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1

Prof. Dr. Rainer Maurer- 1 -

International Financial Markets2. Major Markets and Their Assets

Prof. Dr. Rainer Maurer- 2 -

2. Major Markets and Their Assets2.1. Capital Markets

2.1.1. Credit Markets2.1.2. Stock Markets

2.2. Foreign Exchange Markets2.2.1. Spot Markets2.2.2. Forward Markets

2.3. Derivatives2.3.1. Forwards and Futures2.3.2. 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.

2. Major Markets and Their Assets

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.

Prof. Dr. Rainer Maurer- 3 -

2. Major Markets and Their Assets

Financial Markets

Capital Markets

Stock Market

Money Market

Credit Markets

Governm. Securities

Corporate Debt

Foreign Exchange Markets

Spot Market

Forward Market

Mortgage Debt

Futures Options Swaps

Derivatives

ForwardsProf. Dr. Rainer Maurer

- 4 -

2. Major Markets and Their Assets2.1. Capital Markets

2.1.1. Credit Markets2.1.2. Stock Markets

2.2. Foreign Exchange Markets2.2.1. Spot Markets2.2.2. Forward Markets

2.3. Derivatives2.3.1. Forwards and Futures2.3.2. Options

2. Major Markets and Their Assets2.1.1. Credit Markets

Prof. Dr. Rainer Maurer- 5 -

Different types of securities are traded on credit markets: Securities with fixed interest rates1) 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.

2. Major Markets and Their Assets2.1.1. Credit Markets

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)

Prof. Dr. Rainer Maurer- 6 -

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

2. Major Markets and Their Assets2.1.1. Credit Markets

2

Prof. Dr. Rainer Maurer- 7 -

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%

2. Major Markets and Their Assets2.1.1. Credit Markets

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!

Prof. Dr. Rainer Maurer- 8 -

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 %

2. Major Markets and Their Assets2.1.1. Credit Markets

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!

Prof. Dr. Rainer Maurer- 9 -

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%

2. Major Markets and Their Assets2.1.1. Credit Markets

At this market price, the internal rate of return of this bond exactly equals the market interest rate (=Pari)!

Prof. Dr. Rainer Maurer- 10 -

2. Major Markets and Their Assets2.1.1. 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 returnequals 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 returnequals the market interest rate.

Prof. Dr. Rainer Maurer- 11 -

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 onlyrisk 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.

2. Major Markets and Their Assets2.1.1. Credit Markets

Prof. Dr. Rainer Maurer- 12 -

Sou

rce:

Deu

tsch

e B

unde

sban

k

= Corporate Bonds = Government Bonds

3

Prof. Dr. Rainer Maurer- 13 -

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.

2. Major Markets and Their Assets2.1.1. Credit Markets

Prof. Dr. Rainer Maurer- 14 -

2. Major Markets and Their AssetsSummary: Price Risk of Fixed Rate Securities

i

()

D(i)

S(i)

io

Bo

Date of issue: t

Market interest rate for fixed rate bonds with a maturity of 4 years: io = 5%

=> As already seen above, if the fixed rate of a bond equals exactly 5%, its market price will equal its face value (100 ):

Market for fixed rate securites with a maturity

of 4 years

=Credit Demand

=Credit Supply

Prof. Dr. Rainer Maurer- 15 -

2. Major Markets and Their AssetsSummary: Price Risk of Fixed Rate Securities

i

()

D(i)

S(i)1

i1

Bo

One year later: t+1Market supply (=credit demand) has grown so that interest rate for fixed rate securities with a maturity of 3 years equals: io = 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.

Market for fixed rate securites with a maturity

of 3 years

S(i)2

io

B1

Prof. Dr. Rainer Maurer- 16 -

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, dont 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).

2. Major Markets and Their Assets2.1.1. Credit Markets

Prof. Dr. Rainer Maurer- 17 -

2. Major Markets and Their Assets2.1.1. Credit Markets

The bond market listings of newspapers present both, the market price of a bond and the

calculated internal rate of return.

Prof. Dr. Rainer Maurer- 18 -

To sum up:

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.

2. Major Markets and Their Assets2.1.1. Credit Markets

4

Prof. Dr. Rainer Maurer- 19 -

2. Major Markets and Their Assets2.1.1. Credit Markets

https://twitter.com/JanusCapital/status/590519759797530624

Prof. Dr. Rainer Maurer- 20 -

2. Major Markets and Their Assets2.1. Capital Markets

2.1.1. Credit Markets2.1.2. Stock Markets

2.2. Foreign Exchange Markets2.2.1. Spot Markets2.2.2. Forward Markets

2.3. Derivatives2.3.1. Forwards and Futures2.3.2. Options

2. Major Markets and Their Assets2.1.2. Stock Markets

Prof. Dr. Rainer Maurer- 21 -Source: Bank for International Settlements

Prof. Dr. Rainer Maurer- 22 -Source: Bank for International Settlements

Prof. Dr. Rainer Maurer- 23 -

Stocks1)

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:

2. Major Markets and Their Assets2.1.2. Stock Markets

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.

Prof. Dr. Rainer Maurer- 24 -

= Profit after tax = Money available for stockholders

= Residual Profit

./. 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

Money received from sales

Retained EarningsDividend payments

5

Prof. Dr. Rainer Maurer- 25 -

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.

