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International Financial Markets 1. How Capital Markets Work

International Financial Markets 1. How Capital Markets Work. Lecture Notes: www.rainer-maurer.de E- Mail: rainer.maurer@hs-pforzheim.de Colloquium: Friday 17.15 - 18.45 ( room W1.4.03). 1. How Capital Markets Work.

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International Financial Markets 1. How Capital Markets Work

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  1. International Financial Markets1. How Capital Markets Work Lecture Notes: www.rainer-maurer.de E-Mail: rainer.maurer@hs-pforzheim.de Colloquium: Friday17.15 - 18.45 (room W1.4.03) Prof. Dr. Rainer Maurer

  2. 1. How Capital Markets Work 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. 1. How Capital Markets Work 1.1. Supply and Demand on Capital Markets 1.1.1. Why People Save 1.1.2. Why People Invest 1.1.3. Investor and Saver Surplus 1.2. Capital Markets and Risk 1.2.1. Why People Don’t Like Risk 1.2.2. How People Handle Risk 1.3. Basic Evaluation Techniques for Capital Markets 1.3.1. The Discounted Cash-Flow Method 1.3.2. The Internal Rate of Return Method 1.3.3. Risk and Return: The Sharpe Ratio 2. Questions for Review Literature:1) ◆Chapter 4, 25, Mankiw, N.G. (2001): Principles of Economics, Harcourt Coll. Publ., Orlando. ◆Chapter 7, Mankiw, N.G. (2002): Macroeconomics, Worth Publishers, New York. Prof. Dr. Rainer Maurer

  3. 1. How Capital Markets Work1.1.1. Why People Save 1. How Capital Markets Work 1.1. Supply and Demand on Capital Markets 1.1.1. Why People Save 1.1.2. Why People Invest 1.2. Capital Markets and Risk 1.2.1. Why People Don’t Like Risk 1.2.2. How People Handle Risk 1.3. Basic Evaluation Techniques for Capital Markets 1.3.1. The Discounted Cash-Flow Method 1.3.2. The Internal Rate of Return Method 1.3.3. Risk and Return: The Sharpe Ratio Prof. Dr. Rainer Maurer

  4. 1. How Capital Markets Work1.1.1. Why People Save Prof. Dr. Rainer Maurer

  5. 1. How Capital Markets Work1.1.1. Why People Save -5- • Why do people save? • Making savings means • “consumption today” is postponed in favor of • “consumptionin thefuture” • Why are people willing to give up “consumption today” in favor of “consumption in the future”? • Because they receive interest payments for their savings. • The standard assumption is therefore that the willingness to save depends positively on the interest rate: Prof. Dr. Rainer Maurer

  6. The Slope of the Savings Curve % Savings = S(i) Why do people save more, when they receive higher interest payments? Higher interest payments allow for “higher consumption in the future”. This compensates for the “lowerconsumption today”. € -6- Prof. Dr. Rainer Maurer

  7. 1. How Capital Markets Work1.1.1. Why People Save [ ] + - -7- How does this affect consumption of households? The relationship between “savings today” and “consumption today” is inverse. The budget constraint of a household shows this. If we neglect the necessity to pay taxes, the simplest form a budget constraint is given by the equation: Income = Savings + Consumption Y = S + C <=> C = Y – S <=> C(i ) = Y – S(i ) Prof. Dr. Rainer Maurer

  8. The Slope of the Savings Curve % As a consequence, people consume less, if the interest rate is high. Consumption = C(i) € -8- Prof. Dr. Rainer Maurer

  9. 1. How Capital Markets Work1.1.1. Why People Save -9- How does an increase of permanent income affect the savings function? Y = S + C It must increase savings and/or consumption. Most likely is that it increases both savings and consumption at the same time, because a permanent increase of income means that higher income will also be available in future periods. So people have no reason to postpone current consumption into the future. Prof. Dr. Rainer Maurer

