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==Financial market hypotheses==
===Background===
===Efficient market hypothesis===
The efficient markets hypothesis stipulates that all of the available information that is relevant to the price of an asset is already embodied in that price. It is based upon the argument that there is a large body of investors who react immediately (and at no cost to themselves)  to  any fresh information to buy or sell that asset . For example, if prices are expected to rise tomorrow, investors will buy today and in doing so, cause the price to rise until it is no longer  expected to rise further. The formal statement that "in an informationally efficient market, price changes must be unforecastable if they are properly anticipated" was put forward and proved by Paul Samuelson in 1965 <ref>Paul Samuelson: ''Proof that Properly Anticipated Prices Fluctuate Randomly.'', Industrial Management Review, 6,  1965 </ref>, and there followed a debate as to whether stock markets do in fact operate as efficient markets. That  question was subsequently  explored in studies undertaken and  summarised by  the economist Eugene Fama in 1991 <ref>[http://www.e-m-h.org/Fama70.pdf Eugene Fama: "Efficient Capital Markets: A Review of Theory and Empirical Work", ''Journal of Finance'' Vol 25 No 2]</ref>. 
<ref>[http://www.financeprofessor.com/summaries/fama91efficientcapitalmarketsii.htm Eugene Fama:  "Efficient Capital Markets II", ''Journal of Finance'', December 1991]</ref> and others. Fama concluded that there is no important evidence to suggest that prices do not adjust to publicly available information.
===Financial instability hypothesis===
The financial instability hypothesis, as formulated in 1992 by Hyman Minsky,  states  that the economy has financing regimes under which it is stable, and financing regimes in which it is unstable and that, during periods of sustained growth  it  tends to transform itself from stability to instability.  It  is based upon  the argument that there are three categories of financial  transaction:
*hedge transactions, whose  payment obligations can all  be met from their cash flows;
*speculative transactions  for which interest payments can be met from their cash flows  the repayment of principle has to be  met from cash flows and are met by  rolling over (ie the issue of more debt;.
* "Ponzi" transactions, for which neither interest payments nor capital repayments can be met from cash flows;
- and that the proportions of speculative and Ponzi transactions in the economy tend to increase in time of prosperity.
<ref>[http://www.levy.org/pubs/wp74.pdf Hyman Minsky: ''The Financial Instability Hypothesis'', Working Paper No. 74, The Jerome Levy Economics Institute of Bard College, May 1992]</ref>
===Behavioural  hypotheses===
<ref>[http://web.mit.edu/alo/www/Papers/JPM2004_Pub.pdf Andrew W. Lo: ''The Adaptive Markets Hypothesis'', Journal of Portfolio Management, 30th Anniversary Number, 2004]</ref>
==Financial models==


===The Capital Asset Pricing Model===  
===The Capital Asset Pricing Model===  
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(for a fuller exposition, see Miller & Starr ''Executive Decisions and Operations Research'' Chapter 12,  Prentice Hall 1960)
(for a fuller exposition, see Miller & Starr ''Executive Decisions and Operations Research'' Chapter 12,  Prentice Hall 1960)
==References==
<references/>

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Tutorials relating to the topic of Financial economics.

The Capital Asset Pricing Model

The rate of return, r,  from an equity asset is given by

where

rf  is the risk-free rate of return

rm  is the equity market rate of return

(and rrf is known as the equity risk premium)

and β is the covariance of the asset's return with market's return divided by the variance of the market's return.


(for a proof of this theorem see David Blake Financial Market Analysis page 297 McGraw Hill 1990)

The Arbitrage Pricing Model

The rate of return on the ith asset in a portfolio of n assets, subject to the influences of factors j=1 to k is given by


where


and

is the weighting multiple for factor
is the covariance between the return on the ith asset and the jth factor,
is the variance of the jth factor

Black-Scholes option pricing model

The fair price,P, of a call option on a security is given by:

where:

C is the current price of the security;
is the cumulative probability distribution for the standard normal variate from -∞ to ;
X is the exercise price (see options definition);
r is the risk-free interest rate;
t is the time to expiry of the option;
and are given by the equations:


;
;

and

is the standard deviation (or volatility) of the price of the asset.

The first expression, ,   of the equation is the expected benefit from acquiring a stock outright, obtained by multiplying the asset price by the change in the call premium with respect to a change in the underlying asset price. The second expression,  , is the present value of paying the exercise price on the expiration day. The fair market value of the call option is then calculated by taking the difference between these two parts


The underlying assumptions include:

  • Dividend payments are not included;
  • Options cannot be exercise before the stipulated date;
  • Markets are efficient;
  • No commissions are paid;
  • Volatility is constant;
  • The interest rate is constant; and,
  • Returns are log-normally distributed.

Gambler's ruin

If q is the risk of losing one throw in a win-or-lose winner-takes-all game in which an amount c is repeatedly staked, and k is the amount with which the gambler starts, then the risk, r, of losing it all is given by:

r  =  (q/p)(k/c)

where p  =  (1 - q),  and q  ≠  1/2


(for a fuller exposition, see Miller & Starr Executive Decisions and Operations Research Chapter 12, Prentice Hall 1960)