Questions tagged [minimum-variance]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
2 votes
1 answer
249 views

Minimum variance portfolio in Python

I have a portfolio or $N$ assets in $t=10$ days. ...
user avatar
5 votes
1 answer
113 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}'\...
user avatar
0 votes
0 answers
60 views

Inputs to Min-Var Portfolio

Although I always use daily data, I am wondering if a Min-Var portfolio based on weekly bar data would be more stable (less noise) than using daily bar data as inputs? [I have no interest in the ...
user avatar
0 votes
0 answers
43 views

Optimisation Multiple Constraints - Using CVXOPT

I am trying to solve a linear algebra problem: an optimisation problem and I am using CVXOPT. I've split the problem into 3 components In its simplest form, The general formulation for CVXOPT is ...
user avatar
1 vote
1 answer
115 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 ...
user avatar
  • 21
0 votes
2 answers
120 views

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 ...
user avatar
  • 23
1 vote
1 answer
131 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 ...
user avatar
1 vote
1 answer
455 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-...
user avatar
0 votes
1 answer
73 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 ...
user avatar
1 vote
1 answer
1k 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,...
user avatar
  • 768
0 votes
1 answer
242 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: $$\...
user avatar
  • 413
1 vote
1 answer
92 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?
user avatar
  • 413
1 vote
1 answer
186 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 ...
user avatar
1 vote
0 answers
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, ...
user avatar
  • 131
2 votes
1 answer
994 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 ...
user avatar
  • 131
2 votes
0 answers
140 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!
user avatar
  • 21
3 votes
0 answers
75 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 ...
user avatar
7 votes
1 answer
173 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{...
user avatar
1 vote
0 answers
68 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,...
user avatar
1 vote
1 answer
53 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 ...
user avatar
  • 11
0 votes
1 answer
36 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 ...
user avatar
  • 103
0 votes
2 answers
97 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 ...
user avatar
2 votes
1 answer
224 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 ...
user avatar
  • 308
10 votes
2 answers
453 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. ...
user avatar
  • 447
1 vote
1 answer
61 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 ...
user avatar
  • 189
2 votes
1 answer
542 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 ...
user avatar
  • 215
2 votes
1 answer
869 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?
user avatar
  • 215
4 votes
1 answer
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 ...
user avatar
  • 63
5 votes
1 answer
835 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 : -...
user avatar
  • 59
3 votes
1 answer
303 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 ...
user avatar
5 votes
3 answers
755 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 ...
user avatar
  • 519
7 votes
3 answers
496 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 ...
user avatar
  • 10.9k