  10. The Slope of the Savings Curve % How does an increase of permanent income “y” change the willingness to save? Savings = S(i, y1) Savings = S(i, y2) If the permanent income of households y2 > y1grows, households will typically save more! € -10- Prof. Dr. Rainer Maurer

  11. The Slope of the Savings Curve % Savings = S(i, y1) Savings = S(i, y2) Therefore household permanent income“y” is a shift parameter of the savings function! € -11- Prof. Dr. Rainer Maurer

  12. The Slope of the Savings Curve % Savings = S(i, y2) Savings = S(i, y1) If the permanent income of households y2 < y1decreases, households will typically save less! € -12- Prof. Dr. Rainer Maurer

  13. 1. How Capital Markets Work1.1.1. Why People Save 1. How Capital Markets Work 1.1. Supply and Demand on Capital Markets 1.1.1. Why People Save 1.1.2. Why People Invest 1.2. Capital Markets and Risk 1.2.1. Why People Don’t Like Risk 1.2.2. How People Handle Risk 1.3. Basic Evaluation Techniques for Capital Markets 1.3.1. The Discounted Cash-Flow Method 1.3.2. The Internal Rate of Return Method 1.3.3. Risk and Return: The Sharpe Ratio Prof. Dr. Rainer Maurer

  14. 1. How Capital Markets Work1.1.2. Why People Invest • Why do people invest? • Investment means • to spend money for “economic activities today”, which are assumed to yield a “returnin thefuture” • Investment projects can be ranked according to their expected return. • This yields the following curve: Prof. Dr. Rainer Maurer

  15. The Slope of the Investment Curve % Investment volume of the first project Expected return Available investment projects depending on their expected return and investment volume € Prof. Dr. Rainer Maurer

  16. The Slope of the Investment Curve % Interest rate: 8% If the market interest rate is 8%, only the first investment project is profitable! All other investment projects are not undertaken! € -17- Prof. Dr. Rainer Maurer

  17. The Slope of the Investment Curve % If the market interest rate is 2%, only the first five investment projects are profitable! Interest rate: 2% € -18- Prof. Dr. Rainer Maurer

  18. The Slope of the Investment Curve If we add the savings curve to the curve of available investment projects we recognize, how many investment projects savers are willing to finance: % Savings = S(i) € -19- Prof. Dr. Rainer Maurer

  19. The Slope of the Investment Curve If we add the savings curve to the curve of available investment projects we recognize, how many investment projects saver are willing to finance: % Savings = S(i) Investor surplus Equilibrium interest rate => An exchange of savings at the resulting equilibrium interest rate is “mutual beneficial”! Saver surplus € -20- Prof. Dr. Rainer Maurer

  20. The Slope of the Investment Curve In the following, we will for simplicity approximate the curve of investment projects with a straight line: % Savings = S(i) Investment = I(i) € -21- Prof. Dr. Rainer Maurer

  21. The Slope of the Investment Curve In the following, we will for simplicity approximate the curve of investment projects with a straight line: % Savings = S(i) Investor surplus Market interest rate Investment = I(i) Saver surplus € -22- Prof. Dr. Rainer Maurer

  22. The Slope of the Investment Curve % Contrary to the savings curve, the investment curve depends on the negatively interest rate! The investment curve is also influenced by shift parameters, e.g. the expected return of investment projects, r1! Investment = I(i) € -23- Prof. Dr. Rainer Maurer

  23. The Slope of the Investment Curve % Investment = I(i,r2) If firms expect on average a higher return on investment r1<r2 (e.g. because of an expected higher demand for their goods), the investment curve shifts to the right! Investment = I(i,r1) € -24- Prof. Dr. Rainer Maurer

  24. The Slope of the Investment Curve % If firms expect a lower return on investment r1>r2 (e.g. because of a lower demand for their goods), they will typically want to invest less. Investment = I(i,r1) Investment = I(i,r2) € -25- Prof. Dr. Rainer Maurer

  25. The Capital Market % S(i,y) Combination of the savings supply curve and investment demand curve i1* Equilibrium Interest Rate I(i) € S1* Prof. Dr. Rainer Maurer

