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### Does Modern Portfolio Theory align with EMH?

I came to the conclusion that in literature Markowitz' Portfolio Theory is believed to be compliant with the Efficient Market Hypothesis. The weakest form states that the current price fully ...
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When doing Sharpe optimization $$\max_x \frac{\mu^T x}{\sqrt{x^T Q x}}$$ there is a common trick (section 5.2) used to put the problem in convex form. You add a variable $\kappa$ such that $x = ... 3answers 387 views ### Are minimum-risk and minimum-variance portfolios equivalent? When reading a paper by DeMiguel and Nogales (2007; http://papers.ssrn.com/sol3/papers.cfm?abstract_id=911596), I came across the following formulation: Comparing the proposed minimum-risk ... 2answers 91 views ### Computing$\gamma$and$\mu$at the efficient frontier Consider the condition which the weights of any portfolio belonging to the efficient frontier satisfy: $$\gamma\boldsymbol{wC} = \boldsymbol{m} - \mu\boldsymbol{u}$$ ... 1answer 84 views ### Full Kelly portfolios having same weights as tangency portfolios I'm currently comparing empirically the differences between Markowitz and Kelly portfolios. I calculated the Kelly weights for monthly return observations over 10 years for a sample of 50 stocks from ... 1answer 148 views ### Matlab Portfolio Optimization with bid ask spread I'm trying to find the optimal portfolio of options and stock which minimizes the standard deviation of the portfolio returns but also taking into consideration the bid and ask prices of the assets. ... 1answer 90 views ### dynamic Markowitz portfolio Let's take 4 assets, whose values are known during a period of time of 2 years. Then I calculate the expected returns for each of these 4 assets thanks to these 2 years - historical data. I deduce the ... 1answer 181 views ### Markowitz Mean-Variance Implied Returns What is the closed form solution for the following inverse Markowitz problem? Given a mean-variance optimized fully invested portfolio$X$, a risk aversion parameter$\lambda$and a var-covar ... 0answers 55 views ### Finding mean vector and covariance matrix for annual returns given quarterly returns I am currently trying to calculate a vector for the mean annual returns of 4 different asset classes along with their 4x4 covariance matrix in excel. However, I am having problems since the data I ... 0answers 70 views ### Residual Covariance Matrix, and MVO for Residual Variance and Alpha My overall goal is to find an efficient frontier using QP in terms of$\alpha$and residual variance ($\omega^2$) for a portfolio$P$given a benchmark$B$. We know the equation for residual variance ... 2answers 90 views ### How to perform portfolio optimization with user-defined expected return and variances using R? I found some functions for Markowitz mean variance portfolio optimization in R such as portfolio.optim in tseries package. ... 1answer 272 views ### What are the assumptions of portfolio optimisation with higher moments? I was wondering whether there are a set of assumptions for portfolio optimisation with higher moments (including kurtosis and skewness) as there are for regular mean-variance optimisation? 1answer 445 views ### short-sale constraint with nonpositive-definite matrix in portfolio optimization I need help about portfolio optimization in R. I have inverted matrix and I want to use it as an input in portfolio optimization. It was non-positive definite before I have handled it. In portfolio ... 0answers 115 views ### Behaviour of out of sample efficient frontier I am comparing the efficient frontier of a set of portfolios that are in and out of sample. The first period is from 1991-01-03 until 1992-10-03 and the second one from 1992-10-03 until 1994-03-03. I ... 3answers 348 views ### Finding Expression for Optimal Markowitz Weights So there are two assets with return rates$r_1$and$r_2$which have identical variances and a correlation coefficient$p$. The risk free rate is$r_f$. I need to find an expression for the optimal ... 2answers 111 views ### Modern portfolio theory in practice I am wondering about the Markowitz theory of portfolio construction in practice. Hence, if one wants to know the efficient frontier, what variances can one use. The only method that I can think is the ... 1answer 53 views ### Understanding portfolio weights and purchasing stock in modern portfolio theory Recently I've been learning about the markowitz algorithm. It's pretty interesting, but I'm curious how we apply this in practice. Lets say I have some optimal portfolio:$R_p = x_aR_a + x_bR_b$... 1answer 118 views ### What is the smart way to reallocate money? We are running a portfolio of fund managers in our fund. When one of the managers hits the max DD constraint we pull money from this manager. This may happen in the middle of the allocation period and ... 0answers 19 views ### Should the number of Markowitz Optimization steps be counted as backtest trials? I'm backtesting a strategy that involves monthly investments in a few stocks out of a given set, that is, each month some of the stocks are shortlisted from an index and a long position is taken in ... 0answers 73 views ### Definition of sharpe ratio maximising and variance minimising portfolios In this paper, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2226985, in the derivation of the mean variance efficient portfolio using lagrangians in the appendix, on page 29, the two portfolios ... 0answers 183 views ### Tangent portfolio weights without short sales? Consider a mean-variance investor in a world with a risk-free asset. Let$R_f>0$be the return of the risk-free asset,$\mathbb{E}(R_i)>R_f$the expected return of the risky asset$i$and$SD(...
So the question asks: Consider three uncorrelated stocks in the market. Each stock has variance 1. The expected returns are given by $2, 3$ and $5$ respectively. Find the optimal mean-variance ...
Under a standard portfolio optimization framework we have some idea of a predictive return distribution $r_{t+1}$ and a Utility function $U(r)$, in the best case in a 'nice' form (differentiable etc.)....