in t=3 Costs: Incoming payment: $ Spot rate: 2 $ Spot rate: 1,8 $ Exercise rate: 2 $ Purchase of a $-put option at an exercise rate of 2 $ and an option premium of 500 => Abandonment of the option: $ / 1,8 $ = 2 111,1 => Certain net profit = 2 111,1-500 = 1611, Prof. Dr. Rainer Maure 74

75 Chapter 3: Questions for Review 35. What is the difference between forwards and futures. 36. A mechanical engineering company has the opportunity to sell a machine worth $ with an incoming payment at 1 month term. Production costs of the machine are What is more profitable: A foreign exchange hedge with a future or a credit under the following market conditions: Spot exchange rate: e $ = 1.1, forward rate: f $ = 1.2, interest rate (maturity 1 month): i $ = 2% Chapter 3: Questions for Review You should be able to answer the following questions at the end of this chapter. If you have difficulties in answering a question, discuss this question with me during or at the end of the next lecture or attend my colloquium

76 Chapter 3: Questions for Review 1. What is a security with a fixed rate? 2. What is the internal rate of return of a fixed rate bond, if the face value is 100, the present market price is 90, the fixed rate is 5% and the number of periods to the end of maturity is 1? 3. What is the market price of a fixed rate bond, if the face value is 100, fixed rate is 10%, the market interest rate is 20% and the number of periods to the end of maturity is 4? 4. What is the general relation between the market price of a security and its internal rate of return? 5. If you had the choice between a government bond and a corporate bond with equal face value and equal internal rate of return, which one would you choose and why? Chapter 3: Questions for Review 6. What is a risk premium? 7. What is the price risk of a fixed rate bond and when does it emerge? 8. What is the market value of the following fixed rate bond? 9. What is a stock? 10. Derive the dividend payments of a corporation from the money it receives from the sales of its goods. 11. Why is a stock a riskier security as a fixed rate bond?

77 Chapter 3: Questions for Review 12. What factors influence in general the level of dividend payments? 13. What information is necessary to calculate the fair value of a stock? 14. Give a verbal explanation of a CAP-Modell. 15. What is the price earnings ratio of a stock? 16. Interpret the price earnings ratio? 17. What is the dividend yield of a stock? 18. Interpret the dividend yield? 19. What is the problem of forecasting a stock price on the basis of its past price trend? 20. What are the motives for people to demand foreign exchange? Chapter 3: Questions for Review 21. If the price for 1 kg cookies is 4 in Europe and 2 $ in the USA, what will the equilibrium exchange rate be in the absence of transaction costs (= transport, insurance, taxes)? 22. What is the formula for the purchasing power parity exchange rate? 23. Derive the formula for interest rate parity. 24. What happens with the spot exchange rate of the against the $, when the -interest rate (average) grows and everything else stays unchanged? Give an explanation. 25. What happens with the spot exchange rate of the against the $, when the $-interest rate (average) grows and everything else stays unchanged? Give an explanation

78 Chapter 3: Questions for Review 26. What happens with the spot exchange rate of the against the $, when speculators sell on the forward market and everything else stays unchanged? Give an explanation. 27. What are the two reasons for the -supply curve to slope upward? 28. What are the two reasons for the -demand curve to slope downward? 29. Why do people demand on the forward exchange markets? 30. Explain how a the forward exchange rate market can be used to eliminate exchange rate risk for firms with production costs and sales denominated in different currencies Chapter 3: Questions for Review 31. What are the two reasons for the forward -supply curve to slope upward? 32. What are the two reasons for the forward -demand curve to slope downward? 33. What is a forward contract? 34. Give a graphical exposition of the relation between the value of a forward contract to the buyer (seller) and the price of the underlying asset at maturity date of the contract, if the contract price for the underlying asset is

79 Chapter 3: Questions for Review 35. What is the difference between forwards and futures. 36. What is an European (American) put (call) option? 37. Give a graphical exposition of the relation between the value of an European call (put) option to the holder (writer) and the price of the underlying asset at exercise date of the option, if the contract price for the underlying asset is 50 and the option premium is Why is the risk of option holders and option writers said to be not symmetrical? 39. What are the pros and cons of hedging a future sales in foreign currency with the help of a forward contract and with the help of an option? Chapter 3: Questions for Review 35. What is the difference between forwards and futures. 36. A mechanical engineering company has the opportunity to sell a machine worth $ with an incoming payment at 1 month term. Production costs of the machine are What is more profitable: A foreign exchange hedging with a future or credit under the following market conditions: Spot exchange rate: e $ = 1.1, forward rate: f $ = 1.2, interest rate (maturity 1 month): i $ = 2%

80 Digression: The Inverse Relation between Market Price of Bonds and Market Interest Rate and the Real Estate Crises Negative Relation between Market Value of Bonds and Market Interest Rate: If the market interest rate i goes up, the market value of the bond will go down and vice versa Digression: The Inverse Relation between Market Price of Bonds and Market Interest Rate and the Real Estate Crises Simplified Balance Sheet of a Business Bank Assets Liabilities Mortgage Bonds are collaterized by the value of the real estate objects. Credits to Firms and Housholds Mortgage Backed Bonds Savings from Households For example: In Germany a mortgage credit equals typically about 50% of the market value of a real estate object. => Market Value of Collateral = 50% * Market Value of Real Estate Object

81 Digression: The Inverse Relation between Market Price of Bonds and Market Interest Rate and the Real Estate Crises => Market Value of Collateral = 50% * Market Value of Real Estate Object => The lower the market value of the real estate object the lower is the value of the collateral, with which the mortgage credit is hedged. => The lower the value of the collateral, the higher the default risk of the mortgage credit bonds (because the value of the collateral is what the holder of a mortgage bond gets, in case of a default of the debtor) => The higher the default risk of the mortgage credit bonds, the higher the risk premium that must be paid to a buyer of the bond. => The higher the risk premium the higher the market interest rate for mortgage bonds. => The higher the market interest rate for mortgage bonds the lower the market price of issued mortgage bonds Digression: The Inverse Relation between Market Price of Bonds and Market Interest Rate and the Real Estate Crises => The higher the market interest rate for mortgage bonds the lower the market price of issued mortgage bonds

82 Digression: The Inverse Relation between Market Price of Bonds and Market Interest Rate and the Real Estate Crises The lower the market value of bonds the bigger the hole in the balance sheet of the business bank: Simplified Balance Sheet of a Business Bank Assets Credits to Firms and Housholds Mortgage Backed Bonds Liabilities Savings from Households Digression: The Inverse Relation between Market Price of Bonds and Market Interest Rate and the Real Estate Crises The lower the market value of bonds the bigger the hole in the balance sheet of the business bank: Simplified Balance Sheet of a Business Bank Assets Credits to Firms and Housholds Mortgage Backed Bonds Liabilities Savings from Households Deficit

83 Digression: The Inverse Relation between Market Price of Bonds and Market Interest Rate and the Real Estate Crises Digression: The Inverse Relation between Market Price of Bonds and Market Interest Rate and the Real Estate Crises