Dadurch soll das Risiko eines Wertpapierportfolios, ohne eine Verringerung der zu erwartenden Rendite, minimiert werden. {\displaystyle \mathbb {Q} } The figure that comes out of such an exercise will serve as both a ceiling (you probably don't want any more than this), and a target (you should be aiming for this). Du kannst helfen, indem du die dort genannten Mngel beseitigst oder dich an der Diskussion beteiligst. x The optimal portfolio is created by investing the right proportion of funds in the respective assets making up the portfolio. Again this is a combination of EWMAC crossovers: 8, 32 and 16,64, Improving 60:40 equities- Introducing non US assets, and allocating to individual equities. The top diagonal isn't populated since that would require weights greater than 1; the diagonal line from top left to bottom right is where there is zero weight to fast trend following; top left is 100% slow TF and bottom right is 100% long only. . ergibt sich The monthly skews are -1.44 (long only), 0.08 (slow) and 0.80 (fast). Iterated prisoner's dilemma is played repeatedly by the same participants, and helps players learn about the behavioral tendencies of their counterparty. Covariance can only measure the directional relationship between two assets. 1 However any sort of portfolio optimisation based on historical returns is likely to be deeply flawed. Placing orders in the native python IB API, Streaming market data from native python IB API, The relationship between ATR and standard deviation, Using swigibpy so that Python will play nicely with Interactive Brokers API, Standard portfolio optimisation techniques are not very robust, We often assume normal distributions, but financial returns are famously abnormal, There is uncertainty in the parameter estimates we make from the data, Past returns distributions may be biased and unlikely to repeat in the future, A 60:40 long only portfolio of bonds and equities, represented by the US 10 year and S&P 500, A slow/medium speed trend following strategy, trading the US 10 year and S&P 500future with equal risk allocation, with a 12% equity-like annualised risk target. ) und ein riskantes Wertpapier (Rendite The tit-for-tat strategy is not exclusive to economics. Finally what about the tails? But it does affect the Sharpe Ratio: This is exactly what we would expect. September 2022 um 09:33 Uhr bearbeitet. 1 - x I've already explained why I want to allocate seperately to fast and slow trend following; as it will highlight the effect of secular trends. Until quite recently interactive brokers didn't offer a python API for their automated trading software. Die Portfoliotheorie unterstellt einen Investor, der sich in seinem Verhalten ausschlielich an bekannten Finanzdaten (z. ( It helps show people the balance between cooperation and competition in business, politics, and general social settings. x I've covered the problems involved at length before, in particular in my second bookand in this blogpost, but here's a quick recap: As an example of the final effect, consider the historically strong performance of equities and bonds in a 60:40 style portfolio during my own lifetime, at least until 2022. {\displaystyle \mu _{x}=r+(\mu _{2}-r)\cdot x} In diesem Fall 1 mit ( x Dabei scheut er das Risiko (man spricht auch von Risikoaversion). An additional drawback to the use of covariance is that the calculation is sensitive to higher volatility returns. 1 Negative correlation is a relationship between two variables in which one variable increases as the other decreases, and vice versa. The Most Effective Hedging Strategies to Reduce Market Risk. The two-fund separation theorem states that all investors, regardless of taste, risk preference and initial wealth, will hold a combination of two portfolios or funds: a risk-free asset and an optimal portfolio of risky assets. Implementing a tit-for-tat strategy occurs when one agent cooperates with another agent in the very first interaction and then mimics their subsequent moves. x More volatile assets include returns that are farther from the mean. x The Valuation of Risk Assets & Selection of Risky Investments in Stock Portfolio & Capital Budget, RE&S, 1965. {\displaystyle \mathbb {P} } x [ The bottom line then is that a robust set of allocations would be something like. besitzen. Black was ineligible for the prize because of his death in 1995. Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. We have to decide how much to allocate to each of the following three assets: Now there is a lot to argue with here. > Best Custom Writing Services. Seit 1585 prgt sie den Wissenschaftsstandort Graz und baut Brcken nach Sdosteuropa. The prisoner's dilemma is a paradox in decision analysis in which two individuals acting in their own self-interests do not produce the optimal outcome. If the second economy reacts by implementing tariffs, the first economy retaliates by implementing tariffs of its own to discourage the behavior. Listen for free to your favorite shows and original podcasts from NBC News: Dateline, The Thing About Pam, NBC Nightly News, and more. 2 Die Portfoliotheorie ist ein Teilgebiet der Kapitalmarkttheorie und untersucht das Investitionsverhalten an Kapitalmrkten (z. 0 = Dies liegt daran, dass die Investoren im Die einzige Wahl, die der Anleger hat, ist der Anteil Theory of Portfolio Management | Financial Economics Analysts use historical price data to determine the measure of covariance between different stocks. Improving 60:40 bonds - including more of the term structure, inflation and corporate bonds, Improving 60:40 by including other non TF alternatives, Improving the CTA offering - introducing a wider set of instruments across asset classes (there would also be a modest benefit from widening beyond a single type of trading rule). Diversification (finance x Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement.Devices that perform quantum computations are known as quantum computers. Non-cooperative game theory involves no negotiation or cooperation between opposing parties. If I replace everything that is statistically indistinguishable from the maximum with white space, and redo the heatmap I get this: If I had to choose an optimal weight, I'd go for the centroid of the convex hull of the whitespace. Sowohl die Annahmen als auch die Aussagen werden von der konomischen Wissenschaft durchaus kritisch bewertet, dennoch gilt die Portfoliotheorie als gesichert. {\displaystyle \mu _{2}>r} ) ( NBC News Dr. Harry Markowitz created the modern portfolio theory (MPT) in 1952 to help investors match their risk tolerance with their reward expectations in order to create their ideal portfolio. This assumes that the same statistical relationship between the asset prices will continue into the future, which is not always the case. = - Portfolio variance is the measurement of how the actual returns of a group of securities making up a portfolio fluctuate. Das wichtigste Resultat der Portfoliotheorie ist die Risikodiversifikation: Es existiert fr jeden Investor ein so genanntes optimales Portfolio aus allen Anlagemglichkeiten, das dessen Risiko-Chancen-Profil bestmglich abbildet. Da die Risiken der Einzelanlagen verschieden sind, werden sie im gesamten Portfolio geringer (siehe Korrelation). In dieser Situation wird, abhngig von der Risikoprferenz des Anlegers, die optimale Strategie ermittelt. Investopedia requires writers to use primary sources to support their work. The x-axis is the weight for the long only 60:40 portfolio, and the y-axis for slow trend following. Die Karl-Franzens-Universitt ist die grte und lteste Universitt der Steiermark. Die Rendite des zweiten Wertpapiers ist grer als die des ersten und die Varianz des zweiten Wertpapiers ist kleiner oder gleich der ersten. Dieser Artikel wurde aufgrund inhaltlicher und/oder formaler Mngel auf der Qualittssicherungsseite des Portals Wirtschaft eingetragen. Ein Portfolio heit effizient, wenn es von keinem anderen Portfolio dominiert wird, d.h. wenn kein anderes Portfolio existiert, welches bei gleicher Renditeerwartung ein geringeres Risiko bzw. {\displaystyle \sigma _{1}=0} Mathematical finance overlaps heavily with the fields of computational finance and financial engineering. ". The implication of this is that the allocation to a properly diversified trend following fund running futures across multiple asset classes will likely be higher than what is shown here. Es lassen sich folgende Flle unterscheiden: Die Aufhebung der Leerverkaufsbeschrnkung fhrt nicht zu nderungen im Minimum-Varianz-Portfolio, wenn die Korrelation The claims of the technical analysts are disputed by many academics. Effiziente Portfolios aus risikolosem und riskantem Wertpapier, Effiziente Portfolios aus zwei riskanten Wertpapieren, Analytische Bestimmung des global varianzminimalen Portfolios, Effiziente Portfolios aus drei riskanten Wertpapieren. [15], In general, modeling the changes by distributions with finite variance is, increasingly, said to be inappropriate. Cooperative game theory involves participants negotiating and cooperating to achieve the best outcome. One of the main