VIEWS: 5 PAGES: 63 POSTED ON: 5/9/2010
Lecture Eight Finance Theory The Capital Assets Pricing Model A Keynesian Critique A Keynesian Alternative Recap • “Breakdown” of Phillips curve • Rise of neoclassicism • Critiques of logical foundations of neoclassical micro • Today – Neoclassical foundations of finance theory – Some problems – An alternative view • Fisher‟s “Debt-Deflation theory of Great Depressions” elaborated • Minsky‟s Financial Instability Hypothesis • Peter‟s Fractal Markets Hypothesis – Prospects for US… The Capital Assets Pricing Model • Problem: How to “predict the behaviour of capital markets” • Solution: extension of economic theories of investment under certainty... – to investment under conditions of risk • Based on neoclassical utility theory • Investor maximises utility subject to (s.t.) constraints • Utility is a: – Positive function(+ive fn) of expected return ER – -ive fn of risk (standard deviation) sR • Constraints are available spectrum of investment opportunities The Capital Assets Pricing Model “Efficient” Investment opportunities opportunities on the edge Z inferior to C (lower ER) Indifference and B curves (higher sR) Increasing utility: Optimal Higher expected combination returns & lower risk for this investor Border (AFBDCX) is Investment Opportunity Curve (IOC) The Capital Assets Pricing Model • IOC reflects correlation of separate investments. Consider 3 investments A, B, C: – A contains investment A only • Expected return is ERa, Variance due to A • Risk is sRa Perceived – B contains investment B only correlation of A • Expected return is ERb, with B • Risk is sRb (varies between -1 – C some combination of a of A & (1-a) of B & +1) • ERc=aERa + (1-a)ERb s Rc .s Ra (1 ) s Rb 2. rab . . 1 .s Ra .s Rb 2 2 2 2 The Capital Assets Pricing Model • If rab=1, C lies on straight line between A & B: This is 1 s Rc 2 .s Ra 2 (1 ) 2 s Rb 2 2. rab . . 1 .s Ra .s Rb The Capital Assets Pricing Model • If rab=1, C lies on straight line between A & B: s Rc 2 .s Ra 2 (1 ) 2 s Rb 2 2. rab . . 1 .s Ra .s Rb 2 .s Ra 2 (1 ) 2 s Rb 2 2. . 1 .s Ra .s Rb This can be factored The Capital Assets Pricing Model • If rab=1, C lies on straight line between A & B: s Rc .s Ra (1 ) s Rb 2. rab . . 1 .s Ra .s Rb 2 2 2 2 .s Ra (1 ) s Rb 2. . 1 .s Ra .s Rb 2 2 2 2 .s Ra (1 ).s Rb .s Ra (1 )s Rb 2 Identical to straight line relation for expected return: The Capital Assets Pricing Model sR W h en rab= 1 B t In v e sm en t O ppo r tun ity C C u rv e A ER The Capital Assets Pricing Model • If rab=0, C lies on curved path between A & B: This is zero s Rc 2 .s Ra 2 (1 ) 2 s Rb 2 2. rab . . 1 .s Ra .s Rb Hence this is zero The Capital Assets Pricing Model • If rab=0, C lies on curved path between A & B: s Rc .s Ra (1 ) s Rb 2. rab . . 1 .s Ra .s Rb 2 2 2 2 2 .s Ra 2 (1 ) 2 s Rb 2 The Capital Assets Pricing Model • If rab=0, C lies on curved path between A & B: s Rc 2 .s Ra 2 (1 ) 2 s Rb 2 2. rab . . 1 .s Ra .s Rb 2 .s Ra 2 (1 ) 2 s Rb 2 Straight line relation .s Ra (1 )s Rb 2 Hence lower risk for diversified portfolio (if assets not perfectly correlated) The Capital Assets Pricing Model sR W h en rab< 1 B t In v e sm en t O ppo r tun ity C Fall in sR due to diversification C u rv e when investments A are not perfectly correlated ER The Capital Assets Pricing Model • Sharpe assumes riskless asset P with ERP=pure interest rate, sRP=0. • Investor can form portfolio of P with any other combination of assets • One asset combination will initially dominate all others: The Capital Assets Pricing Model Efficiency: maximise expected return & minimise risk given constraints Only asset combination which can efficiently be combined with riskless asset P in a portfolio The Capital Assets Pricing Model • Assume limitless borrowing/lending at riskless interest rate = return on asset P • Investor can move to anywhere along PfZ line by borrowing/lending • Problem: – P the same for all investors (“simplifying assumption”) – But investor perceptions of expected return, risk, investment correlation will differ • Solution: – assume “homogeneity of investor expectations” [OREF II] – utterly unrealistic assumption, as is assumption of limitless borrowing by all borrowers at riskless interest rate. So... The Capital Assets Pricing Model • Defended by appeal to Friedman‟s “Instrumentalism” (next lecture): – “the proper test of a theory is not the realism of its assumptions but the acceptability of its implications” • Consequence of assumptions: – spectrum of available investments/IOC identical for all investors – P same for all investors – PfZ line same for all investors – Investors distribute along line by borrowing/lending according to own risk preferences: The Capital Assets Pricing Model Thrill seeker... Highly risk-averse The Capital Assets Pricing Model • Next, the (perfect) market mechanism – Price of assets in f will rise – Price of assets not in f will fall – Price changes shift expected returns – Causes new pattern of efficient investments aligned with PfZ line: The Capital Assets Pricing Model Capital market line Range of efficient asset combinations after market price adjustments: more than just one efficient portfolio The Capital Assets Pricing Model • Theory so far applies to combinations of assets • Individual assets normally lie above capital market line (no diversification) • Can‟t relate between ERi & si • Can relate ERi to “systematic risk”: • Investment i can be part of efficient combination g: – Can invest (additional) in i and (1-) in g • =1 means invest solely in i; • =0 means some investment in i (since part of portfolio g); • Some <0 means no investment in i; • Only =0 is “efficient” The Capital Assets Pricing Model Single investment i which is part of Efficient portfolio g combination g Additional investment in i is zero (a=0) here The Capital Assets Pricing Model • Slope of IOC and igg‟ curve at tangency can be used to derive relation for expected return of single asset E Ri P rig s Ri s Rg E Rg P • This allows correlation of variation in ERi to variation in ERg (undiversifiable, or systematic, or “trade cycle” risk) • Remaining variation is due to risk inherent in i: The Capital Assets Pricing Model Risk peculiar to asset i Higher return for assets more strongly affected by trade cycle (systematic risk The Capital Assets Pricing Model • Efficient portfolio enables investor to minimise asset specific risk • Systematic risk (risk inherent in efficient portfolio) can‟t be diversified against • Hence market prices adjust to degree of responsiveness of investments to trade cycle: – “Assets which are unaffected by changes in economic activity will return the pure interest rate; those which move with economic activity will promise appropriately higher expected rates of return.” [OREF II] The Capital Assets Pricing Model • Crux/basis of model: markets efficiently value investments on basis of expected returns/risk tradeoff • Modigliani-Miller extend model to argue valuation of firms independent of debt structure (see OREF II) • Combination: the “efficient markets hypothesis” • Focus on portfolio allocation across investments at a point in time, rather than trend of value over time • Argues investors focus on “fundamentals”: – Expected return – Risk • So long as assumptions are defensible… The Capital Assets Pricing Model • In order to derive conditions for equilibrium in the capital market we invoke two assumptions. First, we assume a common pure rate of interest, with all investors able to borrow or lend funds on equal terms. Second, we assume homogeneity of investor expectations: investors are assumed to agree on the prospects of various investments–the expected values, standard deviations and correlation coefficients described in Part II. Needless to say, these are highly restrictive and undoubtedly unrealistic assumptions. However, since the proper test of a theory is not the realism of its assumptions but the acceptability of its implications, and since these assumptions imply equilibrium conditions which form a major part of classical financial doctrine, it is far from clear that this formulation should be rejected–especially in view of the dearth of alternative models leading to similar results. (Sharpe 1964 [1991]; emphasis added) • But Sharpe later admits to some qualms with this: The CAPM: Reservations • “People often hold passionately to beliefs that are far from universal. The seller of a share of IBM stock may be convinced that it is worth considerably less than the sales price. The buyer may be convinced that it is worth considerably more.” (Sharpe 1970) • However, if we try to be