Ralph Vince - Portfolio Mathematics

JWDD035-Ind JWDD035-Vince February 22, 2007 17:38 Char Count= 0

Index 421

Portfolio trading, efficiency loss in,

185–188

Positive correlation, 32,33

Positive territory, 195

Possible outcomes, 8–11

and standard deviations, 11–15

Powell’s mathematical minimization

routine, 409

Probabilities

one-tailed, 62, 76

two-tailed, 63–64

Probability distributions, 43–98

basics of, 43–45

Bernoulli, 71–72

Binomial, 72

Central Limit Theorem, 52–54

Chi-Square Distribution, 87–88

chi-square test, 88–91

descriptive measures of, 45–47

Exponential, 83–87

Geometric, 78–80

Hypergeometric, 80–81

Lognormal, 67–70

moments of, 47–52

first, 47

fourth (kurtosis), 51

second, 47–49

third (skewness), 49–50

Multinomial, 94–95

Normal, 50

further derivatives of, 65–67

working with, 54–59

normal probabilities, 59–65

Poisson, 81–83

stable Paretian, 95–98

Student’s, 91–94

Uniform, 70–71

Probability statement, 3–5, 6

Pyramiding, 371

Pythagorean Theorem, 201, 204, 205,

371

Random process and gambling theory,

3–41

baccarat, 19–20

determining dependency, 25–27

exact sequences, possible outcomes,

and Normal Distribution, 8–11

house advantage, 15–17

independent versus dependent trials

processes, 5–6

linear correlation coefficient, 32–41

mathematical expectation, 6–8

numbers, 20–21

pari-mutuel betting, 21–24

possible outcomes and standard

deviations, 11–15

runs test, Z scores, and confidence

limits, 27–32

winning and losing streaks in, 24–25

Random walks, 194–197

Reallocation, 333–335

tailoring a trading program through,

343–345

Rectangular Distribution.SeeUniform

Distribution

Reinvestment of returns, 99–116

Risk aversion, 219–221

absolute, 220

constant, 221

relative, 221

Rolle’s Theorem, 203–204

Root finding, mathematical

optimization versus, 312–313

Newton-Rapheson method, 313

Roulette, and mathematical

expectation, 7–8, 18

Ruin, risk of, 378–414

Java code for determining, 392–395

Runs test, 27–32, 195

Sample space, 12

Scenario planning, 162–173

Scenario spectrums, 173–174, 306–312

Separation Theorem, 263

Sharpe ratio, 263–264, 283–285

Sigma, 56

Significance level, 89–91

Simplex algorithm, 315

Simulated annealing, 316

Simultaneous wagering, efficiency loss

in, 185–188