Friday, March 30, 2012

Valuation Under Uncertainty - Corporate Finance

I. Valuation Under Uncertainty

A.   Risk and Diversification

1.    Various types of risk that have previous been assumed away - since investors are risk averse, have to compensate for bearing risk.
(a)   default - promise of payment made at time t is not kept
(b)   expected returned - based on bad guess
(c)   Inflation risk
(d)   Reinvestment risk - can “C” be reinvested at same rate ö mortgage may be repaid when r is low ö no penalty for early payment
(e)   Liquidity risk - won’t be able to sell to get fast cahs
(f)   Currency risk - exchange rate fluctuations
(g)   Political risk - foreign gov’t may expropriate investment.
2.    Five Key terms in Probability Theory:
(a)   Expected Return - expectation of a series of cash flows  
(1)   ER =  3 probi * returni
(b)   Variance ö way to measure difference b/t two games
(1)   Var =  F2 = E (returni - ER)2 / n
(2)   prob = 1/n - if each outcome is equally likely. 
(3)   More iterations, then variance goes now without any corresponding diminution in ER.

(c)   Std Deviation - SQRT of Variance ö way to make variance more intelligible. 
(1)   F = SQRT (F2)
(2)   More iterations, then variance goes now without any corresponding diminution in ER.

(d)   Covariance - relationship between two events
(1)   Expected Value of products of deviations
(2)   Cov (AB) = FAB = E probi * (returniA - ERA) * (returniB - ERB).
(3)   Consider investing in Microsoft and GM.  Covariance tells you how much they vary, and how they vary
(e)   Correlation - tries to simplify covariance
(1)   always between -1 and +1.
(2)   D = Cov (A, B) /  (FA * FB)    
(3)   unitless measure.        

3.    Diversification  IMPORTANT - more interations, then variance goes down - same expected return be lower risk - works as long as additional stocks are not perfectly correlated to an existing stock in portfolio.
4.    End of the Day  NPV =
(a)   Numerator = Ert = embodies all possible states of the world
(b)   Denominator = (1 + r) t = must also be adjusted for risk also!!!
(c)   Formula does not encompass all types of risk (e.g. liquidity, reinvestment risk)

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