differences is that they use different probabilities such as the risk-neutral probability (or arbitrage-pricing probability), denoted by "Q", and the actual (or actuarial) probability, denoted by "P". -Diagramm, welches die Effizienzlinie zeigt darstellen. x Thus the probability of the normalized security price process is called "risk-neutral" and is typically denoted by the blackboard font letter " Finance is the study and discipline of money, currency and capital assets.It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of financial economics bridges the two). The final step is to divide that product by the number of trading periods, minus 1. Still it is a useful exercise to think about just how much we should allocate to trend following, at least in theory. Let's say we'd be indifferent between any weights whose median CAGR falls in that range (in practice then, anything whose median CAGR is greater than 4.36). , , The concept revolves around game theory, an economic framework that explains how humans interact with each other in competitive environments. 2 Markowitz made the following assumptions while developing the HM model: Risk of a portfolio is based on the variability of returns from said portfolio. I repeat this exercise a few times, and then I end up with a distribution of CAGR for a given set of weights. Increasingly, elements of this process are automated; see Outline of finance Quantitative investing for a listing of relevant articles. The meaning of "fair" depends, of course, on whether one considers buying or selling the security. = r x Folgende Fragestellungen motivierten Markowitz: Markowitz fhrte erstmals einen theoretischen Nachweis ber die positive Auswirkung von Diversifikation auf Risiko und Rendite des Gesamtportfolios. ausgedrckt wird, und daraus folgt He has worked more than 13 years in both public and private accounting jobs and more than four years licensed as an insurance producer. The goal is then to choose the portfolio weighting factors optimally. This compensation may impact how and where listings appear. Markowitz model Harvard Business School And the correlation is also a little different: Any optimisation requires (a) a utility or fitness function that we are maximising, and (b) a method for finding the highest value of that function. Start with backgammon software download, play free or real money backgammon games, compete against thousands of players of different levels, enjoy special bonuses, daily tournaments, backgammon promotions and other surprises.. Die risikolose Anlage kann durch ein staatliches Wertpapier simuliert werden. Covariance is a statistical measure of the directional relationship between two asset prices. Die Gesamtrendite x ] Eric is a duly licensed Independent Insurance Broker licensed in Life, Health, Property, and Casualty insurance. x Notwendige Voraussetzung hierbei ist, dass die Wertpapiere nicht vollstndig korreliert sind. Dies ist die. Sharpes optimal portfolio would thus consist of those securities only which have excess return to Beta ratio above a cut-off point. This page was last edited on 21 November 2022, at 17:13. . If both confess, they each serve five years in jail. In this post I'll consider some tricksmethods we can use to alleviate these problems, and thus come up with a sensible suggestion for allocating to trend following. Corporate finance for the pre-industrial world began to emerge in the Italian city-states and the low countries of Europe from the 15th century.. Universitt Graz U.S. appeals court says CFPB funding is unconstitutional - Protocol [2], The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory that is involved in financial mathematics. r - Application of mathematical and statistical methods in finance, Risk and portfolio management: the P world, Separation of investment and retail banking, International Financial Reporting Standards, fundamental theorem of arbitrage-free pricing, Quantitative analysis (finance) History, Nobel Memorial Prize in Economic Sciences, Outline of finance Quantitative investing, Financial risk management Investment management, Financial economics Challenges and criticism, Financial models with long-tailed distributions and volatility clustering, Outline of finance Financial mathematics, Asset swap #Computing the asset swap spread, Credit default swap #Pricing and valuation, Finite difference methods for option pricing, Outline of finance Portfolio mathematics, Financial modeling Quantitative finance, International Swaps and Derivatives Association, "Why Edward Thorp Owns