Financial economics/Tutorials: Difference between revisions

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where
where
::::<math>{beta_{ij}} = \frac{Cov(r_i,d_j)}{Var(d_j)}</math>





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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 y is the weighting multiple for factor j



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)