Questions tagged [minimum-variance]
The minimum-variance tag has no usage guidance.
28
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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 ...
1
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1answer
58 views
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 ...
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58 views
Minimum variance portfolio's analytical solution, but assuming $t$-distribution
$$ \boldsymbol{w} = \frac{\boldsymbol{\Sigma}^{-1} \boldsymbol{1} }{\boldsymbol{1}' \boldsymbol{\Sigma}^{-1} \boldsymbol{1}} $$
is the well known closed-form analytical solution to the minimum ...
1
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1answer
91 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-...
0
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1answer
64 views
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
...
1
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1answer
123 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,...
0
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1answer
71 views
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:
$$\...
1
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1answer
47 views
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?
1
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1answer
127 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 ...
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0answers
626 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, ...
2
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1answer
470 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 ...
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0answers
99 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!
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71 views
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 ...
7
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1answer
147 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{...
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0answers
56 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,...
1
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1answer
48 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 ...
0
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1answer
22 views
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 ...
0
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2answers
82 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 ...
2
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1answer
168 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 ...
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2answers
423 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.
...
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1answer
54 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 ...
2
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1answer
385 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 ...
2
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1answer
317 views
Computing the minimum variance portfolio
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?
4
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1answer
2k 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 ...
5
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1answer
787 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 :
-...
3
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1answer
268 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 ...
5
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3answers
713 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 ...
7
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3answers
472 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 ...