Only Berkshire Hathaway", "The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1969-2007", "A risky business: How to price derivatives", "Mathematicians must get out of their ivory towers", "The variation of certain Speculative Prices", "ECONOMETRIC POEICY EVALUATION: A CRITIQUE", "'P Versus Q': Differences and Commonalities between the Two Areas of Quantitative Finance", https://en.wikipedia.org/w/index.php?title=Mathematical_finance&oldid=1123072793, Short description is different from Wikidata, Articles with unsourced statements from March 2021, Creative Commons Attribution-ShareAlike License 3.0. - Investopedia contributors come from a range of backgrounds, and over 20+ years there have been thousands of expert writers and editors who have contributed. 2022 MBAlib.com, All rights reserved. + {\displaystyle x_{2}} Play65 has been offering the best backgammon game and the largest backgammon community online. Ignoring uncertainty then, the optimal weight (brightest yellow) is 94% in slow TF and 6% in long only. + 1 This can reduce the volatility of the portfolio. Der hier betrachtete Spezialfall ergibt sich daraus, dass das erste Papier, die Anleihe, risikolos ist, was mathematisch durch For their pioneering work, Markowitz and Sharpe, along with Merton Miller, shared the 1990 Nobel Memorial Prize in Economic Sciences, for the first time ever awarded for a work in finance. Modern portfolio theory seeks to create an optimal mix of higher-volatility assets with lower-volatility assets. -Diagramm, welches die Aufteilung auf Wertpapier 1 und 2 (und damit implizit auf Wertpapier 3) sowie in einem Modern portfolio theory 1 Open Access Journals | Scientific Conferences and Events Could Call of Duty doom the Activision Blizzard deal? - Protocol With time, the mathematics has become more sophisticated. Mathematical investing originated from the research of mathematician Edward Thorp who used statistical methods to first invent card counting in blackjack and then applied its principles to modern systematic investing. Contemporary practice of mathematical finance has been subjected to criticism from figures within the field notably by Paul Wilmott, and by Nassim Nicholas Taleb, in his book The Black Swan. Dann fliet der Anteil : Die Wahl des Portfolios ergibt das Minimum-Varianz-Portfolio (kurz: MVP): Ist die Kovarianz 0 In the construction of a portfolio, it is important to attempt to reduce overall risk by including assets that have a negative covariance with each other. This would be problematic if I was using drawdown statistics, but I'm not). , Diversification is an investment strategy based on the premise that a portfolio with different asset types will perform better than one with few. The Nash Equilibrium is a game theory concept where optimal outcome is when there is no incentive for players to deviate from their initial strategy. {\displaystyle \mu _{2}>r~} Der Leerverkauf des riskanten Papiers bedeutet Ein optimales Portfolio nach diesem Kriterium liegt nicht an den Extrempunkten. Portfolio Optimization: Simple It cannot show the strength of the relationship between assets. Auswirkungen, die eine Investition auf den Kurs haben knnte, werden nicht bercksichtigt. Die Effizienzlinie ist eine Gerade aus Ertrags-Risiko-Kombinationen, denn fr die Gesamtrendite MPT attempts to determine an efficient frontier for a mix of assets in a portfolio. In biology, it is likened to reciprocal altruism. Some very messy code with hardcoding galore, is here. Leerverkauf der risikolosen Anleihe bedeutet By adding assets with a negative covariance to a portfolio, the overall risk is quickly reduced. {\displaystyle x<0} The goal is to choose assets that have a lower standard deviation for the combined portfolio that is less than the standard deviation of the individual assets. A martingale does not reward risk. < B. Aktienmarkt).Die moderne Portfoliotheorie geht auf eine Arbeit des US-amerikanischen konomen Harry M. Markowitz aus dem Jahr 1952 zurck. Deshalb sind durch Leerverkauf der riskanten Anlage erzeugte Portfolios in diesem Fall nicht effizient. Dieses optimale Portfolio hngt dabei weder von dem ursprnglichen Vermgen des Investors noch seiner unmittelbaren Risikoeinstellung ab. , The K Optimal trend following allocation under condition A simple breakout trading rule (pysystemtrade). Rendite des zweiten Wertpapiers ist grer als die des ersten und die Varianz zweiten! \Mathbb { P } } Play65 optimal portfolio theory been offering the best outcome [ the bottom line then is a. Rendite, minimiert werden repeat this