2. Major Markets and Their Assets2.1.2. Stock Markets

Prof. Dr. Rainer Maurer- 26 -

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.

2. Major Markets and Their Assets2.1.2. Stock Markets

List of quotations of a stock market broker for a specific stock

2. Major Markets and Their Assets2.1.2. Stock Markets

Supply Curve

Number of stocks

Supply Curve

Number of stocks

List of quotations of a stock market broker for a specific stock

2. Major Markets and Their Assets2.1.2. Stock Markets

6

Menge (kg)

Demand Curve

Number of stocks

Menge (kg)

Demand Curve

Number of stocks

Market Diagram

Supply

Demand

Number of stocks

Demand=350

Supply=350

List of quotations of a stock market broker for a specific stock

2. Major Markets and Their Assets2.1.2. Stock Markets

Market Diagram

Supply

Demand

Number of stocks

Demand=350 Excess Supply

Percentage allotement of demand to supply: 350/450 =

77,7%

Supply=450

Market Diagram Supply

Demand

Number of stocks

7

Prof. Dr. Rainer Maurer- 37 -

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.

2. Major Markets and Their Assets2.1.2. Stock Markets

Prof. Dr. Rainer Maurer- 38 -

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. DT = 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 (PT=5/0,06 = 83,3).

2. Major Markets and Their Assets2.1.2. Stock Markets

Prof. Dr. Rainer Maurer- 39 -

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:

2. Major Markets and Their Assets2.1.2. Stock Markets

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!Prof. Dr. Rainer Maurer

- 40 -

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!

2. Major Markets and Their Assets2.1.2. Stock Markets

Prof. Dr. Rainer Maurer- 41 -

2. Major Markets and Their Assets2.1.2. Stock Markets

ij = yield of a risk-free securitymarket return for one unit

of risk

units of risk attached to

stock j*+

ij = specific risk premium for stock jyield of a risk-free security

+

One often used orientation for the appropriate risk specific discount factor of a stock is the Capital Asset Pricing Model(CAPM):

ij = discount rate of stock j, rj = rate of return of stock j, rM = rate of return of the market portfolio, ro = yield of a risk-free security

ij = *+

Prof. Dr. Rainer Maurer- 42 -

Interpretation:(1) If the yield of stock j displays no correlation with the return of the market portfolio (cov(ij,rM)= 0) the risk equivalent yield of security j equals the yield of the risk-free security (ro).

(2) If the yield of stock j displays perfect correlation with the return of the market portfolio M (cov(ij,rM)/var(rM) = 1) the risk equivalent yield of security j equals the yield of the market portfolio ( ij = r0 + 1* (rM r0) = rM ).

2. Major Markets and Their Assets2.1.2. Stock Markets

ij = *+

ij = *+

Market Beta (chapter 1.2.2)

8

Prof. Dr. Rainer Maurer- 43 -

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(ij,rM) and the future variance of yield of the market portfolio var(rM).

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 ij and rM 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.

2. Major Markets and Their Assets2.1.2. Stock Markets

Prof. Dr. Rainer Maurer- 44 -

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.

2. Major Markets and Their Assets2.1.2. Stock Markets

Details

Prof. Dr. Rainer Maurer- 45 -

2. Major Markets and Their Assets2.1.2. Stock Markets

Key figures for stocks:

The Dividend Yield:

Market price per stock = market value of the stock at period t = PtExample:

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%

Details

Prof. Dr. Rainer Maurer- 46 -

2. Major Markets and Their Assets2.1.2. Stock Markets

Key figures for stocks:

The Dividend Yield:

Interpretation:

The dividend yield is the yield per period an investor will have, if dividendpayments in all future periods stay the same. This number is of particularinterest for investors that need a regular income but dont want to sell theirstock in order to realize price gains (e.g. pension funds, investors borrowingto invest).

Prof. Dr. Rainer Maurer- 47 -

The dividend yield, Dt/Pt, 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.

Details

Prof. Dr. Rainer Maurer- 48 -

2. Major Markets and Their Assets2.1.2. Stock Markets

Key figures for stocks:

The Price Yield:

Market price per stock = market value of the stock at period t = PtExample:

Market Pricet = 120

Market Pricet-1 = 100 => Price Yield =

(120 - 100) /100 = 20 %

9

Details

Prof. Dr. Rainer Maurer- 49 -

2. Major Markets and Their Assets2.1.2. Stock Markets

Key figures for stocks:

The Price Yield:

Interpretation:

The price yield is the yield per period an investor will have, if he buys theshare at the beginning of a period and sells it at the end, neglecting thedividend payment. This number is of particular interest for speculation-oriented investors.

Prof. Dr. Rainer Maurer- 50 -

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.

Prof. Dr. Rainer Maurer- 51 -

Details

Prof. Dr. Rainer Maurer- 52 -

2. Major Markets and Their Assets2.1.2. Stock Markets

Key figures for stocks:

The Total Yield:

Dividend Yieldt = 3,3%

Price Yieldt = 20 %=> Total Yield = 23,3%

Prof. Dr. Rainer Maurer- 53 -

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.

Prof. Dr. Rainer Maurer- 54 -

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".

10

Prof. Dr. Rainer Maurer- 55 -

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 %).

