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30 Cards in this Set

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  • Back
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 risk-free 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 risk-return trade-off.
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 risk-free investments would need to offer with certainty to be considered equally attractive as the risky portfolio.
risk-neutral
A risk-neutral investor judges risky prospects solely by their expected rates of return.
mean-variance (M-V) 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) + (1-p)U(W2)