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Risk free rate must be lower than expected return of global minimum variance portfolio

I heard a professor say: "We know the return of the risk free asset must be less than the expected return of the global minimum variance portfolio, otherwise there would be arbitrage ...
Gustavo Amarante's user avatar
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Portfolio Optimization with ETFs and Futures

I am looking to perform portfolio optimization with a single ETF (or two) and a VIX futures (with the possibility of adding an additional hedging instrument). Here are some features of my portfolio ...
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Asset Management (Inverse Matrix, MVP,TP etc) [closed]

i just found this website and hope someone can help me. We have a midterm and we got 1 old exam but the Prof didnt want to provide the solutions and he is terrible anyway - so it kinda sucks, and i ...
user70385's user avatar
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Calculation of break-even correlation for diversification effect in N-assets case?

I'm thinking about a generalization of the following case: for 2 assets, there is a diversification effect as soon as i obtain a positive weight for the minimum-variance portfolio in the asset with ...
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Calibration of Covariance Matrix for a Cumulative Period Return

I am trying to compute optimized weights (minimum-variance portfolio) for a cumulative return over a period (weekly or fortnightly). In a daily return setting, it is quite simple, I just compute a ...
KaiSqDist's user avatar
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Robust estimates of variance covariance matrix

I am looking for help from other people with experience creating variance covariance matrix that have enough predictive power to actually lower portfolio volatility out of sample. Using real world ...
helloimgeorgia's user avatar
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Minimizing variance of market neutral portfolio given factor covariance matrix and stock return predictions

If I am given a return prediction and factor exposures for say 50 stocks, as well as the factor covariance matrix, what is the process to determine the weightings of the minimum variance portfolio, ...
helloimgeorgia's user avatar
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Can anyone help me to understand why the GMV point is not on the efficient frontier?

I am following a course about portfolio construction with Python. I am able to successfully draw the efficient frontier and capital market line (CML), and the global minimum variance (GMV) point using ...
user3741124's user avatar
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Terminology: "global" in "global minimum-variance portfolio"

I am confused about the meaning of "global" in "global minimum-variance portfolio". The sources that I have encountered so far do not explicitly state what "global" means....
Richard Hardy's user avatar
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1 answer
254 views

Calculating the Minimum Variance Hedge Ratio [closed]

Taken from the book: $\Delta{S}$ - Change in spot price, S, during a period of hedge. $\Delta{F}$ - Change in futures price, F, during a period of hedge. If we assume that the relationship between $\...
Vanconts's user avatar
2 votes
0 answers
113 views

Naive Diversification under mean variance

I'm looking for a way to introduce naive diversification bias in a mean variance framework and had the idea to model it as some sort of "aversion to extreme portfolio weights" of the ...
T123's user avatar
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Minimizing variance of a long short equity portfolio in practice

I understand the finance 101 explanation of how to minimize variance of a long-short portfolio using a covariance matrix. I also know that it doesn't really work because the covariance matrix is ...
helloimgeorgia's user avatar
4 votes
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463 views

Minimum Standard Deviation Portfolio vs Minimum Variance Portfolio

When solving for the minimum variance portfolio, we have the object: $$ f(w) = \frac{1}{2} w^T \Sigma w $$ subject to a basic scaling constraint: $$ \sum_{i=1}^N w_i = 1 $$ or in matrix terms, $w^T \...
rubikscube09's user avatar
2 votes
1 answer
2k views

Minimum variance portfolio in Python

I have a portfolio or $N$ assets in $t=10$ days. ...
user avatar
5 votes
2 answers
250 views

Help guessing the solution to an optimal control problem

I am considering an investor facing a discrete-time multi-period minimization problem $$ \min_{\{v_t\}_{t=0}^\infty}\Bigg[\sum_{t=0}^\infty(1-\rho)^{t+1}\bigg(\frac{1}{2}v_{t}\Omega_{t+1}v_{t}'\...
Casper Eneqvist's user avatar
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1 answer
191 views

how do we use portfolio optimization to hedge an existing portfolio?