Details

Prof. Dr. Rainer Maurer- 56 -

2. Major Markets and Their Assets2.1.2. Stock Markets

Key figures for stocks:

The price earnings ratio (P/E ratio):

Market price per stock = market value of the stock at period t = Pt

Earnings per stock from the recent set of accounts = [(Profit after tax /number of stocks)] = [(Dividend payments + retained earnings) / number ofstocks] (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) = 20

Details

Prof. Dr. Rainer Maurer- 57 -

2. Major Markets and Their Assets2.1.2. Stock Markets

Key figures for stocks:

The price earnings ratio (P/E ratio):

Interpretation:

(1) If retained earnings pay off either in form of future dividend payments orfuture price gains, the P/E ratio is equivalent to the number of years a stockhas to be hold in order to regain the money invested if the earnings staythe same in all future periods.

(2) The inverse of the P/E ratio is equivalent to the Earnings yield, i.e. tothe long run yield per period that can be expected if the earnings in allfuture periods will be the same as the present earnings. Example: a P/Eratio of 20 is equivalent to an earnings yield of 1/20 = 5%.

Prof. Dr. Rainer Maurer- 58 -

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/E-ratio. Such an increase is justified, if the future earnings of a stock grow.

http://www.econ.yale.edu/~shiller/data/ie_data.xls

Standard&Poors Cyclically Adjusted Price/Earnings RatioJanuary 1880 November 2013

Prof. Dr. Rainer Maurer- 59 -

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.

http://www.econ.yale.edu/~shiller/data/ie_data.xls

Standard&Poors 500 Price and EarningsJanuary 1870 November 2013

Prof. Dr. Rainer Maurer- 60 -

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)

Shiller (2005), Irrational Exuberance

(backward looking)

(for

war

d lo

okin

g)

11

Prof. Dr. Rainer Maurer- 61 -

Efficient Market Hypothesis (Eugene Fama,1965):

Prices on traded assets already reflect all past publicly available information.(Weak-form EMH)

Shiller (2005), Irrational Exuberance

(backward looking)

(for

war

d lo

okin

g)

Are these empirical observations

compatible with market efficiency?

Prof. Dr. Rainer Maurer- 62 -

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): http://johnhcochrane.blogspot.de/2013/10/gene-famas-nobel.html)

Shiller (2005), Irrational Exuberance

(backward looking)

(for

war

d lo

okin

g)

Are these empirical observations

compatible with market efficiency?

Prof. Dr. Rainer Maurer- 63 -

Problem with Famas 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, Famas changing risk aversion is an ad-hoc-assumption introduced to immunize the EMH against empirical observations.

Shiller (2005), Irrational Exuberance

(backward looking)

(for

war

d lo

okin

g)

Are these empirical observations

compatible with market efficiency?

Prof. Dr. Rainer Maurer- 64 -

Prof. Dr. Rainer Maurer- 65 -

2. Major Markets and Their Assets2.1. Capital Markets

2.1.1. Credit Markets2.1.2. Stock Markets

2.2. Foreign Exchange Markets2.2.1. Spot Markets2.2.2. Forward Markets

2.3. Derivatives2.3.1. Forwards and Futures2.3.2. Options

2.2. Foreign Exchange Markets

Prof. Dr. Rainer Maurer- 66 -

2.2. Foreign Exchange Markets 2.2.1. 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.

12

Prof. Dr. Rainer Maurer- 67 -

2.2. Foreign Exchange Markets 2.2.1. Spot Markets

Prof. Dr. Rainer Maurer- 68 -

2.2. Foreign Exchange Markets 2.2.1. 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.

Prof. Dr. Rainer Maurer- 69 -

2.2. Foreign Exchange Markets 2.2.1. 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 = PPrice 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 = PPrice per kg foreign cookies = 2 $ = P$Exchange rate = 1$

How would this affect the demand for Euro?Prof. Dr. Rainer Maurer

- 70 -

2.2. Foreign Exchange Markets 2.2.1. 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 tradedbetween the two currency areas, have the same price, whether measured in or measured in $.

This relation is called the purchasing power parity.

Prof. Dr. Rainer Maurer- 71 -

2.2. Foreign Exchange Markets 2.2.1. 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.

- 72 -Prof. Dr. Rainer Maurer

13

- 73 -Prof. Dr. Rainer Maurer Prof. Dr. Rainer Maurer

- 74 -

2.2. Foreign Exchange Markets 2.2.1. Spot Markets

If there are transport costs, the formula for the PPP-exchange (e$) rate has to be modified:

=> 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.

Upper border of the transport costs band

Lower border of the transport costs band

- 75 -Prof. Dr. Rainer Maure

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.

2.2. Foreign Exchange Markets 2.2.1. Spot Markets

- 76 -Prof. Dr. Rainer Maure

39,99 $ / 1,216 $ = 32,88

2.2. Foreign Exchange Markets 2.2.1. Spot Markets

e$ = P$ / P

0,640 $ =39,99 $ / 62,49

=> At an exchange rate of1,216 $ the Euro isovervalued against theDollar

- 77 -Prof. Dr. Rainer Maure

3. Whrungstheorie und Whrungspolitik3.1.3. Kaufkraft- und Zinsparitt

=> Given this trade restriction by Levis(monopolistic competition), no extra supplyof Euro for Dollar is triggered and hence theEuro will not depreciate against the Dollar.

