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Market Analysis & Position Sizing (Both Equally Necessary) = We have a plethora of market analysis, selection and timing techniques…..but We have no method, no framework, no paradigm, for the equally important, dark nether-world of position sizing.

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Part 1 Optimal f

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f = | Biggest Losing Outcome for 1 Unit | / f$ f$ = Account Equity / Units Example: -$10,000 Biggest Losing Outcome, $50,000 Account, and I have on 200 shares, (2 units ): f$ = 50,000 / 2 = 25,000 f = | -10,000 | / 25,000 =.4 Where: Everyone, on Every Trade, on Every “Opportunity” Involving Risk, has an f value (whether they acknowledge it or not): (also f$ = | Biggest Losing Outcome for 1 Unit | / f

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f$ and GHPR Invariant to Biggest Loss BiggestLossf f$GHPR –0.6.1541.125 –1.2541.125 –2.541.125 –51.2541.125 –297.2541.125

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Trajectory Cone (Bell-Shaped on all 3 Axes)

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The distribution can be made into bins. A scenario is a bin. It has a probability and An outcome (P/L)

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2:1 Coin Toss

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Mathematical Expectation 2:1 coin toss: ME =.5 * -1 +.5 * 2 = -.5+1 =.5

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f value example – 2:1 Coin Toss $10 stake Worst Case Outcome -1 I’m wagering $5 (5 units) f$ = 10 / 5 = 2 (one bet for every $2 in my stake) f =|-1| / 2 =.5 When biggest loss is manifest, we lose f% of our stake – 50% in this case

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The Mistaken Impression Multiple made on stake = 1 + ME/|BL| * f (a.k.a Holding Period Return, “HPR”)

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Optimal f is an Asymptote

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The Real Line ( f )

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f after 40 plays

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40 Plays 1 Play

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f after 40 plays At.15 and.40, makes the same, but drawdown changes At f=.1 and.4, makes the same, But drawdown changes!

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f after 40 plays Beyond.5, even in this very favorable game, TWR (multiple) < 1, meaning you are losing money and will eventually go broke if you continue

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f after 40 plays Points of Inflection: Concave up to concave down. Up has gain growing faster than drawdown.(but these too migrate to the optimal point as the number of holding periods grows!)

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f after 40 plays

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Most Favorable Blackjack Condition Optimal f =.06 or risk $1 for every $16.67 in stake

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Part 2 The Leverage Space Portfolio Model

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Modern Portfolio Theory

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Why The Leverage Space Model is Superior to Traditional (Modern Portfolio Theory) Models: 1.Risk is defined as drawdown, not variance in returns. 2.The fallacy and danger of correlation is eliminated. 3.Valid for any distributional form – fat tails are addressed. 4.The Leverage Space model is about leverage, which is not addressed in the traditional models.

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Leverage has 2 Axes – 2 Facets The instant case of how much I am levered up How I progress my quantity with respect to time / equity changes f

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The fallacy and danger of correlation Fails when you are counting on it the most – at the (fat) tails of the distribution. Traditional models depend on correlation – Leverage Space model does not. -cl/gc (all days) r=.18 (cl>3sd) r=.61 (cl<1sd) r=.09 -f/pfe (all days) r=.15 (sp>3sd) r=.75 (sp<1sd) r=.025 -c/msft (all days)r=.02 (gc>3sd) r=.24 (gc<1sd) r=.01

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f after 40 plays

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Why The Leverage Space Model is Superior to Traditional (Modern Portfolio Theory) Models: 1.Risk is defined as drawdown, not variance in returns. 2.The fallacy and danger of correlation is eliminated. 3.Valid for any distributional form – fat tails are addressed. 4.The Leverage Space model is about leverage, which is not addressed in the traditional models. (on both axes of “Leverage”)

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Part 3 The Leverage Space Model Software Implementation

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http://parametricplanet.com/rvince/ScenariosExample.xls Link for how to gather your data and create scenarios & probabilities:

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http://parametricplanet.com/rvince/register.html

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Here is the data I am using (this is from the link example from the previous slide) :

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Date,Equity Jan-07,617.00 Feb-07,664.00 Mar-07,673.00 Apr-07,751.00 May-07,887.00 Jun-07,849.00 Jul-07,781.00 Aug-07,851.00 Sep-07,942.00 Oct-07,834.00 Nov-07,804.00 Dec-07,789.00 Jan-08,791.00 Feb-08,813.00

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Get java at: http://java.com/en/download/index.jsp

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Part 4 The Leverage Space Model Using The Paradigm

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We have seen how position sizing is equally as important as market analysis, selection and timing. The Leverage Space Model is both a (Superior) Portfolio Model, but also a Paradigm for examining “Position Sizing.” With this paradigm, we need no longer operate in this dark nether-world, riddled with heuristics, misinformation, and essentially mere alchemy (e.g. 1% rules, “Half Kelly,” “Fixed Ratio,” “Modern Portfolio Theory”).

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Market Analysis & Position Sizing (Both Equally Necessary) = We have a plethora of market analysis, selection and timing techniques…..but We have no method, no framework, no paradigm, for the equally important, dark nether-world of position sizing.

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http://parametricplanet.com/rvince/register.html

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