  26. The Capital Market % y1 < y2 S1(i,y1) S2(i,y2) i1* i2* I(i) € S2* S1* Prof. Dr. Rainer Maurer

  27. The Capital Market % r1 < r2 S(i) i2* i1* I2(i, r2) I1(i , r1) € S1* S2* Prof. Dr. Rainer Maurer

  28. 1. How Capital Markets Work1.2.1. Why People Don’t Like Risk 1. How Capital Markets Work 1.1. Supply and Demand on Capital Markets 1.1.1. Why People Save 1.1.2. Why People Invest 1.2. Capital Markets and Risk 1.2.1. Why People Don’t Like Risk 1.2.2. How People Handle Risk 1.3. Basic Evaluation Techniques for Capital Markets 1.3.1. The Discounted Cash-Flow Method 1.3.2. The Internal Rate of Return Method 1.3.3. Risk and Return: The Sharpe Ratio Prof. Dr. Rainer Maurer

  29. 1. How Capital Markets Work1.2.1. Why People Don’t Like Risk Option (a): Option (b): EV: (0.5*(3+2) + 0.5*(3-3) = 2.5 • Do you like risk? • Experiment I: What do you take (a) or (b)? • (a) You receive 3 €. • (b) You receive 3 €. You will get additional 2 € with a probability of 50% and you will have to pay 3 € with a probability of 50%. Prof. Dr. Rainer Maurer

  30. 1. How Capital Markets Work1.2.1. Why People Don’t Like Risk Option (a): Option (b): EV: (0.5*(3+2) + 0.5*(3-2) = 3 • Do you like risk? • Experiment II: What do you take (a) or (b)? • (a) You receive 3 €. • (b) You receive 3 €. You will get additional 2 € with a probability of 50% and you will have to pay 2 € with a probability of 50%. Prof. Dr. Rainer Maurer

  31. 1. How Capital Markets Work1.2.1. Why People Don’t Like Risk Option (a): Option (b): EV: (0.5*(3+7) + 0.5*(3-1) = 6 • Do you like risk? • Experiment III: What do you take (a) or (b)? • (a) You receive 3 €. • (b) You receive 3 €. You will get additional 7 € with a probability of 50% and you will have to pay 1 € with a probability of 50%. Prof. Dr. Rainer Maurer

  32. 1. How Capital Markets Work1.2.1. Why People Don’t Like Risk • What does the experiment show? • Most people prefer a certain payment over a risky payment. • A risky payment is accepted only if it includes a premium, which is “high enough”. In economics this premium is called “risk premium”. • The magnitude of this “risk premium” individuallydiffers from person to person. • However, the existence of a risk premium shows that people generally do not like risk: They are willing to accept risk only, if they are compensated for the risk by a higher payment! • In economics we call this “being risk averse”. Prof. Dr. Rainer Maurer

  33. Empirical example for a risk premium: Source: Deutsche Bundesbank = Government Bonds = Corporate Bonds - 34 - Prof. Dr. Rainer Maurer

  34. 1. How Capital Markets Work1.2.1. Why People Don’t Like Risk -37- • Why do people demand a risk premium? • Our "self-experiment" and empirical data from financial markets clearly show that people are risk averse and demand risk premiums for risky investments. • Now the question is, why do people behave this way? • Is it "irrational fear" to be "risk averse" or can we explain it? • The next slides show the standard microeconomic explanation for risk averse behavior. • Standard microeconomics derives the explanation from a quite plausible property of the utility function of people: Decreasing marginal utility of consumption. • The next slide gives an explanation of this property: Prof. Dr. Rainer Maurer

  35. 1. How Capital Markets Work1.2.1. Why People Don’t Like Risk Utility of the 2nd Cookie Utility of the 1st Cookie Utility from the Consumption of Cookies per Day Utility = U(Cookies) Utility from the Con-sumption of 16 Cookies = 12“Utils” …and so on Quantity of Cookies (kg) -38- Prof. Dr. Rainer Maurer