Prof. Dr. Rainer Maurer- 78 -

2.2. Foreign Exchange Markets 2.2.1. Spot Markets

e$

eo

o

The less $ has to be paid for one , the more Euro-goods are cheaper

than $-goods and the more is demanded in exchange for $.

The more $ is paid for one , the more US-goods are cheaper than

Euro-goods and the more is hence supplied in exchange for $.

Equilibrium on the ex-change market in terms of -Supply and -Demand

-Demand

-Supply

14

Prof. Dr. Rainer Maurer- 79 -

2.2. Foreign Exchange Markets 2.2.1. Spot Markets

e$

eo

What happens to the equilibrium exchange rate if inflation in the USA is

higher than inflation in the -Area?

o

-Demand(P$,1)

-Supply(P$,1)

P$1 < P$2

Prof. Dr. Rainer Maurer- 80 -

2.2. Foreign Exchange Markets 2.2.1. Spot Markets

e$

What happens to the equilibrium exchange rate if inflation in the -Area

is higher than inflation in the USA ?

-Demand(P,1)

-Supply(P,1)

eo

o

P1 < P2

Prof. Dr. Rainer Maurer- 81 -

2.2. Foreign Exchange Markets 2.2.1. 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.

Prof. Dr. Rainer Maurer- 82 -

2.2. Foreign Exchange Markets 2.2.1. 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:

Prof. Dr. Rainer Maurer- 83 -

2.2. Foreign Exchange Markets2.2.1. 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.

tAgreement between buyer and seller today

Currency delivered by seller to buyer today

t=0 t+1 t+2 t+3

Prof. Dr. Rainer Maurer- 84 -

2.2. Foreign Exchange Markets2.2.1. 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.

tAgreement between buyer and seller today

Currency delivered by seller to buyer at t+3

t=0 t+1 t+2 t+3

15

Prof. Dr. Rainer Maurer- 85 -

2.2. Foreign Exchange Markets 2.2.1. 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?Prof. Dr. Rainer Maurer

- 86 -

2.2. Foreign Exchange Markets 2.2.1. 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?

Prof. Dr. Rainer Maurer- 87 -

2.2. Foreign Exchange Markets 2.2.1. 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?

Prof. Dr. Rainer Maurer- 88 -

2.2. Foreign Exchange Markets 2.2.1. Spot Markets

Return on investment of 1

in a -bond

Exchange of 1in $

Exchange of $-return in

Return on investment of 1$

in a $-bond

Prof. Dr. Rainer Maurer- 89 -

2.2. Foreign Exchange Markets 2.2.1. 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 Dollar-

bonds.

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.

Prof. Dr. Rainer Maurer- 90 -

2.2. Foreign Exchange Markets 2.2.1. 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 con-

stant, Dollar-bonds offer a higher return than Euro-bonds.

Consequently, investors will want to buy Dollar-bonds and sell Euro-securities.

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.

16

Prof. Dr. Rainer Maurer- 91 -

2.2. Foreign Exchange Markets 2.2.1. 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?

Prof. Dr. Rainer Maurer- 92 -

2.2. Foreign Exchange Markets 2.2.1. Spot Markets

2.2. Foreign Exchange Markets 2.2.1. Spot Markets

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 ex-planation for these devi-ations are transaction costs in buying assets and exchanging cur-rencies. Nevertheless the diagram shows that the correlation between both factors does to a large extent correspond to the prediction of the interest parity theory.

Source: Dt. Bundesb. (Juli, 2005), Daily data 04.01.1999 30.06.2005

Spot exchange rate of the Euro is

undervalued given the interest rates!

Prof. Dr. Rainer Maurer- 94 -

2.2. Foreign Exchange Markets 2.2.1. Spot Markets

e$

-Demand

-Supply

The more $ is paid for one the cheaper US-assets get so that the return on investment in

US-assets grows => The more is supplied to the spot market.

e$,1

o

The more is paid for one $ the cheaper Euro-assets get so that the return on an investment in

Euro-assets grows. => The more is asked for on the spot market.

Prof. Dr. Rainer Maurer- 95 -

2.2. Foreign Exchange Markets 2.2.1. Spot Markets

e$

-Demand(i$1)

-Supply(i$1)

i$1 < i$2

e$,1

What happens to the equilibrium exchange rate if the Fed increases th the Dollar interest rate from i$1 to i$2?

oProf. Dr. Rainer Maurer

- 96 -

2. Major Markets and Their Assets2.1. Capital Markets

2.1.1. Credit Markets2.1.2. Stock Markets

2.2. Foreign Exchange Markets2.2.1. Spot Markets2.2.2. Forward Markets

2.3. Derivatives2.3.1. Forwards and Futures2.3.2. Options

2.2. Foreign Exchange Markets

17

Prof. Dr. Rainer Maurer- 97 -

2.2. Foreign Exchange Markets 2.2.2. 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.

tAgreement between Buyer and Seller today

Currency delivered by Seller to Buyer today

t=0 t=1 t=2t=2 t=3

Prof. Dr. Rainer Maurer- 98 -

2.2. Foreign Exchange Markets 2.2.2. 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.

tAgreement between Buyer and Seller today

Currency Delivered by Seller to Buyer at t+3

t=0 t=1 t=2t=2 t=3

Prof. Dr. Rainer Maurer- 99 -

2.2. Foreign Exchange Markets 2.2.2. Forward Markets

Standard forward exchange contracts are written for one, three, six and 12 month.