more realistic: – “The consequence of accommodating such aspects of reality are likely to be disastrous in terms of the usefulness of the resulting theory... The capital market line no longer exists. Instead, there is a capital market curve–linear over some ranges, perhaps, but becoming flatter as [risk] increases over other ranges. Moreover, there is no single optimal combination of risky securities; the preferred combination depends upon the investors‟ preferences... The demise of the capital market line is followed immediately by that of the security market line. The theory is in a shambles.” (Sharpe 1970 emphasis added) A Keynesian view • Key issue is uncertainty, not risk – Cannot possibly estimate expected returns far into future: • “our basis of knowledge for estimating the yield ten years hence of [an investment] amounts to little... those who seriously attempt to make any such estimate are often so much in the minority that their behaviour does not govern the market.” – Instead, conventions to cope with uncertain future: • “assume that the present is a ... serviceable guide to the future… that the existing state of ... prices ... is based on a correct summing up of future prospects… we endeavor to fall back on the judgment of the rest of the world which is perhaps better informed.” Keynes‟s view • Investors profit by picking shifts in confidence: – “the professional investor and speculator are ... concerned, not with making superior long-term forecasts of the probable yield of an investment over its whole life, but with foreseeing changes in the conventional basis of valuation a short time ahead of the general public… this behaviour... is an inevitable result of an investment market... For it is not sensible to pay 25 for an investment of which you believe the prospective yield to justify a value of 30, if you also believe that the market will value it at 20 three months hence.” [OREF II] • Markets thus conducted by speculation on immediate behaviour of other speculators, rather than rational calculation: Keynes‟s view • Recall earlier lectures on Keynes and uncertainty • The Stockmarket as a beauty contest and “the third degree”: – “… pick out the six prettiest faces … the prize being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole... We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be.” • The practicality of rational calculation?: – “Investment based on genuine long-term expectation is … scarcely practicable. He who attempts it must surely … run greater risks than he who tries to guess better than the crowd how the crowd will behave…” The “Price system” and Asset Markets • Normal micro theory: – Supply a positive function of price – Demand a negative function of price – Supply and demand independent • If price rises – Supply rises – Demand falls – Tendency towards equilibrium • But finance markets – Supply (of assets, shares) possibly a positive function of price – Demand also a positive function of price: The “Price system” and Asset Markets • If price of assets (shares, real estate, etc.) rising, demand also rises • Buyers hope to buy and sell on a rising market • The faster the rate of price increase (generally speaking) the faster the growth of demand • Tendency to move away from “equilibrium” (“fundamental value”, historic price to earnings ratios, etc.) • Price thus destabilises an asset market • An alternative theory to equilibrium-oriented conventional finance theory needed which acknowledges destabilising role of asset prices • Derived from Fisher and Keynes by Minsky Fisher: Keynes‟s unlikely ally • Conventional theory of finance an extension of Fisher‟s Theory of Interest (1930) – The rate of interest “expresses a price in the exchange between present and future goods” – Three elements combine to determine rate of interest: • Subjective: “the marginal preference for present over future goods” – strong preference: borrower; weak preference: lender; balance determines supply of funds • Objective: “investment opportunity” determines demand for funds • The Market: equilibrium interest rate equates supply to demand Fisher: Keynes‟s unlikely ally • “Market for loans” differs from normal market: – normal market, payment made and goods exchanged simultaneously (in absence of credit) – Loans: goods (loaned money) exchanged