Questions tagged [mean-variance]

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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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422 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 ...
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225 views

How good is the inverse-volatility portfolio?

Heuristic portfolio construction techniques include the equally-weighted portfolio (1/N) and the inverse volatility portfolio (IVP), which is based on the low-volatility effect. They can be assembled ...
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632 views

Modelling log-returns and calculating the portfolio return

I know this might be a trivial question, however, I would be grateful for some clarification. I am working on weekly log-return data, doing volatility-foracasting using GARCH models and then using ...
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273 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 ...
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115 views

James-Stein estimator for superior estimates of returns in m.v. portfolio optimization

I am currently learning about statistical techniques to enhance the estimation of input parameters in a m.v. optimization. Specifically I have some doubts about the James-Stein estimator applied as an ...
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77 views

Can variance change over time?

I'm working on a toy project that involves fantasy basketball, I know this is the quantitative finance stackexchange, but it seemed like the best place to ask this question. My goal is to make ...
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50 views

Mean Variance Optimization vs Risk Scaling

What would be the difference between the following. Both techniques will result is an ex-ante risk of $\sigma$. However, that would be achieved via two different values of h. I want to understand ...
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40 views

Tangency portfolio with two additional constraints

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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164 views

In sample and out of sample in Mean Variance Optimization

Hello to everyone and thanks again for your help, i have find this forum really helpful while working on my final dissertation. However I'm here again because I have loads of doubts regarding the in-...
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95 views

Mean-Variance portfolio: How do I compute the variance when the portfolio is normalized

Let's consider the very basic of a Mean-Variance Portfolio: $$ \text{max}_{x} (1-\lambda)\sum_i^n\mu_ix_i-\lambda\sum_i^n\sum_j^n x_i Q_{ij}x_j $$ $$\text{ s.t. }\sum_i^nx_i=1 \text{ , } x_i \geq ...
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329 views

Trouble computing the VaR for Student's t-distribution for a minimum-variance portfolio composed of four cryptocurrencies (BTC, ETH, LTC, and XMR)

I have modelled the time-series of daily log-returns from August 2015 to October 2017 of a minimum-variance portfolio composed of four cryptocurrencies (BTC, ETH, LTC, XMR) by fitting the data to four ...
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118 views

Relation between mean and variance of a portfolio in modern portfolio theory:

I hope that this is the right place to ask my question! Let a market with $N\ge1$ risky assets and denote by $(R_i,i=1,\cdots, N)$ their returns and $R$ the vector of these $N$ returns. In addition, ...
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34 views

Selecting the best characteristic portfolio per rebalance date

An investor typically decides a portfolio objective and sticks with that objective for every rebalance date in the portfolio's life. Common characteristic portfolios that the investor chooses are: ...
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66 views

Mean Semivariance Optimization VS PMPT

Mean Semivariance optimization defines semivariance, variance only below the benchmark/required rate of return, as: $(1/T).\sum_{t=1}^{T} [Min(R_{it}-B,0)]^2$ where $B$ is the benchmark rate, $R_{i}$...
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52 views

Stochastic discount factor for factor research

Often, after presenting a new factor technique, the paper calculates an SDF by doing $\Sigma ^{-1}\mu_F$ i.e. mean variance optimization on the factors. What is the significance of doing this ?
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1answer
207 views

Leverage constraints

I am trying to complete my project on Mean-Variance Leverage Optimization, and I have found lots of helpful advice on this forum. I wanted to ask you if you have some idea on how to implement a ...
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284 views

Mean Variance Optimization of 2000 pairs of securities (Python)

I would like to take the opportunity to ask for your help on an assignment I'm trying to complete. For this 'Modern Robo Advisory' course we are asked to solve a (target) goal-based investment ...
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105 views

“Porting” an alpha strategy to a different benchmark

I'm reading about the mean-variance optimization of active portfolios. A bit of prior background from the book I'm reading: the author discusses the mean-variance optimal portfolios without cash, ...
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49 views

How to hedge a MV portfolio against crises

I have constructed an adjusted Mean-Variance portfolio optimization method that optimizes the exposure in a set of X assets. The portfolio works perfectly fine during normal periods (even when there ...
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126 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 ...
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117 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 ...
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41 views

Is non-linear correlation an issue in portfolio optimization?

Portfolio weights are linear combinations of assets. How can it be true then for there to be, and how can someone prove that there is any, non-linear correlation issues in portfolio optimization? Is ...
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19 views

Risk aversion coefficients for multi objective quadratic programming

I am solving different quadratic programming optimizations in a setting that involves the usual mean variance problem plus other objectives. My concern is how to choose the many so-called risk ...
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45 views

Mean variance portfolio - alternative formulations

From this lecture on YouTube the lecturer states that there are three ways to form the mean variance portfolio (minimize variance for a given return, maximize return for a given variance, maximize a "...
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Calculating R* in a two-asset world

In chapter 5 of John Cochrane's Asset pricing, we derive a state-space interpretation of the mean variance frontier by defining $R^*$ and $R^{e*}$. A little forward, we have this formulation: $$R^* = \...
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88 views

Finding the Efficient Frontier in Tensorflow

I have two assets A and B. Asset A has an expected return of 0.92% with a standard deviation of 2.10. Asset B has an expected return of 1.39% and a standard deviation of 2.20. I want to find the set ...
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36 views

How to obtain tangency portfolio of the resampled efficient frontier in MATLAB?

I have generated the resampled frontier according to Michaud's approach. In order to compare it with the classical mean variance approach I want to invest in the respective tangency portfolios. While ...
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42 views

Notation for the variance in papers

Here is a screenshot from : LIM Quadratic hedging and mean variance portfolio selection with random parameters in an incomplete market When I deal with mean variance portfolios, I usually see the ...
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101 views

Units of Risk: Variance vs Standard Deviation

Suppose you are trading two mean-reverting assets, A and B, and that $Covar(A, B) > 0$. You are currently long one unit of A, and are considering buying one unit of B. Compared to the situation ...