Prof. Dr. Rainer Maurer- 100 -

2.2. Foreign Exchange Markets 2.2.2. 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 20 000 $ payable at the date of delivery.

The production costs for this car are 8 000 . At the current spot market exchange rate of 2$ the company could cover its costs (total sales = 20 000 $ / 2$ = 10 000 ).

If the would appreciate to an exchange rate of 4$, the company made a loss of

20 000 $ / 4$ 8 000 = 3000 .

Prof. Dr. Rainer Maurer- 101 -

2.2. Foreign Exchange Markets 2.2.2. Forward Markets

An American manufacturer of refrigerators sells 100 refrigerators to an European dealer one month forward at a price of 10 000 payable at the date of delivery.

The production costs for 100 refrigerators are 18 000 $. At the current spot market exchange rate of 2$ the company could cover its costs (total sales = 10 000 * 2$ = 20 000 $).

If the would depreciate to an exchange rate of 1$, the company made a loss of

10 000 * 1$ 18 000 $ = 8000 $.

Prof. Dr. Rainer Maurer- 102 -

2.2. Foreign Exchange Markets 2.2.2. 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 20 000 $ in exchange for 10 000 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.

18

Prof. Dr. Rainer Maurer- 103 -

2.2. Foreign Exchange Markets 2.2.2. Forward Markets

f$, t, t+1

Forward -Demand

Forward -Supply

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.

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.

Prof. Dr. Rainer Maurer- 104 -

2.2. Foreign Exchange Markets 2.2.2. 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:

Prof. Dr. Rainer Maurer- 105 -

2.2. Foreign Exchange Markets 2.2.2. 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

=>

=>

fProf. Dr. Rainer Maurer

- 106 -

2.2. Foreign Exchange Markets 2.2.2. 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

Prof. Dr. Rainer Maurer- 107 -

2.2. Foreign Exchange Markets 2.2.2. Forward Markets

Consequently, the forward exchange market is hit by interest rate changes in the opposite way as the spot exchange market!

Prof. Dr. Rainer Maurer- 108 -

2. Major Markets and Their Assets

2.1. Capital Markets

2.1.1. Credit Markets

2.1.2. Stock Markets

2.2. Foreign Exchange Markets

2.2.1. Spot Markets

2.2.2. Forward Markets

2.3. Derivatives

2.3.1. Forwards and Futures

2.3.2. Options

2.3. Derivatives

19

Prof. Dr. Rainer Maurer- 109 -

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.

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.

2.3. Derivatives2.3.1. Forwards and Futures

=>A forward exchange contract is a forward with a currency as underlying asset!Prof. Dr. Rainer Maurer

- 110 -

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: For the buying party:

2.3. Derivatives2.3.1. Forwards and Futures

20 - 20

50 - 50

Prof. Dr. Rainer Maurer- 111 -

Value of forward contract ()

Market value of stock ()

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

Market value of stock ()

Delivery Price

Delivery Price

Prof. Dr. Rainer Maurer- 112 -

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)

=Ft+x= K - Pt+1= 100 - 80 = 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 : + 150 (selling the stock) - 50 (selling the forward contract)

=Ft+x= K - Pt+1= 100 - 150 = 100

=> Held together with the corresponding stock, the forward contract completely eliminates risk for the selling party.

2.3. Derivatives2.3.1. Forwards and Futures

Prof. Dr. Rainer Maurer- 113 -

Example: Complete risk elimination for the buying party 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: + 100 (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: + 100 (selling short the stock) - 150 (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.

2.3. Derivatives2.3.1. Forwards and Futures

Prof. Dr. Rainer Maurer- 114 -

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 = Pt+1 - K = 110 - 100

Assumption: stock price decreases to: 90 => price of forward contract for buying party

= 10 = Pt+1 - K = 90 - 100

Percentage decrease in stock price: 18 % (=(110-90) / 110)

Percentage decrease in forward price: 200% (=(10-(-10))/10 )

2.3. Derivatives2.3.1. Forwards and Futures

20

Prof. Dr. Rainer Maurer- 115 -

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 = Pt+1 - K = 110 - 100

Assumption: stock price rises to: 120 => value of forward contract for buying party

= 20 = Pt+1 - K = 120 - 100

Percentage increase in stock price: + 9 % (= (120-110)/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.

2.3. Derivatives2.3.1. Forwards and Futures

Prof. Dr. Rainer Maurer- 116 -

Value of forward contract ()

Market value of stock ()

Example for Higher Risk: The leverage effect

+200 % = (30-10)/10

Value of forward contract ()

Market value of stock ()-18 % = (90-110)/110

-200 % = (-10 -10)/10+18 % = (130-110)/110

Prof. Dr. Rainer Maurer- 117 -

2.3. Derivatives2.3.1. Forwards and Futures

Details

3.3. Derivatives3.3.1. Forwards and Futures

The pricing of forwards / futures:

As shown by the above diagrams, the value (or price) of a forwardcontract (F) to the buyer (= the one who must buy the underlying asset atthe delivery price) at maturity date (t+x) is equal to the difference betweenthe delivery price (=K) and the market price of the underlying asset atmaturity date Pt+x:

The price before maturity date (t+n, 0

21

Details

3.3. Derivatives3.3.1. Forwards and Futures

The settlement of forwards / futures - e.g. a commodity forward:Possible ways of settlement if Pt+x > K:

(1) Settlement by delivery of hop by the Bavarian farmer to the Hamburgbrewery at price K.

