Questions tagged [markowitz]

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For mean-variance portfolio optimization, shouldn't all the allocations sum to 1?

Reading a paper by Black and Litterman, I'm having trouble understanding the set of valid allocations in which we're trying to optimize expected returns. In Table III, the authors show two portfolios ...
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116 views

Is it possible to construct an efficient frontier without the mean?

If we assume the estimator for a sample mean is biased and if the optimal portfolio weights vary with the estimated mean, is there a way (similar to the zero beta portfolio approach wrt the risk free ...
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Why does the mean term have a higher effect than the covariance term in MV optimization? [closed]

I am trying to use the mean-variance (MV) optimization framework. When I change the mean term using future-ground-truth return (I am not supposed to do so), it has a higher effect on the MV ...
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Why do we use half of the risk in objective function of markowitz portfolio theory

In some documents I have seen objective function of markowitz portfolio theory is as follows. minimize 1/2 * w'Σw where w is weights Σ is covariance matrix I could ...
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3 votes
1 answer
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Markowitz portfolio with factor/position constraints

General Markowitz-style optimization (problem objective of $w^T \mu - \lambda w^T \Sigma w$) yields simple optimal weights policy $w \propto \Sigma^{-1} \mu$. However, I would like to add a series of ...
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How to show that the normalized portfolio given by the Markowitz portfolio optimization model is efficient?

How can I show this? It looks relatively easy but am not sure if I am doing it right.
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Error in eqsumW[2, -1] : subscript out of bounds - SolveRsocp

I am working on a research project where the goal is to get the highest possible return with different portfolios at a given risk rate. For this I would like to use the function "SolveRsocp" ...
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3 votes
1 answer
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Weights don't add up to one Markowitz Portfolio Model

I have recently implemented MPT in Python, however, when I allow negative weights (short selling), they do not add up to one. Isn't it suppose not to happen? On the other hand, when I don't allow, ...
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Time-complexity of Markowitz portfolio optimization

What is the time-complexity of Markowitz mean-variance portfolio optimization (MVO)? I am unable to find any clear explanation of this on the internet and in academic papers. These are my questions: ...
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1 vote
1 answer
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Monte Carlo vs. Block Bootstrapping vs. Bootstrapping

Because I can fit e.g. ~25 distributions via empirical cumulative distribution fitting to correlated data (including stable dist.), and then simulate the original data based on correlation (covariance)...
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Inputs to Min-Var Portfolio

Although I always use daily data, I am wondering if a Min-Var portfolio based on weekly bar data would be more stable (less noise) than using daily bar data as inputs? [I have no interest in the ...
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2 answers
137 views

Number of Observations for Non-Singular Covariance Matrix Estimation

Marcos López de Prado writes the following in his book Advances in Financial Machine Learning: In general, we need at least \frac{1}{2} N (N+1) independent and ...
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Maximum Sharpe ratio and mean-variance optimization

I want to understand why this holds: $argmax_w ( \frac{\mu^T w}{\sqrt{w^T\Sigma w}})=\Sigma^{-1}\mu $ I just found this post: Derivation of the tangency (maximum Sharpe Ratio) portfolio in Markowitz ...
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Geometry of Efficient Frontier of Portfolios

I have been reading about Portfolio Theory, and though the algebra of it seems quite intuitive, I am having a hard time understanding it's geometry. For the sake of simplicity, I will only talk about ...
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1 answer
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Portfolio Optimization constrained to maximum N% of short selling portfolio weights

For mean-variance portfolio optimization with short-selling allowed, but restricted to a certain percentage of the portfolio weights (lets assume N), we can constrain it in the follwoing way: (from j=...
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Herfindahl-Hirsch-Index for FX Portfolios

Assume we have an FX portfolio with $n$ currency pairs, such that $w_i$ is the weight of currency pair $i \in \{1, \dots, n\}$ in the portfolio, and $\sum_{i=1}^n w_i = 1$. All pairs have USD as one ...
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Construct portfolio with assets having expected negative returns

