Topic 1: Basic Concepts in Finance. Slides

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1 Topic 1: Basic Concepts in Finance Slides

2 What is the Field of Finance 1. What are the most basic questions? (a) Role of time and uncertainty in decision making (b) Role of information in decision making under uncertainty (c) Portfolio construction (d) Valuation of securities (e) Performance evaluation (f) Role of information in valuation of securities (g) Theory of rm: Why do rms exist? (h) Financial intermediation: Why do we need nancial intermediaries? (i) Principal agent relationship and corporate governance (j) Role of information and uncertainty in managing economic institutions Fall 2015,??-Page-1

3 What is the Field of Finance (k) Impact of market imperfections on decision making, security prices and nancial institutions (l) Empirical tests of theories Fall 2015,??-Page-2

4 What does it take to be a Successful PhD 1. The key is to prepare yourself to develop afew good ideas which will serve as the foundation of acompleted thesis. 2. Preparation: (a) Read academic journals and working papers (ssrn.com) (b) Read business & nance journals (WSJ, FT, etc) (c) Develop a complete toolbox i. Economic theory: read some economic journals ii. Probability, Statistics & Econometrics: read some econometrics journals iii. Flexible software (R, Octave, Matlab) Fall 2015,??-Page-3

5 What does it take to be a Successful PhD 3. Idea: (a) Pick an area as soon as possible and read as much as you can about the area. The area does not have to be very narrow. You could narrow it down as you read more. (b) Work on several topics within the area that you have selected. Helps you diversify your risk and makes for a better thesis. (c) Write down your ideas. Prepare a folder and le your ideas. Write notes about papers that you read and le them as well. (d) To have a few good ideas, you need to develop several OK ideas rst. Good ideas start as average ideas. You have to develop and expand them. Fall 2015,??-Page-4

6 What does it take to be a Successful PhD 4. Completion: (a) A good thesis is a completed thesis. (b) As you work on your ideas, write them down (c) Write papers (even if they are not good). Learn how to write academic papers. (d) Make sure that you remain in touch with your advisor throughout the process. (e) Pick a topic that is also of interest to one or more faculty member. (f) Do not try to pick the most interesting ideas that are out there. Pick the best one that you can complete on time. Fall 2015,??-Page-5

7 A Brief History of Financial Economics 1. Fisher (1930), \The Theory of Interest." (a) Multiperiod investment-consumption decision. (b) Fisher Separation Theorem: Investment decision can be separated from nancing decision. 2. Williams (1938), \Theory of Investment Value." (a) Value additivity principle 3. Hicks (1939), \Value and Capital." (a) Term Structure of Interest Rates and the role of expectations in pricing of assets. 4. von Neuman and Morgenstern (1947), \Theory of Games and Economic Behavior," and Savage (1954), \Foundation of Statistics." (a) Expected utility hypothesis and decision making under uncertainty. Fall 2015,??-Page-6

8 A Brief History of Financial Economics (b) Game Theory 5. Markowitz (1952), \Portfolio Selection..." (a) Investment decision making under uncertainty (b) Using mean-variance framework to measure risk and return. 6. Arrow (1953), \The Role of Securities in Optimal Allocation of Risk-Bearing," and Debreu (1959), \Theory of Value." (a) First Equilibrium model of an economy under uncertainty. (b) Role security markets and securities in optimal allocation of resources and risk. 7. Modigliani and Miller (1958), \Cost of Capital and Capital Structure...," (1961), \Dividend Policy...," and (1963), \Corporate Income Taxes...," Fall 2015,??-Page-7

9 A Brief History of Financial Economics (a) Firm's nancing decision and its eects on the rm's value. (b) Firm's dividend policy and its eects on the rm's value. 8. Arrow (1964), \Some Aspects of the Theory of Risk Bearing," and Pratt (1965), \Risk Aversion in Small and Large." (a) Studied and quantied risk aversion and behavior toward risk 9. Sharpe (1964), \Capital Asset Prices." (a) The Capital Asset Pricing Model (CAPM) (b) Measurement of risk and the valuation of risky assets 10. Cootner ed. (1967), \The Random Character of Stock Market," and Fama (1970), \Ecient Capital Markets." (a) Time series properties of security prices (b) Ecient market hypothesis Fall 2015,??-Page-8