Advantage to the farmer: Despite of the fact that he could have realized ahigher profit without the forward contract (Pt+x > K), he has realized a safeprofit per unit hop equal to K minus his production costs.

Advantage to the brewery: The brewery has a safe profit from its exportcontract, 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 bearthe transportation, storage and insurance cost from Bavaria to Hamburg.

Details

3.3. Derivatives3.3.1. Forwards and Futures

The settlement of forwards / futures - e.g. a commodity forward:

Possible ways of settlement if Pt+x > K:

(2) Settlement in cash by the Bavarian farmer to the Hamburg brewery atprice K:

The farmer sells his hop at the spot market price of Pt+x to a Bavarianbrewery and pays to the Hamburg brewery the value of the forward contractat maturity date t+x: Ft,t+x and keeps the difference Pt+x - Ft,t+x= K as hissales 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 Pt+x from an EastFrisian Farmer and uses the Ft,t+x payment from the Bavarian farmer tofinance this purchase in part. => Net costs of buying the hop at the spotmarket: Pt+x - Ft,t+x = K. So the brewery has finally bought its hop at thedelivery price K!

Value of the buying position in the forward contract Ft,t+x = Pt+x - K

Details

3.3. Derivatives3.3.1. Forwards and Futures

The settlement of forwards / futures - e.g. a commodity forward:

Possible ways of settlement if Pt+x > K:

Advantage to the farmer: The same as in (1)

Advantage to the brewery: The same as in (2)

Advantage of settlement in cash compared to settlement by delivery:Avoidance of transportation, storage and insurance cost from Bavaria toHamburg.

Value of the buying position in the forward contract Ft,t+x = Pt+x - K

Details

3.3. Derivatives3.3.1. Forwards and Futures

The settlement of forwards / futures - e.g. a commodity forward:

Possible ways of settlement:

(3) Daily settlement in cash at t+n with 00, what is equal to the net value of the daily payments ofthe farmer to the brewery (and vice versa), as the following example shows:

Value of the buying position in the forward contract Ft,t+x = Pt+x - K

Details

3.3. Derivatives3.3.1. Forwards and Futures

The settlement of forwards / futures - e.g. a commodity forward:

Possible ways of settlement:

(3) Daily Settlement in cash at t+n with 00 Ft,t+2=Pt+2 -K/(1+i)10

Ft,t+3=Pt+3 -K>0

Ft,t+3 - Ft,t+2>0

Payment: Farmer to Brewery

Payment: Farmer to Brewery

Payment: Brewery to Farmer

Ft,t + (Ft,t+1 - Ft,t ) - (Ft,t+1- Ft,t+2 )+ (Ft,t+3 - Ft,t+2 ) = Ft,t+3

Value of the buying position in the forward contract Ft,t+x = Pt+x - K

Details

3.3. Derivatives3.3.1. Forwards and Futures

The settlement of forwards / futures - e.g. a commodity forward:

Possible ways of settlement:

(3) Daily Settlement in cash at t+n with 00

Ft,t+1- Ft,t+2>0

Ft,t+3=Pt+3 -K>0

Ft,t+3 - Ft,t+2>0

Payment: Farmer to Brewery

Payment: Farmer to Brewery

Payment: Brewery to Farmer

Ft,t + (Ft,t+1 - Ft,t ) - (Ft,t+1- Ft,t+2 )+ (Ft,t+3 - Ft,t+2 ) = Ft,t+3

Value of the buying position in the forward contract Ft,t+x = Pt+x - K

Ft,t+2=Pt+2 -K/(1+i)1

22

Details

3.3. Derivatives3.3.1. Forwards and Futures

The settlement of forwards / futures - e.g. a commodityforward:Advantage to the farmer: The same as in (1)

Advantage to the brewery: The same as in (2)

Advantage of daily settlement in cash compared to settlement in cash at theend of maturity: Reduction of the risk that the counterparty will fail toexecute an agreed transaction (fraudulence or bankruptcy)

Value of the buying position in the forward contract Ft,t+x = Pt+x - K

3.3. Derivatives3.3.1. Forwards and Futures

K/(1+r)(x-n)

Pt+n

Ft+n= Pt+n- K/(1+r)(x-n)

K = Pt*(1+r)(x-n)

Prof. Dr. Rainer Maurer- 129 -

2.3. Derivatives2.3.1. Forwards and Futures

Forwards Futures

Contract between two private parties

Contracts listed on a stock exchange

Custom-made (underlying assets, prices, rates, maturity)

Standardized contracts

One specified delivery date Several optional delivery dates

Typically delivery of underlying assets or clearing at the end of maturity

Typically evening-up in cash before maturity

What are futures?