now; repayment (principal + interest) occurs later • Two special assumptions needed to eliminate this difference: – (A) The market must be cleared--and cleared with respect to every interval of time. (B) The debts must be paid. (Fisher 1930: 495) • Fisher‟s book published in 1930 • In 1929, Fisher comments “Stocks appear to have reached a permanently high plateau”… and then came October 23rd: “Black Wednesday”… Alternative Finance (1): Financial Instability • Fisher & Keynes blended into alternative theory of finance by Minsky: the “Financial Instability Hypothesis” – partial objective: to explain Great Depressions – overall objective: an alternative economics to neoclassical micro/macro Minsky‟s interpretation of Keynes • Two price levels – Commodity prices set by markup on cost of production – Assets / equipment prices based on expected revenue • Volatile basis for expectations essential – Future fundamentally uncertain: “we simply do not know”, so conventions developed: • Present accepted as a “serviceable guide” to the future • Current expectations presumed correct • Mass sentiment • Finance demand for money – “it is ... the „financial‟ facilities which regulate the pace of new investment” [Keynes 1937] Minsky‟s Hypothesis • Economy in historical time • Debt-induced recession in recent past • Firms and banks conservative re debt/equity ratios, asset valuation • Only conservative projects are funded • Recovery means conservative projects succeed • Firms and banks revise risk premiums – Accepted debt/equity ratio rises – Assets revalued upwards The Euphoric Economy • Self-fulfilling expectations – Decline in risk aversion causes increase in investment • Investment expansion causes economy to grow faster – Asset prices rise, making speculation on assets profitable – Increased willingness to lend increases money supply (endogenous money) – Riskier investments enabled, asset speculation rises • The emergence of “Ponzi” (Bondy?) financiers – Cash flow from “investments” always less than debt servicing costs – Profits made by selling assets on a rising market – Interest-rate insensitive demand for finance The Assets Boom and Bust • Initial profitability of asset speculation: – reduces debt and interest rate sensitivity – drives up supply of and demand for finance – market interest rates rise • But eventually: – rising interest rates make many once conservative projects speculative – forces non-Ponzi investors to attempt to sell assets to service debts – entry of new sellers floods asset markets – rising trend of asset prices falters or reverses Crisis • Ponzi financiers go bankrupt: – can no longer sell assets for a profit – debt servicing on assets far exceeds cash flows • Asset prices collapse, drastically increasing debt/equity ratios • Endogenous expansion of money supply reverses • Investment evaporates; economic growth slows or reverses • Economy enters a debt-induced recession ... The Aftermath • High Inflation? – Debts repaid by rising price level – Economic growth remains low: Stagflation – Renewal of cycle once debt levels reduced • Low Inflation? – Debts cannot be repaid – Chain of bankruptcy affects even non-speculative businesses – Economic activity remains suppressed: a Depression • Big Government? – Anti-cyclical spending and taxation of government enables debts to be repaid – Renewal of cycle once debt levels reduced Modelling Minsky • A taste of dynamics: a model of Minsky built on Marx‟s model of cyclical economy: – “accumulation slackens in consequence of the rise in the price of labour, because the stimulus of gain is blunted. The rate of accumulation lessens; but with its lessening, the primary cause of that lessening vanishes, i.e. the disproportion between capital and exploitable labour power… The price of labor falls again to a level corresponding with the needs of the self-expansion of capital… To put it mathematically, the rate of accumulation is the independent, not the dependent variable; the rate of wages the dependent, not the independent variable.” (Marx 1867, 1954: 580- 581) Modelling Minsky • Mechanism is: – high rate of growth causes high level of employment – high level of employment causes increase in wage level – increase in wage level reduces profit – reduced profit reduces investment – lower investment