AlgoQuant Demos
Markowitz Portfolio Optimization
Harry Markowitz introduced and later won the Nobel Prize for the Modern Portfolio Theory in his 1952 article and 1959 book. His theory attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets.
Ref: http://www.numericalmethod.com/trac/numericalmethod/wiki/Model/Markowitz
Mean-Variance Portfolio Optimization When Means and Covariances Are Unknown
Markowitz’s celebrated mean-variance portfolio optimization theory assumes that the means and covariances of the underlying asset returns are known. In practice, they are unknown and have to be estimated from historical data. Plugging the estimates into the efficient frontier that assumes known parameters has led to portfolios that may perform poorly and have counter-intuitive asset allocation weights; this has been referred to as the “Markowitz optimization enigma.” This paper explains the root cause of the enigma and propose a new approach to resolve it. Specificially, it assumes that the mean and the covariances are unknown. The classical quadratic optimization problem therefore becomes a stochastic optimization problem. Not only is the new approach shown to provide substantial improvements over previous methods, but it also allows flexible modeling to incorporate dynamic features and fundamental analysis of the training sample of historical data, as illustrated in simulation and empirical studies.
Ref: http://arxiv.org/abs/1108.0996
Well Diversified Efficient Portfolios
Investors scarcely use mean-variance optimization when deciding on their actual portfolios. One of the main reasons they give is that efficient portfolios are systematically concentrated in a few assets. This article shows that such an allocation is achieved when portfolio risk and return are seen as infinitely accurate magnitudes. However, if the frontier is considered within some infinitesimal tolerance, as in a one-hundredth neighborhood, there are thousands of efficient portfolios and, indeed, many of them are well diversified.
Ref: http://www.bcentral.cl/eng/studies/working-papers/pdf/dtbc336.pdf
Pair/Basket Trading Using Cointegration
Engle and Granger introduced and later won the Nobel Prize for their work in the cointegration theory. Johansen subsequently provided the estimation method using maximum likelihood. Cointegration identifies common stochastic trend(s) in a basket of assets such that a linear combination of them is a stationary. Traders can then apply a mean reversion strategy to the synthetic asset to make a profit.
Ref: http://en.wikipedia.org/wiki/Cointegration
Fama-MacBeth Regression
Fama-MacBeth regression estimates the parameters for asset pricing models such as the Capital Asset Pricing Model (CAPM) for, for example, the betas and risk premia for any risk factors that are expected to explain asset prices.
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