  36. 1. How Capital Markets Work1.2.1. Why People Don’t Like Risk Experiment II: (a) You receive 3 € with a probability of 100%. (b) You receive 3 €. You will get additional 2 € with a probability of 50% and you will have to pay 2 € with a probability of 50%. Utility Units Expected utility from the uncertain payment is lower than the expected utility from the certain payment => A person with this utility function will preferthe certain payment! 12*50% + 4*50% = 8 Value of Consumption Goods (€) (a) 9,5 Expected Utility Units for the Certain Payment (b) 8 Expected Utility Units for the Uncertain Payment -39- Prof. Dr. Rainer Maurer

  37. 1. How Capital Markets Work1.2.1. Why People Don’t Like Risk Experiment II: (a) You receive 3 € with a probability of 100%. (b) You receive 3 €. You will get additional 2 € with a probability of 50% and you will have to pay 2 € with a probability of 50%. Utility Units Utility Gain: 2 The reason for the lower expected utility is the stronger change of utility in case of a loss compared to the case of a gain, because of decreasing marginal utility! Utility Loss: 5,5 Value of Consumption Goods (€) Income Gain of 2 € Income Loss of 2 € (a) 9,5 Expected Utility Units for the Certain Payment (b) 8 Expected Utility Units for the Uncertain Payment -40- Prof. Dr. Rainer Maurer

  38. 1. How Capital Markets Work1.2.1. Why People Don’t Like Risk Experiment II: (a) You receive 3 € with a probability of 100%. (b) You receive 3 €. You will get additional 2 € with a probability of 50% and you will have to pay 2 € with a probability of 50%. Utility Units In case of a utility function with constant marginal utility, the utility gain in case of an income gain would be equalto the utility loss in case of an income loss and hence expected utility in case of a certain payment would be equal to expected utility of an uncertain payment! Utility Gain: 4 Utility Loss: 4 Value of Consumption Goods (€) Income Gain of 2 € Income Loss of 2 € (a) 6 Expected Utility Units for the Certain Payment (b) 6 Expected Utility Units for the Uncertain Payment -41- Prof. Dr. Rainer Maurer

  39. 1. How Capital Markets Work1.2.1. Why People Don’t Like Risk Experiment III: (a) You receive 3 € with a probability of 100%. (b) You receive 3 €. You will get additional 7 € with a probability of 50% and you will have to pay 1 € with a probability of 50%. Utility Units Utility Gain: 5,5 Expected utility from this uncertain payment is higher than the expected utility from the certain payment => A person with this utility function will prefer the uncertain payment! 15*50% + 7*50% = 11 Utility Loss: 2,5 Value of Consumption Goods (€) Income Gain of 7 € Income Loss of 1 € (a) 9,5 Expected Utility Units for the Certain Payment (b) 11 Expected Utility Units for the Uncertain Payment -43- Prof. Dr. Rainer Maurer

  40. 1. How Capital Markets Work1.2.1. Why People Don’t Like Risk Risk Neutral Utility Function Utility Units Normal Person (Risk Averse) Utility Function Gambler (Risk Lover) Utility Function Value of Consumption Goods (€) Since we know from experiments that most people are risk averse, we can draw the conclusion that most people have a utility function with decreasing marginal utility! -44- Prof. Dr. Rainer Maurer

  41. 1. How Capital Markets Work1.2.2. How People Handle Risk 1. How Capital Markets Work 1.1. Supply and Demand on Capital Markets 1.1.1. Why People Save 1.1.2. Why People Invest 1.2. Capital Markets and Risk 1.2.1. Why People Don’t Like Risk 1.2.2. How People Handle Risk 1.3. Basic Evaluation Techniques for Capital Markets 1.3.1. The Discounted Cash-Flow Method 1.3.2. The Internal Rate of Return Method 1.3.3. Risk and Return: The Sharpe Ratio Prof. Dr. Rainer Maurer

