Financial economics/Tutorials

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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

r = r β(r - rf)

'

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

where



  • No dividends from underlying asset.
  • European exercise terms (so warrants will not be exercised early)
  • Efficient markets
  • No commissions
  • Constant volatility
  • Constant interest rates
  • Returns are lognormally 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)