reduces growth rate – lower growth rate reduces employment – lower employment leads to falling wage level – falling wage level restores profitability, restarting cycle Modelling Minsky • Minsky‟s theory explicitly based on time and changes in variables over time • Can‟t be modelled using simultaneous equations (which ignore time) • Instead have to use – Differential equations (rate of change of y with respect to time is a function of…) – Computer simulation (artificial economies with time- based variables) • Differential equations (normally) show rate of change of one variable as a function of values of another. • Much of classical economics can be described as “verbal differential equations”. An example: Malthus on population: Digression: Dynamics & Equations • “I think I may fairly make two postulata. First, That food is necessary to the existence of man. Secondly, That the passion between the sexes is necessary and will remain nearly in its present state...” • “ Population, when unchecked, increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio. A slight acquaintance with numbers will shew the immensity of the first power in comparison of the second.” • These can be put into “verbal differential equations”: – In the absence of food shortages, population grows exponentially – Food increases linearly • In actual differential equations, we get: Malthus‟s Population Dynamics d b Births minus 1 dP P dt deaths A small constant for high F/P ratios but Percentage rate rises dramatically as F/P falls below a of change of critical levelP population d F , P F dF a dt No “ceteris paribus”: Feedback A from F to P. constant Slope of food Modelling this: output Malthus‟s Population Dynamics Putting it all together, we get: “Nonlinear” 1 dP 2 negative b P P P dt C a t feedback Population growth in contribution the absence of food from population shortages Linear attenuating 5 2 10 1.557997 .10 5 feedback from food (C is initial 5 1.5 10 Z 1 1 10 5 level) I don‟t think Malthus i 5 10 4 ever realised that this was (roughly) the path 100 0 0 200 400 600 800 1000 he predicted for population... 0 1 .10 0 3 Z i Modelling Minsky • Same type of logic needed to express Minsky‟s model of finance – Specify relationships in terms of “rate of change of y is a function of…” – Relate all elements in causal chain until it “loops back” on itself • (Malthus‟s theory is incomplete here; there is no “feedback” from population to food) – No more “ceteris paribus” since everything determines everything else, but in a time sequence. • So to model Minsky, we start with Marx 1867 and Goodwin 1967... Modelling Minsky • Causal chain “accelerator” – Capital (K) determines Output (Y) Y K v – Output determines employment (L) L Y – Employment determines wages a productivity (w) – Wages (w´L) determine profit (P) dw U w f – Profit determines investment (I) dt N – Investment I determines capital K Y w L Phillips curve – chain is closed dK k Y K dt K I k K Investment Depreciation function An Economic Model without Finance Basic Goodwin Growth Cycle 1 0.95 Proportion 0.9 0.85 0.8 0.75 0 5 10 15 20 Time Wage Share Employment Equilibrium Wage Share Equilibrium Employment A Economic Model with Finance • Add debt: Debt – Firms borrow when desired investment exceeds profits dD r D I Y W – Debt solely used to dt finance investment Interest rate – Profit is now output Gross Profit net of wages and debt repayment Y w L r D A Economic Model with Finance A Economic Model with Finance The “Inefficient Markets Hypothesis” • Argument that investors – react slowly to news – over-react – ignore “reversion to the mean” • Series of good reports leads to expectation of more good news • Firm valuation rises, seen as “growth stock” – rise becomes self-fulfilling; bandwaggon buying • Firm cannot sustain above sector/economy performance indefinitely • Initial “bad news” reports ignored as firm “reverts to mean” • Finally, “bear” valuations set in; bandwaggon selling – “growth stock” underperforms in medium term The “Inefficient Markets Hypothesis” • 90% of price variability due to internal dynamics of speculators watching other speculators: – EMH idea of investors focusing solely upon expected risk/return wrong: Instead, speculators watch other speculators The “Fractal Markets Hypothesis” • Puzzle – If EMH is