Ralph Vince - Portfolio Mathematics

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

420 INDEX

Nonstationary distribution, 26

Normal Distribution, 8–11, 17, 52

standardized, 55

working with, 54–59

Normal Probability Distribution.See

Normal Distribution

Numbers game, 20–21, 22

Odds.SeeProbability statement

One-tailed probabilities, 62, 76

Optimalf, xvii, xviii, xix, 117–205, 209,

215–217, 226–229, 231–232,

277–281, 298, 311–312, 335–340,

342, 345

asymmetrical leverage, 118–120

characteristics of, 175–205

arc sine laws and random walks,

194–197

combined bankroll versus

separate bankrolls, 180–182

drawdown, time spent in, 197–198

geometric mean, estimated,

198–201

optimalffor small traders just

starting out, 175–176

portfolio insurance and, 335–340

sensitivity to the biggest loss,

193–194

simultaneous wagering or

portfolio trading, efficiency loss

in, 185–188

specified goal, time required to

reach, 188–191

threshold to geometric, 177–180

trading, fundamental equation of,

202–203

trading systems, comparing,

192–193

treating each play as if infinitely

repeated, 182–185

whyfis optimal, 203–205

consequences of straying too far

from, 145–151

definition, 117–118

drawdown and largest loss with,

141–145

equalizing, 151–157

figuring geometric mean using

spreadsheet logic, 127

finding by the geometric mean,

122–125

finding via parabolic interpolation,

157–162

geometric average trade, 127–128

importance of, 132–140

Kelly formula, 24, 120–122

in mean variance portfolios,

277–281

scenario planning, 162–173

scenario spectrums, 173–174

simpler method for finding, 128–130

virtues of, 130–132

Parabolic interpolation, 157–162, 315

Pareto-Levy distributions.SeeStable

Paretian distribution

Pari-mutuel betting, 21–24

horse racing and, 23–24

Pearson, Karl, 97

Pearson’s coefficients of skewness, 50

Pearson’s r.SeeLinear correlation

coefficient

Phase length test, 39–40

Point of inflection, 355–358

Poisson Distribution, 52, 81–85

Portfolio and systems management,

367–376

long-term trend followers

commonalities, 368

differences, 368–369

further characteristics of, 369–372

Portfolio construction, classical,

231–260

Markowitz model, 232–235

Modern Portfolio Theory, 231–232

problem, definition of the, 235–246

row-equivalent matrices, solutions

of linear systems using, 246–252

results, interpreting the, 252–260

Portfolio insurance, 335–340

Portfolio Management Formulas

(Vince), 315