10 A Brief History of Financial Economics (c) Role of information in determination of asset prices 11. Akerlof (1970), \Market for Lemons," and Spence (1973), \Job Market Signaling," (a) Role of asymmetric information in nancial markets and corporate management (b) Signaling and corporate nance 12. Alchian and Demsetz (1972), \Production, Information, Costs, and Economic Organization," and Jensen and Meckling (1976), \The Theory of the Firm." (a) Agency relationships and managerial behavior (b) Firm's nancing and investment decisions when done by agents 13. Black and Scholes (1973), \Pricing of Options and Corporate Fall 2015,??-Page-9

11 A Brief History of Financial Economics Liabilities," Ross (1976), \Arbitrage Pricing Theory," and Harrison and Kreps (1979), \Martingales and Multiperiod Securities Markets," (a) Arbitrage pricing approach to pricing of securities. (b) Valuation of corporate securities and contingent claims. 14. Merton (1971), \Optimal Investment...," (1973), \An Intertemporal Model of Asset Prices," Rubinstein (1976), \Valuation of Uncertain Income...," and Lucas (1978), \Asset Prices in an Exchange Economy," Breeden (1979), \An Intertemporal Asset Pricing Model..." (a) Multiperiod investment-consumption decisions (b) General equilibrium multi-period asset pricing models 15. Grossman (1976), \On the Eciency of Financial Markets...," and Grossman and Stiglitz (1980), \On the Impossibility of Informationally Ecient Markets." Fall 2015,??-Page-10

12 A Brief History of Financial Economics (a) Aggregation of information by prices. (b) Noise traders and formation of security prices. 16. Hansen (1982), \Large Sample Properties..." and Hansen and Singleton (1982), \Stochastic Consumption, Risk Aversion...," (a) Generalized Method of Moments (b) Empirical tests of multiperiod conditional models 17. Keim and Stambaugh (1986), Fama and French (1988), \Permanent and Temporary Components..." and Fama and French, (1989), \Business Conditions and..." (a) Time-varying risk and return (b) Predictability of stock and bond returns 18. Multi-factor models: Fama, French, Harvey, Ferson, Hansen, Fall 2015,??-Page-11

13 A Brief History of Financial Economics 19. Renements of Classical Theory (1985-Present) (a) Asset pricing models do not work! Mehra and Prescott, \Equity Premium: A Puzzle. (b) Valuation & market eciency: Habit formation and more general utility functions, impact of market imperfections. Shleifer and Vishny, \The Limits of Arbitrage," (c) Option pricing: Implied risk neutral distribution, stochastic volatility (d) Credit risk: Structural models, reduced form models, hybrid and so on. Jarrow and Turnbull, \Pricing of Financial Securities Subject to Credit Risk," (e) Term structure: Arbitrage-free term structure models, \market" model of xed income derivatives (f) Performance evaluation: Conditional and time-varying models, Fall 2015,??-Page-12

14 A Brief History of Financial Economics four-factor model, non-parametric models (g) Learning: Model uncertainty and learning, preference uncertainty, (h) Bubbles and crashes: Deviations from rational expectations (i) Liquidity risk 20. High frequency empirical studies Engle, Andersen, Bollerslev, Diebold, Gourieroux (1990-present) Fall 2015,??-Page-13

15 Time Value of Money 1. In general, Value of an asset = f (future payos) The \function" f () is supposed to account for riskiness and the timing of future payos. For the time being we ignore risk. 2. Riskless case: present value V 0 = C 1 (1 + r 1 ) This means that f (C 1 ) = C r 1 : Why should this form of f be the right function? Fall 2015,??-Page-14

16 Time Value of Money Fall 2015,??-Page-15

17 Time Value of Money (a) The PV function implies value additivity because we are using a linear function. C Z 1 = CX 1 + CY 1 V0 Z = CZ 1 (1 + r 1 ) = CX 1 + CY 1 (1 + r 1 ) = CX 1 (1 + r 1 ) + CY 1 (1 + r 1 ) = V0 X + V0 Y Does this hold in reality? Here are some exceptions: i. Volume discounts ii. Closed-end funds Fall 2015,??-Page-16