Prof. Dr. Rainer Maurer- 130 -

2. Major Markets and Their Assets

2.1. Capital Markets

2.1.1. Credit Markets

2.1.2. Stock Markets

2.2. Foreign Exchange Markets

2.2.1. Spot Markets

2.2.2. Forward Markets

2.3. Derivatives

2.3.1. Forwards and Futures

2.3.2. Options

2.3. Derivatives2.3.1. Forwards and Futures

Prof. Dr. Rainer Maurer- 131 -

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.

2.3. Derivatives2.3.2. Options

Prof. Dr. Rainer Maurer- 132 -

The are two types of call and put options:European optionsAmerican 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 timeup to a particular date.

In the following, we will discuss only European options.

2.3. Derivatives2.3.2. Options

Particular exercise date

Any time up to a particular date

Right to buy

European call option American call option

Right to sell European put option American put option

23

Prof. Dr. Rainer Maurer- 133 -

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?

2.3. Derivatives2.3.2. Options

Prof. Dr. Rainer Maurer- 134 -

Value of option ()

Value of a call option to the holder at exercise date (exercise price = 100)

Market value of stock () Market value of stock ()

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 lower than exercise price => Not profitable to use the call option!

Market price of the holder position of

the option

Market price of the writer position of

the option

Details

3.3. Derivatives3.3.2. Options

The price of options at the exercise date:

As shown by the above diagrams, the market value of a call option (C) to theholder at exercise date (t+x) is equal to the difference between the marketprice of the underlying asset at exercise date Pt+x and the exercise price(=K):

Prof. Dr. Rainer Maurer- 136 -

Value of option ()

Market value of stock () Market value of stock ()

Value of a put option to the holder at exercise date (exercise price = 100)

Value of a put option to the writer at exercise date (exercise price = 100)

Value of option ()

Market value higher than exercise price => Not profitable to use the put option!

Market value higher than exercise price => Put option not

used!

Market price of the holder position of

the option

Market price of the writer position of

the option

Details

3.3. Derivatives3.3.2. Options

The price of options at the exercise date:

As shown by the above diagrams, the market value of a put option (C) to theholder at exercise date (t+x) is equal to the difference between the exerciseprice (=K) and the market price of the underlying asset at exercise datePt+x:

Prof. Dr. Rainer Maurer- 138 -

Option terminology: When an option has a positive price it is said to be in-the-

money.

=> 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-the-money.

2.3. Derivatives2.3.2. Options

24

Details

3.3. Derivatives3.3.2. Options

The price of options before the exercise date:

The price of a call option before the excercise date (t+n, 0

25

- 145 -Prof. Dr. Rainer Maure

- 145 -Prof. Dr. Rainer Maurer

tt=0 t=1 t=3

Incoming payment: 20 000 $

t=2

Spot rate: 2$ Spot rate: e$ ?

Trading transaction: 20 000 $ in t=3 Costs: 9 000

Incoming payment from transaction:.20 000 $ used to pay back credit: . 20 000 $ *(1,02) . - 20 000 $ = 400 $

$-credit: 20 000 $ Interest rate1): 2% Exchange in at spot rate: . 20 000 $ / 2$. - 9 000 . = 1 000

Exchange of 200 * 2$ in 400 $ for interest payment in t=3

=> Certain net profit = 1000 - 200 = 800 1)M

onth

lyin

tere

stra

te=

year

lyra

teof

8,24

%=

((1,

02)(1

/3) )1

2-11. Foreign Currency Credit:

- 146 -Prof. Dr. Rainer Maure

- 146 -Prof. Dr. Rainer Maurer

tt=0 t=1 t=3

Incoming payment: 20 000 $

t=2

Spot rate: 2$ Spot rate: e$ ?

Trading transaction: 20 000 $ in t=3 Costs: 9 000

Incoming payment from transaction:.20 000 $ used for exchange in at the agreed forward rate: . .20 000 $ / 2,1$ .. - 9 000 = 523,8

Selling 20 000 $ forward t=3

at the current forward rate of 2,1$

=> Certain net profit = 523,8

Forward rate: 2,1$

2. Currency Future:

- 147 -Prof. Dr. Rainer Maure

- 147 -Prof. Dr. Rainer Maurer

tt=0 t=1 t=3

Incoming payment: 20 000 $

t=2

Spot rate: 2$ Spot rate: 2,4$

Trading transaction: 20 000 $ in t=3 Costs: 9 000

=> Exercise of the option: . 20 000 $ / 2$. - 9 000 = 1 000

Purchase of a 20000 $-put optionat an exercise rate of 2$ and an option premium of500

=> Certain net profit = 1 000 - 500 = 500

Exercise rate: 2$

3. Currency Option:

- 148 -Prof. Dr. Rainer Maure

- 148 -Prof. Dr. Rainer Maurer

tt=0 t=1 t=3

Incoming payment: 20 000 $

t=2

Spot rate: 2$ Spot rate: 1,8$

Trading transaction: 20 000 $ in t=3 Costs: 9 000

=> Abandonment of the option: . 20 000 $ / 1,8$. . - 9 000 = 2 111,1

Purchase of a 20000 $-put optionat an exercise rate of 2$ and an option premium of500

