Ralph Vince - Portfolio Mathematics
194 THE HANDBOOK OF PORTFOLIO MATHEMATICS scenario and build from there. The problem is that we do not know exactly what our lar ...
Characteristics of Optimalf 195 nearly random as determined by the runs test and the linear correlation coefficient (serial corr ...
196 THE HANDBOOK OF PORTFOLIO MATHEMATICS Thus, if we were to toss a coin 10 times (N=10) we would have the following probabilit ...
Characteristics of Optimalf 197 Now here is thesecond arc sine law, which also uses Equation (5.09) and hence has the same proba ...
198 THE HANDBOOK OF PORTFOLIO MATHEMATICS Consider that the arc sine laws worked on an arithmetic mathematical expectation of ze ...
Characteristics of Optimalf 199 Equation (4.05)]. This gives us an optimalfof .0678 for A and .4 for B. The geometric means for ...
200 THE HANDBOOK OF PORTFOLIO MATHEMATICS This function is true only when the return (i.e., the HPR) is constant, which is not t ...
Characteristics of Optimalf 201 FIGURE 5.2 Pythagorean Theorem in money management The exponent of the estimated TWR,T, will tak ...
202 THE HANDBOOK OF PORTFOLIO MATHEMATICS The Fundamental Equation of Trading We can glean a lot more than just how trimming the ...
Characteristics of Optimalf 203 changes are the result of inefficiencies in the way we are carrying out our trading, as well as ...
204 THE HANDBOOK OF PORTFOLIO MATHEMATICS first derivative of the fundamental equation of trading (i.e., the estimated TWR) is c ...
Characteristics of Optimalf 205 And we see that the function peaks at .25, where the slope of the tangent is zero, exactly at th ...
206 ...
CHAPTER 6 Laws of Growth, Utility, and Finite Streams S ince this book deals with the mathematics involving growth, we must disc ...
208 THE HANDBOOK OF PORTFOLIO MATHEMATICS FIGURE 6.1 The three growth functions Next, we have the exponential growth function, l ...
Laws of Growth, Utility, and Finite Streams 209 callosum between population growth and the new framework presented in this book. ...
210 THE HANDBOOK OF PORTFOLIO MATHEMATICS Consider the first toss. There is a 50% probability of winning $2 and a 50% probabilit ...
Laws of Growth, Utility, and Finite Streams 211 quit after one play to .5 for both the first play and the second. That is, if we ...
212 THE HANDBOOK OF PORTFOLIO MATHEMATICS Now, we can express all tosses subsequent to the first toss as TWRs by multiplying by ...
Laws of Growth, Utility, and Finite Streams 213 time, thefthat is optimal is that which maximizes the geometric mean HPR. In a n ...
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