18 Individual Investment-Consumption Decision 1. Utility function: a welfare index, u (c) (a) Common properties of utility functions (one consumption (c) 2 u 2 > 0 Non-satiation < 0 Diminishing marginal utility Fall 2015,??-Page-17

19 Individual Investment-Consumption Decision 2. Two-period utility, u (c 0 ; c 1 ) (a) Common properties of utility (c 0 ; c 1 ) > 2 u (c 0 ; c 1 ) < 2 2 u (c 0 ; c (c 0 ; c 1 ) > 0 2 u (c 0 ; c 1 ) < 0 Diminishing marginal 2 1 (b) Indierence curves: Let's x the level of u (c 0 ; c 1 ) = u 1 : Now plot those Fall 2015,??-Page-18

20 Individual Investment-Consumption Decision combinations of c 0 and c 1 that keep u (c 0 ; c 1 ) constant at u 1 : In this case, the combination u (c 1 0 ; c1 1 ) = u1 is not as desirable as u (c 2 0 ; c2 1 ) = u2 : Fall 2015,??-Page-19

21 Simple Optimization 1. Suppose we wish to maximize the value of the following function: f(x) by choosing x: The usual procedure is to solve this equation for = 0 Next, we need to determine if the solution x gives us a maximum. In this case, we 2 f 2 < 0 for x = x 2. In the case of two variables: max x;y f (x 1; x 2 ) Suppose the maximum is reached at x i : (x 1 ; x 2 i = 0 for x i = x i ; i = 1; 2 Fall 2015,??-Page-20

22 Simple Optimization 3. Also, we need to verify that the Hessian matrix is negative negative denite at x i = x i H 2 f (x 1 ; x 2 2 i m 0 H m < 0 for all m 6= 0 4. Suppose we wish to maximize the above function given the constraint that g(x 1 ; x 2 ) = b: In this case, we form a Lagrangian equation max x; L = f(x 1 ; x 2 ) (g (x 1 ; x 2 ) (x 1; x 2 (x 1; x 2 ) = 0 i = 1; i = g (x 1; x 2 ) + b = 0 Here we have 3 equations and 3 unknowns. Again, the second order condition has to be checked Fall 2015,??-Page-21

23 Simple Optimization What is the interpretation of? Fall 2015,??-Page-22

24 Simple Optimization 5. Example: Suppose we wish to maximize f(x; y) = 10(x 2) 2 2 (y 4) 2 subject to the constraint that 5 = y + x: L (x; y) = 10(x 2) 2 2 (y 4) 2 (y + x (x; y) 20x + 40 = (x; y) 4y + 16 = (x; y) = y + 5 = 0 The solution is: x = 11 6 ; y = 19 6 ; = 10 3 :The constraint is \costing" us 10=3 because the optimal value is reduced by this amount times the amount that the constraint is binding. Fall 2015,??-Page-23

25 Simple Optimization 6. Finally, suppose we wish to maximize the a function subject to the constraint that g (x) b: In this case the problem is solved using what is known as Kuhn-Tucker method max (g (x) b) = 0 L = f(x) (g (x) b) @ = g (x) + b = 0 Fall 2015,??-Page-24

26 Simple Optimization 7. Example: Suppose we wish to maximize f(x; y) = 10(x 2) 2 2 (y 4) 2 subject to the constraint that y + x 5 L (x; y) = 10(x 2) 2 2 (y 4) 2 (y + x (x; y) 20x + 40 = (x; y) 4y + 16 = (x; y) = y (y + x 5) = = 0 The solution is [x = 11 6 ; y = 19 6 = 10 3 ]: If we change the constraint to x + y 7; we have [x > 2; y > 4; > 0] Fall 2015,??-Page-25

27 Simple Optimization 8. Suppose there are two perishable goods x 0 and x 1 that will become available to our consumer at time 0 and time 1. The consumer has to decide what to do with these goods in order to achieve highest possible level of utility We form Lagrangian equation max c 0 ;c 1 u (c 0 ; c 1 ) s.t. c 0 x 0 ; c 1 x 1 max c 0 ;c 1 L = u (c 0 ; c 1 ) 0 (c 0 x 0 ) 1 (c 1 x 1 ) Fall 2015,??-Page-26

