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30 Cards in this Set
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simple prospect

an investment opportunity in whicha certain initial wealth is placed at risk, and there are only two possible outcomes.


speculation

The assumption of considerable business risk in obtaining commensurate gain.


commensurate gain

Positive risk premium  an expected profit greater than the riskfree alternative.


considerable risk

The risk is sufficient to affect the decision.


gamble

To bet or wager on an uncertain outcome.


gamble vs. speculation  economically speaking

A gamble is the assumption of risk for no purpose but enjoyment of the risk itself, whereas speculation is undertaken in spite of the risk involved because one perceives a favorable riskreturn tradeoff.


fair game

A prospect that has zero risk premium.


risk averse

A risk averse person will reject investment portfolios that are fair games or worse.


utility function

U = E(r)  .005*A*Sigma_Sq


A

Index of investor's risk aversion.


certainty equivalent rate

The rate that riskfree investments would need to offer with certainty to be considered equally attractive as the risky portfolio.


riskneutral

A riskneutral investor judges risky prospects solely by their expected rates of return.


meanvariance (MV) criterion

E(r_a) >= E(r_b)
and sigma_a <= sigma_b and at least one inequality is strict (rules out equality). 

hedging

Investing in an asset with a payoff pattern that offsets exposure to a particular source of risk.


covariance

Measures how much the returns on two risky assets move in tandem.


Cov(r_a,r_b)

SUM_s[ Pr(s)*
[r_a(s)  E(r_a)] * [r_b(s)  E(r_b)] 

correlation coefficient

Scales the covariance to a value between 1 and +1.


sigma_sq_P
(P = portfolio) 
w_sq_1 * sigma_sq_1 +
w_sq_2 * sigma_sq_2 + 2*w_1*w_2 * Cov(r1,r2) 

median

The outcome value that exceeds the outcome values for half the population and is exceed by the other half.


mode

The outcome with the highest probability.


mean absolute deviation (MAD)

SUM( P(s) * r(s)  E(r)


second central moment around the mean

Variance


skewness (3rd central moment)

Asymmetry of a dist'n
(+) right skewness () left skewness M3 = SUM(P(s)*[r(s)  E(r)]^3) 

moments

1st = reward
2nd & higher = uncertainty of reward Even = likelihood of extreme values Odd = asymmetry 

utility value

U = E(r)  b0*Sigma_sq + b1*M3  b2*M4 + b3*M5 ...


Samuelson's "Fundamental Approximation Theorem of Portfolio Analysis in Terms of Means, Variances, and Higher Moments" proves:

1. The importance of all moments beyond the variance is much smaller than that of the expected value and variance. Disregarding moments higher than the variance will not affect portfolio choices.
2. The variance is as important as the mean to investor welfare 

Major assumption of Samuelson's "Fundamental Approximation Theorem of Portfolio Analysis in Terms of Means, Variances, and Higher Moments"

Compactness  if the risk can be controlled by the investor. Equivalent to the continuity of stock prices.


alternate assumption to normal dist'n assumption  lognormal

Continuously compounded annual rate of return (r) is normally dist'd.
r_e = effective annual rate = e^r  1 r_e is dist'd lognormally 

r_e(t) for short holding periods

e^(rt)  1 for short time (t)
mean and variance are proportional to mean and variance of annual, continuously compounded ROR on stock and to the time interval (t). 

expected utility function

E[U(W)] = pU(W1) + (1p)U(W2)
