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-1
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0answers
16 views

how to obtain optimal portfolio with different borrowing and lending rates?

I have some risky assets and risk free assets and I am trying to find out optimal portfolio with constraints like following. Suppose I wish to obtain an expected return of 12%, what portfolio will ...
0
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1answer
31 views

Critical Appraisal of Approaches countering Parameter Uncertainty in Portfolio Optimization

It is very hard to come up with legit and solid advantages and drawbacks of the various approaches wich are trying to counteract parameter uncertainty in portfolio optimization procedures. In my ...
2
votes
1answer
35 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 ...
2
votes
1answer
72 views

formulating MVO with costs

I am trying to formulate this simple MVO utility function with a linear transaction cost penalty added using Quadprog in MATLAB tcost = 0.001; lambda = 4; mu = vector of expected returns (say 4x1) S ...
0
votes
2answers
73 views

Mean Variance Analysis: what does the solution of the following exercise tells me?

I'm new in here and I hope this is the right board to ask this question. I'm at second year of university and in the Informatics II course the lecturer made us solve the following mean variance ...
0
votes
0answers
101 views

Calculating the efficient frontier from expected returns and SD

I'm trying to calculate the efficient frontier (and the optimal portfolio at the Sharpe ratio) given two vectors for a portfolio: (1) expected returns and (2) historical standard deviations. I would ...
0
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0answers
47 views

Transform MPT optimization problem

I am trying to teach myself about MPT and optimization. I understand that MPT solutions can be found using three equivalent optimization problems: Minimizing variance for given return limit ...
2
votes
1answer
92 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?
4
votes
1answer
242 views

Mean-variance portfolio & quadratic programming

I am somewhat confused when it comes to modern portfolio theory, mean-variance portfolio optimization and its quadratic programming formulation. Issue 1: Formulation of mean-variance portfolio ...
2
votes
1answer
66 views

Why does my posterior mean differs from Idzorek's results?

I have implemented two different expressions (Idzorek p.6, Walters p.51) of a posterior mean return calculation within a Black-Litterman framework. My results are the same, irrespective of the ...
7
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0answers
199 views

Portfolios from Sorts

Some time ago Almgren and Chriss proposed a method for portfolio optimization based on sorting criteria such as $r_1 > r_2 >... > r_N$ instead of explicit expected returns: see portfolios ...
4
votes
0answers
391 views

Formula for the efficient portfolios (mean-variance optimisation)?

Consider the setting of mean-variance portfolio optimisation: $n$ assets with expected returns $\overline{r}_1,...,\overline{r}_n$ and standard deviations $\sigma_1,...\sigma_n$. For a certain fixed ...
1
vote
2answers
592 views

Covariance of a GMV portfolio with any asset

Why is that the covariance of a global minimum variance (GMV) portfolio in the efficient frontier with any asset is always the same?
2
votes
3answers
3k views

Derivation of the tangency (maximum Sharpe Ratio) portfolio in Markowitz Portfolio Theory?

I have seen the following formula for the tangency portfolio in Markowitz portfolio theory but couldn't find a reference for derivation, and failed to derive myself. If expected excess returns of $N$ ...
0
votes
1answer
111 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 ...
4
votes
2answers
2k views

Typical risk aversion parameter value for mean-variance optimization?

What are typical values for risk aversion parameters $\lambda$ used in mean-variance optimization? Please provide references. Just to be clear, I'm talking about the $\lambda$ in $U(w) = w'\mu - ...
5
votes
1answer
345 views

Robust-Bayesian optimization in Markowitz framework

Suppose we are in the mean-variance optimization setting with a vector of returns $\alpha$ and a vector of portfolio weights $\omega$. In a robust setting, the returns are assumed to lie in some ...
4
votes
0answers
248 views

Analyzing the angle between vector of weights and vector of returns in mean-variance optimization

I am using the paper "A Sharper Angle on Optimization" by Golts and Jones (2009) as a basis for my (minor) masters thesis in mathematical finance. The paper focuses on the mean-variance analysis of ...
4
votes
1answer
940 views

Michaud's Resampled Efficient Frontier - Out of Sample Simulation Testing

I will be putting ALL my account points on bounty to whoever answers this question [if your answer is crap but it's the only answer, you're getting the 165 points]. You will have to wait 2 days or so ...
6
votes
2answers
919 views

Comparing MVO with Resampled Efficient Frontier

My question: How can I compare the Resampled Frontier (REF) to the standard MVO frontier when I have been provided with $\mu$, $\Omega$, and don't have access to true future data to test real out of ...
6
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4answers
1k views

Fastest solver possible for portfolio optimization

I am using quadprog in MATLAB for very simple mean-variance optimization, with less than 100 assets. It is quite fast but if I run a strategy with daily ...
2
votes
1answer
369 views

Unsystematic and systematic risk of a portfolio

I have 8 country stock indexes and 1 world stock index. I do not actually have time series data but I'm given the following data: $\mu$, the vector of expected future returns for all 8 country ...
4
votes
3answers
1k views

Markowitz mean-variance optimization as “error maximization”

I hear it said a lot that standard MV optimization "maximizes errors". But I can't find a good explanation for what exactly they mean by this "maximization" of estimation error. I understand that if ...
3
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3answers
12k views

How to calculate expected return based on historical data for Mean Variance Analysis

I've recently started reading some books on asset allocation and portfolio theory but I don't work in the field and don't have much knowledge yet. So I've been reading up on mean-variance analysis ...
15
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4answers
1k views

Does mean-variance portfolio optimization provide a real edge to those who use it?

Mean-variance optimization (MVO) is a 50+ year concept, and perhaps the first seminal idea of quantitative finance. Still, as far as I know, less than 25% of AUM in the US is quantitatively managed. ...
15
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5answers
2k views

What methods do you use to improve expected return estimates when constructing a portfolio in a mean-variance framework?

One of the main problems when trying to apply mean-variance portfolio optimization in practice is its high input sensitivity. As can be seen in (Chopra, 1993) using historical values to estimate ...