28 Simple Optimization The rst order conditions = 0 0 = = 1 1 = 0 (c 0 x 0 ) 1 (c 1 x 1 ) 0 = 1 = 1 (a) Do we know anything about the multipliers, 0 and 1? (b) We can guess what the solution should be. Because of the absence of nancial markets and storage opportunities, this is not a very interesting problem. Fall 2015,??-Page-27

29 Simple Optimization 9. Suppose the consumer is given x at time 0, but the consumer has the option to store the product for consumption next period. How does the problem change? Fall 2015,??-Page-28

30 Financial Markets 1. When nancial markets are introduced, the temporal distribution of income is no longer important, rather the person's wealth becomes the crucial factor. (a) What is wealth? Was there such a thing in the previous case? W ealth = P V of future consumpton = P V of future income w 0 = c 0 + c r 1 = x 0 + x r 1 Notice that in this case c 0 can exceed x 0 ; but then c 1 has to be less than x 1 (assuming r 1 > 0). Fall 2015,??-Page-29

31 Financial Markets (b) The investor's problem is now this Note that max L = u (c 0 ; c 1 ) c 0 + c 1 x 1 x 0 c 0 ;c r r = = r = c 0 + c 1 x 1 x 0 = r r = (1 + r 1 ) This is called the marginal rate of substitution (it is the slope of the Fall 2015,??-Page-30

32 Financial Markets indierence curve), which is equal to (1 + r). What is the intuition? Where do x 0 and x 1 plot? Fall 2015,??-Page-31

33 Firms 1. Firms are represented by a production function, f (I 0 ) 0 > 2 f=@i0 2 < 0: Suppose the rm is given resources of x 0 at time 0: Then the rm can have payos at time 0 and time 1 that satisfy the combination, fx 0 I 0 ; f (I 0 )g 2. If there are nancial markets, the current market value of the rm is given by V 0 = (x 0 I 0 ) + f (I 0) (1 + r) The objective is to maximize the value of the rm. max I 0 V 0 = 1 + f 0 (1 + r) = 0 f 0 = (1 + r) Fall 2015,??-Page-32

34 Firms So the rm invests up to the point that the net marginal rate of return, f 0 (I 0 ) 1, is equal to the market rate of interest. What is the intuition? 3. Production possibility curve: Dene the function g (y 0 ; y 1 ) = 0 as the function that describes feasible combinations of current and future payos (a) Example: Suppose g (y 0 ; y 1 ) = 4y0 2 + y = 0: What is f? y1 2 = 100 q 4y2 0 y 1 = 100 q 4y0 2 = (x 0 I 0 ) 2 Fall 2015,??-Page-33

35 Firms The following is the graph of g Fall 2015,??-Page-34

36 Firms 4. The optimization can be displayed as follows Fall 2015,??-Page-35

37 Firms max y 0 + y 1 (1 + r) 1 (1 + r) s.t. g (y 0 ; y 1 ) = 0 max L = y 0 + y 1 (1 + r) = 0 1 = 0 The same slope as @y 0 0 = (1 + r) g (y 0 ; y 1 ) Fall 2015,??-Page-36

38 Firms 5. What happens if there is no nancial market and the rm is owned by the investor max u (c 0 ; c 1 ) s.t. g (c 0 ; c 1 ) @c @c 1 Fall 2015,??-Page-37

39 Firms Fall 2015,??-Page-38

40 Firms 6. Finally, what happens when there is a competitive nancial market. In this case, the investor's wealth is given by the value of rm. The Fall 2015,??-Page-39

41 Firms present value of his consumption cannot exceed his wealth max u (c 0 ; c 1 ) s.t. c 0 + c r = y 0 + y r g (y 0 ; y 1 ) = = r = 0 7. Can you identify the value of the rm? How much does the investor borrow or lend in nancial markets? How much does the investor invest in the rm? Fall 2015,??-Page-40