I have been asked to select a n stocks among N stocks, to construct a portfolio. Some of them have have negative weekly returns on average. If I want to select these n stocks by constructing an '...
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1 answer
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Mixed-integer programming approach for index tracking

Suppose you currently own a portfolio of eight stocks. Using the Markowitz model, you computed the optimal mean/variance portfolio. The weights of these two portfolios are shown in the following table:...
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Statistical methodology for proving the stability in time of asset allocation weights

I am comparing the set of weights obtained by the classical Markowitz allocation process with those of another asset allocation technique I have devised. Markowitz's weights are unstable, as the ...
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How to deal with securities that has short historical data when performing mean-variance portfolio analysis?

I am trying calculate expected return and risk (stdev) based on historical data using Mean Variance Analysis framework. Let's say the portfolio has 10 stocks, 9 of them have more than 10 years history ...
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2 votes
1 answer
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Optimal Portfolio Formulation

I'm currently studying Luenberg's Article "Projection Pricing" (Jrl of Optimization Theory and Applications, Vol. 109, No. 1, pp. 1–25, April 2001) and there is a claim that I can't prove. ...
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1 vote
2 answers
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State-of-the-art MVO methods?

I learned Markowit'z mean-variance optimzation in school. Now I've been googling a bit, and to my surprise, Markowit'z is STILL being used by most people, AFAIK. Are there really not some state-of-the-...
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Optimal Portfolios with Skewed and Heavy-Tailed Distributions

I am learning about portfolio theory and been using Markowitz. I wondered, however, if I can use distributional and asymmetric information of the returns to solve the problem. For instance, I have a ...
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-1 votes
1 answer
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Portfolio variance $<=$ weighted average of individual variances [closed]

In portfolio theory, I often (with some justifications but the message is the same) come across the following statement: "The most important quality of portfolio variance is that its value is a ...
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1 answer
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Mean estimate in portfolio optimization (Markowitz) [duplicate]

The Markowitz mean-variance portfolio optimization problem is to find the optimal allocation, $w_{optimal}$ by solving: \begin{equation} w = \mathrm{argmax} \ \mu_{t}^Tw - \frac{\gamma}{2}w^{T}\...
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2 answers
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Why isn't the asset with minimum variance given a 100% portfolio weight? [closed]

The maximum expected return portfolio is the one that assigns a 100% weight to the asset with the highest expected return amongst all assets under consideration. Shouldn't then the asset with the ...
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1 vote
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Standard deviation formula with Short selling- Markowitz model

I have 2 fast quastions. Before I begin I want to show you that I found minus before SD of bills in the book Principles of corporate finance(1.screen). I know SD of bills is zero and minus in this ...
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2 answers
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Why is there a $\frac{1}{2}$ in front of the portfolio variance formula? [closed]

Can someone explain me where $\frac12$ came from in the expression $\frac{1}{2} \omega'\Sigma \omega$? That is the expression to be minimized io order to get the minimal variance portfolio (with also ...
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Closed-form analytical solution for Markowitz efficient portfolio without short-selling

In a portfolio without risk-free assets I know that the efficient portfolio si given by: $\omega=\frac{1}{BC-A^2}[\mu(C\Sigma^{-1}R-A\Sigma^{-1}\mathbb{1})+B\Sigma^{-1}\mathbb{1}-A\Sigma^{-1}R]$, ...
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How to add the effect of skewness in the portfolio optimisation objective function?

I have the following risk adjusted portfolio which I optimise, where gamma is the risk return trade off, $r$ are the returns and $C$ is the covariance matrix which considers scenarios, so it is not ...
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Optimizing Portfolio Return by Targeting Variance

I understand Markowitz and targeting returns to minimize our variance. I know this optimization problem well and its constraints. However when the reverse scenario is to be considered I get very ...
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Portfolio Optimization sum of weights constraint with short selling

For mean-variance portfolio optimization with short-selling allowed I have seen 2 ways to specify the portfolio constraint. In most resources I've seen, such as https://www.coursera.org/learn/...
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4 votes
1 answer
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Do normal returns make the mean-variance portfolio model perform properly?