I am working on a risk management project and want to create a custom hedge portfolio to add on to an existing portfolio. I am wondering how do we treat the existing portfolio in the optimization ...
ktong's user avatar
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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 ...
Fabio's user avatar
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Ridge and Quadratic Programming for Portfolio Norm Optimization

Much like this post: https://stats.stackexchange.com/questions/119795/quadratic-programming-and-lasso, I'm trying to integrate RIDGE Penalty in a dedicated quadratic solver. In my case, I am working ...
Samuel Normandeau's user avatar
1 vote
1 answer
910 views

How do i find the covariance between two portfolios?

I know that the formula for covariance is But this is for two securities. How do I find the covariance between two portfolios? more specifically between the global minimum variance (GMV) and the mean-...
Karmanya GB's user avatar
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1 answer
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Cross hedge: Which commodity to hedge when you have to hedge the jet fuel price but you have option between two commodities

If we have an option between two commodities to hedge jet fuel and the commodities have results as follows: minimum variance hedge ratio: 1.07 for commodity 1 and 2.53 for commodity 2 ...
Jai Suneja's user avatar
1 vote
1 answer
2k views

Is this methodology for finding the minimum variance portfolio with no short-selling sound?

I have below here an excerpt from a book on (among other things) mean-variance analysis showing how to find the minimum variance portfolio (Risk and Portfolio Analysis: Principles and Methods, by Hult,...
Oscar's user avatar
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is it possible to get minimum variance line having only covariance matrix?

Hey I have covariance matrix: $$C=\begin{pmatrix} 0,01 & 0.01 & 0\\ \\ 0.01 & 0,02 & -0.01 \\ \\ 0 & -0.01 & 0,03 \end{pmatrix}$$ So the variance of porfolio is: $$\...
Mr.Price's user avatar
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1 answer
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Do the wallet weights with the minimum variance need to be nonzero?

I wonder if we have n risky assets, does the portfolio with the minimum variance always have non-zero weights or can any weight be 0?
Mr.Price's user avatar
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1 answer
285 views

Portfolio/sub-portfolio optimization

I have a finite amount of 26 assets, the total amount of these assets needs to be allocated to 9 portfolios. Each portfolio has its own required return which needs to be met, using a min-variance ...
uhrskov91's user avatar
1 vote
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1k views

Minimum Variance Portfolio Problem Python

I have a problem with the MVP-optimization and scipy. My code is the following. The Maximum-Sharpe-Ratio-Portfolio works. But if I want to optimise the MVP, scipy optimiser doesn't seem to work, ...
Tom's user avatar
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2 votes
1 answer
1k views

Portfolio Optimization and Global Minimum Variance Portfolio (GMV)

I have few questions about classic mean-variance-optimization in general. I have a series daily returns of 15 assets and I want to combine these assets in a portfolio. 1) Do you think that 1 year of ...
Tom's user avatar
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0 answers
284 views

Residual Risk and Variance

I've solved part a, but am struggling with b and c. $x_m$ is the market portfolio vector, and I think $T$ should be a diagonal matrix. Any hints greatly appreciated!
chillz's user avatar
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3 votes
0 answers
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Fixed Income portfolio type

Could someone kindly point me toward a primer that would cover the various type of fixed income portfolio strategies under modern portfolio theory ? In a nutshell, I would like to know what kind of ...
Julien Tabulazero's user avatar
7 votes
1 answer
187 views

Finding a minimum variance portfolio when using a regulariser?

