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Questions tagged [mean-variance]

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Closed form Mean variance solution w/ positive weights constraint

There exists a closed form solution for unconstrained MVO, as well as MVO with weight constraint $\sum w_i = 1$. See Derivation of the tangency (maximum Sharpe Ratio) portfolio in Markowitz Portfolio ...
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Portfolio optimization with non-linear cost

I am trying to solve a mean-variance problem with a non-linear market impact cost term in there. This is the problem I am trying to solve $$ \max_x \left ( \alpha x - \gamma x' \Sigma x - a\sqrt{|x-...
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Smart transaction cost model (for spread contracts)

In futures there exist exchange traded calendar spread contracts, which trade as a single unit (think May/June Crude Oil). The bid ask spread for the spread contracts is the same as that of the ...
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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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How to find beta from the information given? [closed]

This is an exam question. I know that to find beta I need the covariance between the portfolio and asset A but don't know how to find it.
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“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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Equivalence between Order of Optimization for Mean Variance

When calculating mean variance portfolios, the general strategy is to minimize variance subject to expected return being higher than some benchmark $\mu$. An alternative approach to this problem ...
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1answer
86 views

Economic intuition behind pricing cash flow

I read the book of Skiadas Asset Pricing Theory 2009. I don't quite understand what does mean pricing cash flow. In the book it's written: $\textbf{Definition 2.9}$ A cash flow $x^*$ is a pricing ...
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Generalized Mean Variance Portfolio

Utility based portfolio optimization deals with the problem of finding the optimal portfolio $x_T$ by maximizing the utility/objective function $O(x_T,x_0)$ where $x_0$ is the current portfolio. In ...
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454 views

mean variance optimization vs max sharpe ratio

I keep reading/hearing that the results from mean-var optimization is max Sharpe ratio. It seems making sense if you fix either target return or target risk, but in general, it doesn't seems right, ...
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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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1answer
146 views

Solving a system of two equations with non-convex matrix multiplication for MV optimization

Scenario: I am trying to do a variation of the MV optimization for a portfolio. In this instance, I already have a vector of mean returns ($\mu$), a vector of ones, a covariance matrix ($\Sigma$), and ...
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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 ...
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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. ...
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2answers
108 views

Help on minimum variance optimization on U.S. Equity/Bond ETFs - Intuition

I run a MVP on 10 ETFs: SPY, SDY, IWB, XLP, VGT, BND, XLF, IJR, XLY, XLI from 2008 to 2016 on monthly return data. The weighs array (I am using a MATLAB function "Portfolio" - constraints are simple: ...
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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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1answer
192 views

Optimize portfolio of non-normal binary return assets

I am facing t = 1,..T investment periods where each period I have x$ to invest. Suppose each period I can build a portfolio from thousands of assets (some are uncorrelated whilst some are highly ...
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1answer
503 views

For any efficient portfolio, does there exist another efficient portfolio which has zero correlation with it?

For any portfolio on mean-variance efficient frontier, does there exist a portfolio on the frontier which has zero correlation with it? I tried to play around with the covariance, by setting ...
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Covariance between GMV portfolio and any other asset = Var(GMV), proof by contradiction

I need to prove by contradiction that Var(GMV)=Cov(GMV,a) where a is any other portfolio. I think this can be done by constructing a portfolio of x in the a asset and (1-x) in the GMV portfolio to ...
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2answers
191 views

Mean-variance portfolio returns illogical weights

I have a dataset with 5 assets. I apply mean-variance portfolio: ...
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1answer
346 views

CVXPY 's constrains doesn't work

I am trying to implement a max return optimization with a large number of assets. I am not sure why this problem won't work. ...
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2answers
1k views

Risk contribution of part of a portfolio

Is it quantitatively sound to say that if I have assets $x, y,$ and $z$ in a portfolio, and that the total variance of the portfolio is defined as $\sigma_p ^2 = w_x^2\sigma_x^2 + w_y^2\sigma_y^2 +...
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Mean and standard deviation of price series with Kalman

I like to calculate the mean and standard deviation of a price series, using the Kalman filter. I am somehow stuck with the deviation, or have some problem in understanding, which my research could ...
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1answer
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Mean Variance portfolio optimisation (Long Only) CVXPY including cardinality constraint

I am working on a portfolio optimisation that requires me to constrain on the number of assets used, e.g from S&P500 build a 20 asset portfolio that is feasible. After doing some research I came ...
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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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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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1answer
246 views

Dollar-Neutral in addition to Market-Neutral?

What is the point/benefit of using a dollar-neutral strategy in addition to a Beta-neutral strategy? What exactly does a dollar-neutral strategy buy the investor? What's useful about balancing long ...
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Minimum Variance Portfolio problem [closed]

Minimum Variance Portfolio Suppose there are N stocks in the investmentable universe and we have a fully invested portfolio investing 100% of the capital. The Covariance matrix is denoted as ∑. We ...
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1answer
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Are financial returns considered more volatile in recessionary times as opposed to expansionary times?

I need help in understanding some results that I have obtained. I am doing some out-of-sample performance analysis for different targets of volatility in mean-variance optimization where I solely ...
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398 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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3answers
306 views

Is this realized “efficient” frontier reasonable?

I have performed some out-of-sample analysis of mean-variance optimization with monthly rebalancing. Studying the "realized efficient frontier", I am worried that something is wrong. Since the ...
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2answers
534 views

Monte Carlo based mean variance optimization

I was asked this question in an interview some years ago. It struck me as a poorly formed question. I thought I would put it out there to the community to see if I just simply missed something. ...
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1answer
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Are Variances generally stable for any given instrument?

My hesitation, as I look at getting into forecasting based on observed variances, is the nagging question - if variances are not constant per-instrument, is it any good to use the last month or year's ...
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1answer
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Calculate mean variance portfolio

I am trying to calculate the mean variance portfolio using the plug-in approach. First I generate some artificial data: x <- replicate(10,rnorm(1000)) Then I ...
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1answer
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Can the differential operator be removed to get the mean/variance of an Ito process?

If $X_t$ is an Ito process, such that: $dX_t = \mu(t, X_t)dt + \sigma(t, Xt)dW_t$ where $W_t$ is a standard brownian motion. Then we can say that: $E(dX_t) = \mu(t, X_t)dt$ and that $Var(dX_t) = \...
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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. ...
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259 views

Mean Variance Portfolio theory and real-world problem?

There are many assumptions on mean-variance portfolio theory and they seem to be very unrealistic, for example 1) investors have the same information at the same time: calculating expected returns ...
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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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1answer
337 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. ...
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1answer
215 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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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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1answer
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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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3answers
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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 ...
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1answer
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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
223 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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1answer
3k 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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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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1answer
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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?
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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 ...