Ralph Vince - Portfolio Mathematics
154 THE HANDBOOK OF PORTFOLIO MATHEMATICS We have already obtained a new geometric mean by equalizing the past data. Thef$ varia ...
Optimalf 155 Return now to what was said at the outset of this discussion. Given a stream of trade P&Ls, the optimal fwill m ...
156 THE HANDBOOK OF PORTFOLIO MATHEMATICS dollars and euros? Is a .30-point move at .4500 the same as a .40-point move at .6000? ...
Optimalf 157 Further, the risk involved with a trade is a function of the chronology of the trade, a fact we would be forced to ...
158 THE HANDBOOK OF PORTFOLIO MATHEMATICS FIGURE 4.12 A function with two local extremes previous parabola’s abscissa. Convergen ...
Optimalf 159 This abscissa is at .499439. The TWR corresponding to thisfvalue is 1.146363. When we encounter a difference in abs ...
160 THE HANDBOOK OF PORTFOLIO MATHEMATICS FIGURE 4.13 Parabolic interpolation performed on TWRs of 20 sequences of +2,− 1 equal ...
Optimalf 161 Note that here, for a local minimum, the first operator is a plus (+) sign, not a minus (−) sign as when we were lo ...
162 THE HANDBOOK OF PORTFOLIO MATHEMATICS or G= ⎛ ⎝ ∏T i= 1 ⎛ ⎝ ( 1 + ( Ai W f ))Pi⎞ ⎠ ⎞ ⎠ 1 /Pi (4.18a) where: T=Number of dif ...
Optimalf 163 be, and on and on. Whenever we think of the future, we tend to think in terms of a single most likely outcome. As a ...
164 THE HANDBOOK OF PORTFOLIO MATHEMATICS Therefore, oftentimes, scenario planning puts us in a position where we must make a de ...
Optimalf 165 made broader so that you don’t need 10,000 scenarios to cover 99% of the spectrum. In making your scenarios broader ...
166 THE HANDBOOK OF PORTFOLIO MATHEMATICS The sum of our probabilities equals 1. We have at least one scenario with a negative r ...
Optimalf 167 The next step is to add this value to 1. This gives us: 1 +(−.01)=. 99 Last, we take this answer to the power of th ...
168 THE HANDBOOK OF PORTFOLIO MATHEMATICS calculating this, we can state that we must raise the TWR to the power of 1 to give us ...
Optimalf 169 between 2 and 3 standard deviations in price to the upside (whatever dol- lar amount that would be to you trading o ...
170 THE HANDBOOK OF PORTFOLIO MATHEMATICS is using, let’s say he can discern the following scenarios for this potential trade: S ...
Optimalf 171 Scenario Probability Result A.3 − 20 B.4 0 C.3 30 Mathematical expectation=$3. 00 Optimal f=. 17 Geometric mean= 1. ...
172 THE HANDBOOK OF PORTFOLIO MATHEMATICS the money risked on the decision at hand. Since, in almost every case, the money riske ...
Optimalf 173 Note that we have created our own binned distribution in creating our scenarios here. Similarly, if we know the dis ...
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