I am aware that the minimum variance portfolio of a market with $n$ securities can be shown to be: \begin{equation} w^* = (1^T_n\Sigma^{-1}1_n)^{-1}\Sigma^{-1}1_n, \\ s.t. \ \ 1^T_nw = 1 \end{...
PsychicSteven717's user avatar
1 vote
0 answers
72 views

Minimum Lower Partial Moment (n=2) hedging ratio

I would like to better have understanding on the minimum-LPM hedging. I have understood that the co-LPM matrix cannot be modeled by GARCH type models that are used to estimate to the covariance matrix,...
Techonomist's user avatar
1 vote
1 answer
61 views

What price data should I used when making minimum mean variance portfolio, optimal risky portfolio and efficient frontier using Markowitz? [closed]

I need to make optimal risky portfolio, minimum variance portfolio and efficient frontier using Markowitz . But i don't know whether to used close price data or adjusted data. If i'm using adjusted ...
dynra's user avatar
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1 answer
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What is the u vector in the expression for the weights of the min variance portfolio

I was working on my finical math homework where I need to find the minimum variance portfolio. I need to use the following matrix expression. Nowhere in the class notes does the instructor say what ...
chasep255's user avatar
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2 answers
110 views

Portfolio Theory: Must VarCovar Matrix be based on return var/covar?

I am trying to estimate the minimum variance portfolio where the assets are currency derivatives. In the specific case it does not make sense to base correlations or variance on asset returns. I am ...
user20423's user avatar
2 votes
1 answer
353 views

How to calculate a hypothetical minimum-variance point?

If we have $N$ assets which are uncorrelated, but have the same mean return of $\mu$ but the variances are different where $\sigma_i^2$ is the variance of each asset $i = 1, 2,...,N$ how can you write ...
klib's user avatar
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10 votes
2 answers
478 views

How to evaluate minimum-variance strategies against perfect information mvp

The minimum variance portfolio should minimize the standard deviation (variance) of the portfolio at time $t+1$. The covariance matrix $\Sigma_{t+1}$ needs to be estimated in order to form the mvp. ...
Kevin  Pei's user avatar
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1 vote
1 answer
66 views

Portfolio Selection formulation

I was just wondering why in http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1601412 on page 22, the constraint (48) is a strict equality for the minimum variance formulation. Whereas in a different ...
Jonkie's user avatar
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2 votes
3 answers
749 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 ...
user2034's user avatar
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2 votes
1 answer
2k views

Computing the minimum variance portfolio for only two risky assets

Given two risky assets and their corresponding covariance matrix, how do I compute the global minimum variance portfolio, its standard deviation and its expected return?
user2034's user avatar
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4 votes
1 answer
3k views

Portfolio Optimization with Monte Carlo Simulation - How to do it with Excel?

If I have three asset classes and their historical weekly returns for five years, how can I construct a minimum variance portfolio and an efficient frontier plot with Excel? To do that do I have to ...
nouveau's user avatar
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5 votes
1 answer
894 views

Electricity market : how to design an optimal hedging strategy using spot and futures markets for an industrial consumer?

Here is the problem : we should adopt the point of view of an industrial company which purchases electricity as an input in its production line and which wants to achieve the following two goals : -...
Vincent's user avatar
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3 votes
1 answer
325 views

Minimum Variance Hedge Ratio in Binomial Framework

In order to find the minimum variance hedge ratio when holding a portfolio of vanilla call options and hedging with stock, you can do an OLS regression. In a binomial model framework, given ...
quantguy's user avatar
5 votes
3 answers
811 views

Are minimum-risk and minimum-variance portfolios equivalent?

When reading a paper by DeMiguel and Nogales (2007; http://papers.ssrn.com/sol3/papers.cfm?abstract_id=911596), I came across the following formulation: Comparing the proposed minimum-risk ...
Marie. P.'s user avatar
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7 votes
3 answers
531 views

What is the canonical reference for Minimum Variance Portfolio's uniqueness?

I am writing a white paper in which I am trying to compare a strategy to different well-known - and classic - asset allocation optimization approaches. One of the methods I chose is the minimum ...
SRKX's user avatar
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