so wrong intellectually, how come it almost seems right in the data? • Solution: a highly chaotic distribution is very hard to distinguish from a truly random distribution • Chaos/Complexity – Deterministic system (no shocks involved) which generates highly complex, aperiodic cycles • Discussed in lecture on dynamics • Applied to finance, the “Fractal Markets Hypothesis” – Apparently random movements of stock market in fact mask a “fractal” dynamic process • so what‟s a fractal? The “Fractal Markets Hypothesis” • A pattern produced by a highly nonlinear self-referential process… • Or in English: – Take an initial number • Apply some (possibly simple but) nonlinear transformation to it • Use the resulting number as the next input to be transformed – Resulting time series can appear highly random, but at the same time • is generated by a process with no chance (risk) involved • has an underlying structure, which can however be very hard to discern The “Fractal Markets Hypothesis” • Peters applies fractal analysis to time series generated by asset markets – Dow Jones, S&P 500, interest rate spreads, etc. – finds a “fractal” structure – intellectually consistent with • Inefficient Markets Hypothesis • Financial Instability Hypothesis – Based upon • heterogeneous investors with different expectations, different time horizons – trouble breaks out when all investors suddenly operate on same time horizon with same expectations The “Fractal Markets Hypothesis” • Take a typical day trader who has an investment horizon of five minutes and is currently long in the market. The average five-minute price change in 1992 was -0.000284 per cent [it was a “bear” market], with a standard deviation of 0.05976 per cent. If, for technical reasons, a six standard deviation drop occurred for a five minute horizon, or 0.359 per cent, our day trader could be wiped out if the fall continued. However, an institutional investor–a pension fund, for example–with a weekly trading horizon, would probably consider that drop a buying opportunity because weekly returns over the past ten years have averaged 0.22 per cent with a standard deviation of 2.37 per cent. In addition, the technical drop has not changed the outlook of the weekly trader, who looks at either longer technical or fundamental information. Thus the day trader‟s six-sigma [standard deviation] event is a 0.15-sigma event to the weekly trader, or no big deal. The weekly trader steps in, buys, and creates liquidity. This liquidity in turn stabilises the market. (Peters 1994) Conclusion • View of finance depends on whether take equilibrium or dynamic view – equilibrium: • optimum allocation of funds, rational markets – dynamic: • speculative markets, accumulation of debt, possibility of crisis • Current crises difficult, if not impossible, to explain in equilibrium terms – Rapid movements in markets (e.g., sevenfold devaluation of Indonesian rupiah in a week by money markets) can‟t be due to similar fall in real productivity of Indonesian economy – Finance and economic outcomes clearly linked (rather than independent as in standard theory) Conclusion: Asian Crisis • Debt-deflation probable cause of Asian crisis – Originating in Japan‟s “Bubble Economy” 1987-90 – Huge bad debts carried by banks after crash of real estate market – Boom in Asia partly funded by Japanese/American banks seeking profit after collapse of own markets in 90/91 – Crash in Asia amplified by free capital markets • Currencies devalued on fear of inability to repay loans – Devaluation (4-fold for Thailand, 7-fold for Indonesia) guarantees loans cannot be repaid • Depression ensues – “Solution” must involve repudiation of debt Conclusion: New York New York… • Current US economic boom (now probably over) underwritten by asset price boom – Boom due to • “Euphoric” expectations on Internet • Feedback from rising prices to rising prices • Debt Financing of share purchases – The bust? Complicated by Mutual Funds, but • At 35:1, P:E ratio highest in (non-Depression) history • Broad market in decline now for more than 2 years; boom focused in very narrow range of stocks (as in 1929) • USA debt/output ratio 150% (vs 60% in 1929 [Fisher 1933]) • Inflation on border of deflation (as in 1929)… • one major difference: Big Government – impact discussed in Week 11