The Markowitz mean-variance model is known to suffer from estimation error due to financial returns not meeting the assumptions of a normal distribution, providing portfolio weights that underperform ...
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1 vote
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how to relate risk aversion and sharpe ratio in optimisation

I am trying to optimise the following: U(w)=w′μ−λ/2w′Σw which is the typical risk aversion problem. I would like to set lambda in order to have the max sharpe but I cannot find in literature what is ...
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2 votes
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Transform this non-linear portfolio optimization problem into a quadratic optimization problem

I have a portfolio optimization problem similar to this question here, with a V-shape transaction costs such that we pay a fee proportionally to the sum of absolute rebalancing: $$TC(\omega) = \frac{1}...
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1 vote
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Can simple risk management outperform portfolio optimization like this, or is there most likely an error?

I am using a simulation approach to compare the performances achievable by simple risk management and portfolio optimization for portfolio selection. My problem is that my results indicate that simple ...
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3 votes
1 answer
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Mean-Variance optimization with no short selling

I am wondering how I can find the vector of Lagrange multipliers $\mu$ for the non-negativity constraint of the following problem: $$ L(w,\lambda, \mu) = w^{T}\Sigma w - \lambda(w -1) + \mu w $$ So ...
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4 answers
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Understanding what is 'special' about the security market line

I am trying to get my head around the CAPM model and all the intricacies of portfolio management. I have written some code to help me visualise what happens to the risk-return characteristics of my ...
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4 votes
1 answer
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Can a capital market line have a negative slope?

I am struggling to interpret my mean-variance / efficient frontier / capital market line results. I have no issues calculating the efficient frontier. However, I do increase the risk-free rate from ...
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Which riskfree rate to use for Maximum Sharpe Ratio Portfolio?

I am conducting out of sample backtests of the MV framework. But how exactly do I derive the Maximum Sharpe Ratio portfolio for this? The standard forumula of the Sharpe Ratio is given by: $$\frac{(...
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6 votes
1 answer
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Markowitz portfolio in reality

I am in academia and begin to work on topics including portfolio optimization. I just read lots of paper discussing different extensions to the Markowitz approach, given different (possibly ...
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2 answers
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What does the concept "standard Markowitz approach" include?

Does "standard Markowitz approach" include only mean-variance approach or does it also include other approach such as minimum-variance approach?
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Spot Rates on Treasuries

I am trying to find the spot rates for 1mo, 3mo, and 6mo tbills. This would just be their yields as listed on the treasury website, correct or am I missing something?
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4 votes
6 answers
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Is a more robust Covariance estimation possible?

I'm working on a mean-variance optimization problem, but instead of financial securities I'm choosing a 'portfolio' of N athletes. It is a 1-period optimization problem over one generic statistic ...
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financial markets

Let's suppose the following model of financial markets : Market-Maker : the sell financial derivatives, the hedge all the risk after calculating their sensibilities to market risk factors. Thus ...
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4 votes
1 answer
197 views

Tangency portfolio with two additional constraints so that portfolio weights are unconstrained

I know that the formula for determining the weights of the Tangency portfolio is given as $w_{tan}$ = $\frac{\Sigma \mu}{\iota^{\prime}\Sigma\mu }$, but I was wondering how to derive the weights in ...
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4 votes
1 answer
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Where to get MSCI World Index constituents (+ weights)

Where can I download The MSCI World index constituents and their weights (daily update) The current prices of the constituents plus three years of EOD (or weekly) history Corporate actions of the ...
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3 votes
2 answers
787 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 ...
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2 votes
2 answers
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Estimated betas and optimal portfolio

I ran a regression on 20 assets to estimate their beta with different methods. I would like to see the differences of these estimation differences in terms of mean-variance optimal portfolio. How can ...
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5 votes
1 answer
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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 ...
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