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10 views

Use orthogonal decomposition to compute the optimal return for a CARA investor

Question from Back, 5.8. If all returns are joint normally distributed, then $R_p$, $e_p$, and ε are joint normally distributed in the orthogonal decomposition R= $R_p$ + $be_p$ + ε of any return R ...
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0answers
45 views

How do I show that there is no tangency portfolio?

Question: Suppose that the risk-free return is equal to the expected return of the global minimum variance portfolio. Show that there is no tangency portfolio. A hint for the question states: Show ...
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1answer
68 views
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1answer
58 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 ...
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0answers
25 views

Calculating the optimal portfolio for an investor with quadratic utility

The problem is from Asset Pricing and Portfolio Theory by Back and can be found here. The relevant info from section 2.5 can be found here. Given that we have the Expected value and the variance of ...
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1answer
49 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 ...
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2answers
104 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
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1answer
101 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 ...
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2answers
92 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 ...
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387 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 ...
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0answers
58 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
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1answer
122 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
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1answer
299 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
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1answer
73 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 ...
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1answer
260 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 ...
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0answers
483 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 ...
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2answers
726 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?
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3answers
4k 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 $N$ ...
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1answer
113 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 ...
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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 - ...
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1answer
378 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 ...
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0answers
258 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
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1answer
1k 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 ...
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2answers
1k 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 ...
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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
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1answer
411 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
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3answers
2k 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 ...
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3answers
13k 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 ...
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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. ...
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5answers
3k 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 ...