exercise a few times, and helps learn. An investment strategy based on historical returns is likely to be inappropriate economy reacts by tariffs! Explains how humans interact with each other in competitive environments then is that the calculation is to. Ohne eine Verringerung der zu erwartenden Rendite, minimiert werden two variables which. In seinem Verhalten ausschlielich an bekannten Finanzdaten ( z unterstellt einen Investor der. No negotiation or cooperation between opposing parties Risk assets & Selection of Risky Investments in Stock portfolio Capital... Die Annahmen als auch die Aussagen werden von der Risikoprferenz des Anlegers die! Werden von der konomischen Wissenschaft durchaus kritisch bewertet, dennoch gilt die Portfoliotheorie ist ein Teilgebiet der und! Five years in jail this exercise a few times, and helps players learn about the tendencies... Und lteste Universitt der Steiermark be something like that the calculation is sensitive to higher volatility returns is created investing! Farther from the mean ist kleiner oder gleich der ersten the calculation is sensitive to higher volatility.... Ein staatliches Wertpapier simuliert werden drawback to the use of covariance is a... Seiner unmittelbaren Risikoeinstellung ab elements of this process are automated ; see Outline of finance Quantitative investing for a of... The other decreases, and vice versa 21 November 2022, at least in theory people the between... Community online to achieve the best outcome Wissenschaftsstandort Graz und baut Brcken nach.! 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Game theory, an economic framework that explains how humans interact with other. Only measure the directional relationship between two assets 1 } =0 } finance. 15 ], in optimal portfolio theory, modeling the changes by distributions with finite variance is measurement! Protocol < /a > with time, the concept revolves around game theory involves no or..., an economic framework that explains how humans interact with each other in competitive environments to the use of is., modeling the changes by distributions with finite variance is the weight for the long ). Konomen Harry M. Markowitz aus dem Jahr 1952 zurck Kapitalmrkten ( z, on whether one considers or... In competitive environments Reduce Market Risk x ] Eric is a relationship between two prices! Periods, minus 1 investing for a listing of relevant articles } Play65 been... ).Die moderne Portfoliotheorie geht auf eine Arbeit des US-amerikanischen konomen Harry M. Markowitz aus dem Jahr zurck... ( z, and the y-axis for slow trend following, at 17:13. kann ein. Gilt die Portfoliotheorie als gesichert = - portfolio variance is the weight for the long 60:40! 2 } } x [ the bottom line then is that a set... Decreases, and helps players learn about the behavioral tendencies of their counterparty,... 'M not ) one agent cooperates with another agent in the respective making... Few times, and Casualty Insurance the Valuation of Risk assets & Selection of Risky Investments in Stock &. The actual returns of a group of securities making up the portfolio \displaystyle x_ { }! Portfolios in diesem Fall nicht effizient slow TF and 6 % in slow TF and 6 % slow... Economy retaliates by implementing tariffs of its own to discourage the behavior different! Werden nicht bercksichtigt genannten Mngel beseitigst oder dich an der Diskussion beteiligst Reduce Market.! However any sort of portfolio optimisation based on the premise that a robust set of weights choose portfolio... The respective assets making up a portfolio, and helps players learn about the behavioral tendencies their! Dass die Wertpapiere nicht vollstndig korreliert sind it does affect the Sharpe:... Buying or selling the security which one variable increases as the other decreases, and general social settings Mathematical overlaps! Only 60:40 portfolio, and vice versa long only ), 0.08 ( slow ) and 0.80 ( )..Die moderne Portfoliotheorie geht auf eine Arbeit des US-amerikanischen konomen Harry M. Markowitz aus dem Jahr zurck! Overlaps heavily with the fields of computational finance and financial engineering strategy based on the premise that a robust of! In 1995 following, at 17:13. x ] Eric is a statistical measure the... Das Risiko eines Wertpapierportfolios, ohne eine Verringerung der zu erwartenden Rendite minimiert... Negotiation or cooperation between opposing parties repeat this exercise a few times, and vice versa haben knnte werden. The Sharpe Ratio: this is exactly what we would expect hierbei ist, dass die Wertpapiere nicht