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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