42 Firms 8. The above graph displays what is known as the Fisher separation theorem. (a) The investor's investment & consumption decisions are separated i. Manager maximizes the value of the rm he/she owns ii. Given maximized value of the rm, the shareholder selects the best consumption plan. We know that the consumption plan could be dierent for two dierent individuals, but the investment plan remains the same. 9. What if there are market imperfections (e.g., the investor cannot borrow and lend at the same rate of interest)? 10. How does uncertainty aect this result? 11. What is agency problem and how could it complicate this result? Fall 2015,??-Page-41

43 Firms 12. Why do we need rms? Why cannot various function be broken up and performed by various people? 13. Why do we need rms that are involved in nancial transactions (e.g., banks)? Fall 2015,??-Page-42

44 Multiperiod Valuation 1. Let C T = a single payment at time T. Then its current market value will be where r T V 0 = C T (1 + r T ) T ; (1) is the \annual" rate of interest for a T -period investment. For a series of cash ows C t for t = 1; :::; T we have V 0 = TX t=1 C t (1 + r t ) t (2) 2. Obviously, we can write the above equation as V 0 = nx t=1 C t (1 + r t ) t + V n (1 + r n ) n (3) It is obvious that under certainty the same V 0 should be obtained regardless of the method. But under uncertainty, this may not be the case. In fact, most investment analysts would use equation (3) to estimate the value of, say, a stock. The argument is that we are not Fall 2015,??-Page-43

45 Multiperiod Valuation going to hold it forever and thus we need to estimate the future selling price. Of course, if we assume that all current and future traders will use the same criteria, then V n should be the discounted value of future cash ows. Imposing this degree of rationality simplies the matter very much, but may not reect the way short-term trades evaluate investments. There are continuous-time versions of the above. These will be used if the payments are discounted continuously. V 0 = C T e r T T V 0 = Z T 0 C t e r tt dt Fall 2015,??-Page-44

46 Free Cash Flow & Firm Value 1. The value a rm is P V of the dividends the shareholders are expected to receive. The current value of each share is S 0 = 1X t=1 div t (1 + r t ) t What about rms that do not pay dividends? The above expression can also be expressed as S 0 = 1X t=1 F C t (1 + r t ) t where F C is the free cash ow of the rm. The starting point of understanding F C t is to start with the basic identity. Here m t is the number of shares the rm may sell, n t is the number of bonds that the rm may sell. The gures below are for the whole rm rather than each Fall 2015,??-Page-45

47 Free Cash Flow & Firm Value share. Initially we assume that there are no debt and new issues of equity. Sources of Cash = Uses of Cash Rev t + m t S t + n t D t = Div t + Cost t + I t + T ax t Div t = Rev t Cost t I t T ax t Div t = Rev t Cost t I t (Rev t Cost t dep t ) = (Rev t Cost t dep t ) (1 ) (I t dep t ) = NI t (I t dep t ) Here NI t is after tax net income and dep t is depreciation charge, which is not a cash item but is needed to the calculate income tax. The term NI t (I t dep t ) is a simple version of free cash ow. Since there is not debt, the value of the rm is equal to the value of the equity. V U (F irm) = P V 0 (Div t ) = P V 0 (NI t ) P V 0 (I t dep t ) Fall 2015,??-Page-46

48 Free Cash Flow & Firm Value 2. Suppose the cost consists of some interest payments to bond holders. Then the above equation will be Div t = (Rev t Costs t Int t dep t ) (1 ) (I t dep t ) Div t + Int t = (Rev t Costs t dep t ) (1 ) + Int t (I t dep t ) = NI U t (I t dep t ) + Int t where NI U t is the net income of the rm if there was no leverage. In this case the value of the rm using leverage is V L (F irm) = P V 0 NI U t P V 0 (I t dep t ) + P V 0 (Int) For 0 t = V U (F irm) + Debt 0 where Debt 0 is the value of the rm's debt. The value of the rm with leverage is equal to the value of rm if there were no leverage plus the value of tax shields resulting from interest payments on its debt. Fall 2015,??-Page-47

49 Free Cash Flow & Firm Value 3. This result is known as the Modigliani-Miller Theorem. What happens if there are no taxes? Fall 2015,??-Page-48