Lecture Eight Finance Theory
The Capital Assets Pricing Model
A Keynesian Critique
A Keynesian Alternative

Recap:

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:

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:

The Capital Assets Pricing Model Indifference
curves Investment
opportunities Z inferior to C (lower ER) and B (higher sR) Border (AFBDCX) is Investment Opportunity Curve (IOC)

The Capital Assets Pricing Model:

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,
Risk is sRa
B contains investment B only
Expected return is ERb,
Risk is sRb
C some combination of a of A & (1-a) of B
ERc=aERa + (1-a)ERb

The Capital Assets Pricing Model:

The Capital Assets Pricing Model If rab=1, C lies on straight line between A & B:

The Capital Assets Pricing Model:

The Capital Assets Pricing Model If rab=1, C lies on straight line between A & B:

The Capital Assets Pricing Model:

The Capital Assets Pricing Model If rab=1, C lies on straight line between A & B:

The Capital Assets Pricing Model:

The Capital Assets Pricing Model

The Capital Assets Pricing Model:

The Capital Assets Pricing Model If rab=0, C lies on curved path between A & B: This is zero Hence this is zero

The Capital Assets Pricing Model:

The Capital Assets Pricing Model If rab=0, C lies on curved path between A & B:

The Capital Assets Pricing Model:

The Capital Assets Pricing Model If rab=0, C lies on curved path between A & B: Straight line relation Hence lower risk for diversified portfolio
(if assets not perfectly correlated)

The Capital Assets Pricing Model:

The Capital Assets Pricing Model

The Capital Assets Pricing Model:

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:

The Capital Assets Pricing Model Efficiency: maximise expected return
& minimise risk given constraints

The Capital Assets Pricing Model:

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:

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:

The Capital Assets Pricing Model

The Capital Assets Pricing Model:

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:

The Capital Assets Pricing Model Range of efficient asset combinations
after market price
adjustments: more than just one efficient portfolio

The Capital Assets Pricing Model:

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) a in i and (1-a) in g
a=1 means invest solely in i;
a=0 means some investment in i (since part of portfolio g);
Some a<0 means no investment in i;
Only a=0 is “efficient”

The Capital Assets Pricing Model:

The Capital Assets Pricing Model

The Capital Assets Pricing Model:

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 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:

The Capital Assets Pricing Model

The Capital Assets Pricing Model:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

Malthus’s Population Dynamics Percentage rate of change of population Births minus deaths Slope of food output A constant A small constant for high F/P ratios but rises dramatically as F/P falls below a critical level No “ceteris paribus”: Feedback from F to P. Modelling this:

Malthus’s Population Dynamics:

Malthus’s Population Dynamics Putting it all together, we get: Population growth in the absence of food shortages “Nonlinear” negative feedback contribution from population Linear attenuating feedback from food (C is initial level) I don’t think Malthus ever realised that this was (roughly) the path he predicted for population...

Modelling Minsky:

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:

Modelling Minsky Causal chain
Capital (K) determines Output (Y)
Output determines employment (L)
Employment determines wages (w)
Wages (w´L) determine profit (P)
Profit determines investment (I)
Investment I determines capital K
chain is closed “accelerator” productivity Phillips curve Investment function Depreciation

An Economic Model without Finance:

An Economic Model without Finance

A Economic Model with Finance:

A Economic Model with Finance Add debt:
Firms borrow when desired investment exceeds profits
Debt solely used to finance investment
Profit is now output net of wages and debt repayment Debt Interest rate Gross Profit

A Economic Model with Finance:

A Economic Model with Finance

A Economic Model with Finance:

A Economic Model with Finance

The “Inefficient Markets Hypothesis”:

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”:

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”:

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”:

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”:

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”:

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:

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:

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…:

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

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