=> Certain net profit = 2 111,1 - 500 = 1611,1

Exercise rate: 2$

3. Currency Option:

Prof. Dr. Rainer Maurer- 149 -

Chapter 3: Questions for Review

35. What is the difference between forwards and futures.

36. A mechanical engineering company has the opportunity tosell a machine worth 30 000 $ with an incoming paymentat 1 month term. Production costs of the machine are24 000 . What is more profitable: A foreign exchangehedge with a future or a credit under the following marketconditions: Spot exchange rate: e$ = 1.1, forward rate: f$= 1.2, interest rate (maturity 1 month): i$ = 2%

Prof. Dr. Rainer Maurer- 150 -

Chapter 3: Questions for Review

You should be able to answer the following questions at theend of this chapter. If you have difficulties in answering aquestion, discuss this question with me during or at the end ofthe next lecture or attend my colloquium.

26

Prof. Dr. Rainer Maurer- 151 -

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 , thefixed rate is 5% and the number of periods to the end ofmaturity is 1?

3. What is the market price of a fixed rate bond, if the facevalue is 100 , fixed rate is 10%, the market interest rate is20% and the number of periods to the end of maturity is 4?

4. What is the general relation between the market price of asecurity and its internal rate of return?

5. If you had the choice between a government bond and acorporate bond with equal face value and equal internalrate of return, which one would you choose and why?

Prof. Dr. Rainer Maurer- 152 -

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?

Prof. Dr. Rainer Maurer- 153 -

Chapter 3: Questions for Review

12. What factors influence in general the level of dividendpayments?

13. What information is necessary to calculate the fair valueof 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?Prof. Dr. Rainer Maurer

- 154 -

Chapter 3: Questions for Review

21. If the price for 1 kg cookies is 4 in Europe and 2 $ in theUSA, what will the equilibrium exchange rate be in theabsence of transaction costs (= transport, insurance, taxes)?

22. What is the formula for the purchasing power parityexchange rate?

23. Derive the formula for interest rate parity.

24. What happens with the spot exchange rate of the againstthe $, when the -interest rate (average) grows andeverything else stays unchanged? Give an explanation.

25. What happens with the spot exchange rate of the againstthe $, when the $-interest rate (average) grows andeverything else stays unchanged? Give an explanation.

Prof. Dr. Rainer Maurer- 155 -

Chapter 3: Questions for Review

26. What happens with the spot exchange rate of the againstthe $, when speculators sell on the forward market andeverything else stays unchanged? Give an explanation.

27. What are the two reasons for the -supply curve to slopeupward?

28. What are the two reasons for the -demand curve to slopedownward?

29. Why do people demand on the forward exchangemarkets?

30. Explain how a the forward exchange rate market can beused to eliminate exchange rate risk for firms withproduction costs and sales denominated in differentcurrencies.

Prof. Dr. Rainer Maurer- 156 -

Chapter 3: Questions for Review

31. What are the two reasons for the forward -supply curve toslope upward?

32. What are the two reasons for the forward -demand curveto slope downward?

33. What is a forward contract?

34. Give a graphical exposition of the relation between thevalue of a forward contract to the buyer (seller) and theprice of the underlying asset at maturity date of thecontract, if the contract price for the underlying asset is200 .

27

Prof. Dr. Rainer Maurer- 157 -

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 thevalue of an European call (put) option to the holder(writer) and the price of the underlying asset at exercisedate of the option, if the contract price for the underlyingasset is 50 and the option premium is 20 .

38. Why is the risk of option holders and option writers said tobe not symmetrical?

39. What are the pros and cons of hedging a future sales inforeign currency with the help of a forward contract andwith the help of an option?

Prof. Dr. Rainer Maurer- 158 -

Chapter 3: Questions for Review

35. What is the difference between forwards and futures.

36. A mechanical engineering company has the opportunity tosell a machine worth 30 000 $ with an incoming paymentat 1 month term. Production costs of the machine are24 000 . What is more profitable: A foreign exchangehedging with a future or credit under the following marketconditions: Spot exchange rate: e$ = 1.1, forward rate: f$= 1.2, interest rate (maturity 1 month): i$ = 2%

Prof. Dr. Rainer Maurer- 159 -

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

Prof. Dr. Rainer Maurer- 160 -

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

Savings from Households

Credits to Firms and Housholds

Mortgage BackedBonds

Mortgage Bonds are collaterized by the value

of the real estate objects.

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

Prof. Dr. Rainer Maurer- 161 -

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.

Prof. Dr. Rainer Maurer- 162 -

=> The higher the market interest rate for mortgage bonds the lower the market price of issued mortgage bonds.

28

Prof. Dr. Rainer Maurer- 163 -

Simplified Balance Sheet of a Business Bank

Assets Liabilities

Savings from Households

Credits to Firms and Housholds

Mortgage BackedBonds

The lower the market value of bonds the

bigger the hole in the balance sheet of the

business bank:

Prof. Dr. Rainer Maurer- 164 -

Simplified Balance Sheet of a Business Bank

Assets Liabilities

Savings from Households

Credits to Firms and Housholds

Mortgage BackedBonds

The lower the market value of bonds the

bigger the hole in the balance sheet of the

business bank:

Deficit

Prof. Dr. Rainer Maurer- 165 -

Prof. Dr. Rainer Maurer- 166 -