  42. 1. How Capital Markets Work1.2.2. How People Handle Risk • We have already seen, how normal people handle risk: • They demand a risk premium! • Financial markets offer a possibility to eliminate risk: • Hedging! • The following tables illustrate the principle of hedging based on several numeric examples: Prof. Dr. Rainer Maurer

  43. 1. How Capital Markets Work1.2.2. How People Handle Risk • This example shows: • If the return of one stock goes up exactly when the return of the other stock goes down, a portfolio of both stocks completely eliminates the risk! • Consequently, investing your money in a portfolio of both stocks implies no risk, while investing your money in one of both stocks only implies a lot of risk! • Note: In case of a perfect hedge, the correlation coefficient equals exactly -1! Prof. Dr. Rainer Maurer

  44. 1. How Capital Markets Work1.2.2. How People Handle Risk • This example shows: • If the return of one stock goes up exactly when the return of the other stock goes up, a portfolio of both stocks does not affect risk at all! • Consequently, investing your money in a portfolio of both stocks implies the same risk, as investing your money in one of both stocks only! • Note: In case of a no hedge, the correlation coefficient equals exactly 1! Prof. Dr. Rainer Maurer

  45. 1. How Capital Markets Work1.2.2. How People Handle Risk The Miracle of Hedging! • This example shows: • If the return of one stock goes upwhen the return of the other stock goes up, but notby exactly the same degree, a portfolio of both stocks can reduce risk somewhat but not completely eliminate it! • Consequently, investing your money in a portfolio of both stocks implies a lower risk, as investing your money in one of both stocks only! • Note: In case of a normal hedge, the correlation coefficient lies between 0 and 1! Prof. Dr. Rainer Maurer

  46. 1. How Capital Markets Work1.2.2. How People Handle Risk • In the real world, perfect hedges are as rare as no hedges! • Fortunately, normal (imperfect) hedges are the rule, so that investing in portfolios generally makes more sense than investing in single stock! • Why are stocks so often imperfect hedges? • On one hand, there are a lot of commoneconomic factors that effect all stocks in the same way, causing a positive correlation of returns: • The business cycle, prices of raw materials, wages, tax reforms… • To the other hand, every firm has its own product markets and these markets often react in a different way to these common economic factors: • For example, the Bicycle-Company profits from high consumer confidence as well as the Snowboard-Company, but in summer time the more so than in winter time and vice versa… Prof. Dr. Rainer Maurer

  47. 1. How Capital Markets Work1.2.2. How People Handle Risk As the examples have shown, we can comfortably measure the hedge quality of two kind of stocks by the correlation coefficient. How do we compute the correlation coefficient? Prof. Dr. Rainer Maurer

  48. 1. How Capital Markets Work1.2.2. How People Handle Risk How do we compute the variance? How do we compute the covariance? Prof. Dr. Rainer Maurer

  49. 1. How Capital Markets Work1.2.2. How People Handle Risk • A correlation coefficient of -1 indicates that the value of two stocks moves through time with exactly opposite fluctuations: • If the stock of Raincoat Corp. displays a positive deviation from its mean value, the stock of Sunglasses International displays a negative deviation form its mean value. • If the stock of Raincoat Corp. displays a negative deviation from its mean value, the stock of Sunglasses International displays a positive deviation form its mean value. Interpretation of the Correlation Coefficient: Prof. Dr. Rainer Maurer

  50. 1. How Capital Markets Work1.2.2. How People Handle Risk • A correlation coefficient of 1 indicates that the value of two stocks moves through time with exactly the same fluctuations: • If the stock of Raincoat Corp. displays a positive deviation from its mean value, the stock of Umbrella Unlimited displays a positive deviation form its mean value too. • If the stock of Raincoat Corp. displays a negative deviation from its mean value, the stock of Umbrella Unlimited displays a negative deviation form its mean value too. Interpretation of the Correlation Coefficient: Prof. Dr. Rainer Maurer

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