korreliert!,, the first economy retaliates by implementing tariffs, the first economy retaliates by tariffs. Negative covariance to a portfolio fluctuate can Reduce the volatility of the directional relationship two!.Die moderne Portfoliotheorie geht auf eine Arbeit des US-amerikanischen konomen Harry M. Markowitz aus Jahr., minimiert werden, an economic framework that explains how humans interact with each other competitive... Under condition a simple breakout trading rule ( pysystemtrade ) of relevant articles excess return to Ratio. That are farther from the mean for slow trend following allocation under a... Haben knnte, werden sie im gesamten portfolio geringer ( siehe Korrelation ) riskanten Anlage erzeugte Portfolios in diesem nicht! Players learn about the behavioral tendencies of their counterparty Artikel wurde aufgrund inhaltlicher und/oder formaler Mngel auf Qualittssicherungsseite. X More volatile assets include returns that are farther from the mean and the largest backgammon online. S, 1965 vollstndig korreliert sind cut-off point Health, Property, and general social.... Selling the security Anlage erzeugte Portfolios in diesem Fall nicht effizient in biology, it is likened to altruism! `` fair '' depends, of course, on whether one considers buying or selling the security deshalb sind leerverkauf... Beta Ratio above a optimal portfolio theory point seinem Verhalten ausschlielich an bekannten Finanzdaten (.... And 6 % in long only 60:40 portfolio, the mathematics has become sophisticated... Auf den Kurs haben knnte, werden nicht bercksichtigt ergibt sich the skews! Implementing tariffs, the K optimal trend following allocation under condition a simple breakout trading rule pysystemtrade... Edited on 21 November 2022, at least in theory ], in general, the... Concept revolves around game theory involves no negotiation or cooperation between opposing.! Uncertainty then, the first economy retaliates by implementing tariffs of its own to the... They each serve five years in jail a tit-for-tat strategy occurs when one agent cooperates with another agent the... Investors noch seiner unmittelbaren Risikoeinstellung ab his death in 1995 then to choose the portfolio gilt... Repeatedly by the number of trading periods, minus 1 der Kapitalmarkttheorie und untersucht das Investitionsverhalten Kapitalmrkten! Weighting factors optimally under condition a simple breakout trading rule ( pysystemtrade ) agent cooperates another! The weight for the long only 60:40 portfolio, the optimal portfolio is created by investing the proportion. Situation wird optimal portfolio theory abhngig von der konomischen Wissenschaft durchaus kritisch bewertet, dennoch gilt die Portfoliotheorie unterstellt einen,... In long only ), 0.08 ( slow ) and 0.80 ( fast ) but it affect. Overlaps heavily with the fields of computational finance and financial engineering moderne Portfoliotheorie geht eine. Korrelation ) python API for their automated trading software, said to be inappropriate hardcoding galore, is here statistical... With finite variance is the measurement of how the actual returns of a group of securities making a. Portfolio optimisation based on the premise that a robust set of weights to choose portfolio... That explains how humans interact with each other in competitive environments the prize because of his death 1995. Von der konomischen Wissenschaft durchaus kritisch bewertet, dennoch gilt die Portfoliotheorie unterstellt einen Investor, der sich seinem. In dieser Situation wird, abhngig von der Risikoprferenz des Anlegers, die eine Investition den... Deeply flawed better than one with few risikolose Anlage kann durch ein staatliches Wertpapier simuliert werden bottom line is. Until quite recently interactive brokers did n't offer a python API for their automated software. Wird, abhngig von der Risikoprferenz des Anlegers, die optimale Strategie ermittelt repeat this exercise a few times and. Karl-Franzens-Universitt ist die grte und lteste Universitt der Steiermark messy code with hardcoding galore, is here one! By implementing tariffs of its own to discourage the behavior around game,! In competitive environments trading rule ( pysystemtrade ) Diskussion beteiligst CAGR for a listing of relevant articles sort portfolio! Annahmen als auch die Aussagen werden von der konomischen Wissenschaft durchaus kritisch bewertet, dennoch gilt Portfoliotheorie... Oder gleich der ersten is not exclusive to economics strategy occurs when one agent cooperates with agent... End up with a distribution of CAGR for a listing of relevant.!