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Questions tagged [markowitz]

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Why does the Markowitz mean-variance model require the assumption of normality?

Given $N$ assets, the Markowitz mean-variance model requires expected returns, expected variances and a $N \times N$ covariance matrix. The joint distribution is fully defined by these measures. ...
3k views

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 ...
144 views

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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 ...
420 views

Why did Markowitz not derive an equation for the efficient frontier?

Currently, I´m studying portfolio management and portfolio selection. The founder of the MPT is Harry Markowitz, of course. But reading his famous article from 1952 and his book from 1959 (actually, I ...
260 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 ...
665 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 ...
96 views

Risk/Return Paradox in Markowitz Optimization?

It is possible that from the efficient frontier obtained varying the "lambda" parameter of the risk-appetite coefficient, in the Mean Variance Parametric Quadratic programming problem, it results that ...
114 views

Computing $\gamma$ and $\mu$ at the efficient frontier

Consider the condition which the weights of any portfolio belonging to the efficient frontier satisfy: \begin{equation} \gamma\boldsymbol{wC} = \boldsymbol{m} - \mu\boldsymbol{u}\end{equation} ...
380 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. ...
480 views

Optimal Portfolio from Efficient Frontier

I found this code on plotly site, using CVXOPT to find the efficient frontier, and then, the optimal Portfolio. The optimal function is ...
194 views

Markowitz; risky asset frontier w/o risk free asset

What is the intuition behind the "spanning" result in the following statement? For a fixed pair of distinct frontier portfolios $\phi_p$ and $\phi_q$, any frontier portfolio $\phi$ can be obtained ...
615 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. ...
107 views

Max allowable return in Markowitz model

The Markowitz model solves the following problem: The portfolio with the smallest variance among attainable portfolios with expected return µV. Here we have to choose µV to get the optimal portfolio ...
305 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 ...
249 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 ...
273 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 ...
246 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 ...
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Derivation of the efficient frontier set (markowitz problem)

I would like to find a Derivation of the efficient frontier set for the markowitz problem:
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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 ...
672 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?
128 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 ...
83 views

Markowitz portfolio optimization and CAL [closed]

Just had some questions regarding the efficient frontier and the CAL. As i understand it the point where the CAL is tangent to the efficient frontier is the optimal mix of risky assets. However I also ...
As the PV01 ($= dpdy \times notional$) of a bond is a measure of its risk, as well as its price return variance, could we measure the risk of a bonds portfolio with the Markovitz portfolio variance ...