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7 votes

Portfolio Optimization and Global Minimum Variance Portfolio (GMV)

1) To be honest, any horizon is problematic in this respect. Simple sampling statistics 101 will tell you that the standard error around any estimate of true mean returns is the root time * variance. ...
demully's user avatar
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5 votes
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Finding a minimum variance portfolio when using a regulariser?

You're not going to get an analytic formula except in special cases of function $\rho(x)$. And you're probably going to want $\rho$ convex. If $\rho$ is convex, the problem is a convex optimization ...
Matthew Gunn's user avatar
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5 votes
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Minimum Standard Deviation Portfolio vs Minimum Variance Portfolio

Recall the conclusion of the Lagrange multiplier theorem. If $w^*$ is an optimal solution for the objective function $f(w)$ and constraint $g(w) = 0$, then there is a unique Lagrange multiplier $\...
RRL's user avatar
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4 votes
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Terminology: "global" in "global minimum-variance portfolio"

I think it's just a common misnomer, on Google Scholar I found a 1980 article by R. Roll: "Orthogonal Portfolio's" but I doubt the term was coined there. I do think I understand why a global ...
Bob Jansen's user avatar
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4 votes

Why is there a $\frac{1}{2}$ in front of the portfolio variance formula?

This has already been dealt with multiple times. As @Dom explains, the purpose is to simplify partial derivatives. For exposition's sake, assume there are only two assets with weight vector $\omega=(\...
Daneel Olivaw's user avatar
3 votes

Cross hedge: Which commodity to hedge when you have to hedge the jet fuel price but you have option between two commodities

The objective of hedging is to reduce the variance of the (position+hedge) portfolio. So which of these two solutions gives a smaller variance? You could calculate it numerically and compare the ...
nbbo2's user avatar
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3 votes
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Do the wallet weights with the minimum variance need to be nonzero?

There can be zero weights, and for that matter there can be (and often will be) negative weights as well unless you specifically have a constraint saying there can't be. Consider the case where you ...
Oscar's user avatar
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2 votes
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What is the u vector in the expression for the weights of the min variance portfolio

yes u is the unit vector of all ones
foshizzle's user avatar
  • 432
2 votes

Portfolio/sub-portfolio optimization

Identifying your variables: You will need a weight for each of the 26 assets in each of the 9 portfolios. Suppose you take each portfolio in turn and create a stacked vector: $\mathbf{w} = [w_{1,1} \...
Attack68's user avatar
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2 votes

How do I show that there is no tangency portfolio?

Any point on the efficient frontier is the sum $$ Z +\lambda X, \qquad \lambda\in\mathbb{R},$$ where $Z$ is the minimum variance fully invested portfolio and $X$ is an efficient zero-cost portfolio. ...
Iron Soles's user avatar
2 votes

How do I show that there is no tangency portfolio?

Recalling that: \begin{align} \begin{cases} A = \mu'\Sigma^{-1}\mu\\ B = \mu'\Sigma^{-1}\iota\\ C = \iota'\Sigma^{-1}\iota\\ \pi_{gmv} = \frac{1}{C}\Sigma^{-1}\iota\\ \pi_{\mu} = \frac{1}{B}\Sigma^{-1}...
Bernardo Scarpelli's user avatar
2 votes
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Is this methodology for finding the minimum variance portfolio with no short-selling sound?

The intuition that "if I have an N stock portfolio and an (N+1)th stock becomes available, buying some of it will lower portfolio variance" is not correct. It is true if all stocks are uncorrelated, ...
nbbo2's user avatar
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2 votes
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Ridge and Quadratic Programming for Portfolio Norm Optimization

The model you were assigned comes from the following paper: de Miguel et al (2009) A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms Instead of ...
develarist's user avatar
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2 votes

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

Let us fix the asset universe with $N$ assets whose returns are multivariate normally distributed with covariance matrix $\Sigma$. You are already invested in $K<N$ assets (your portfolio) and you ...
Kermittfrog's user avatar
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2 votes
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Risk free rate must be lower than expected return of global minimum variance portfolio

The capital market line used in the context of the efficient frontier represents the allocation of capital between the riskless asset and an optimal portfolio (say the tangent portfolio of highest ...
KaiSqDist's user avatar
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2 votes

Portfolio Optimization with ETFs and Futures

I did the same experiment using yahoo finance to get charts. I took the SPY, the VIX and third ETF for comparison. First have a look at the volatility of the 3 vehicles: You can see that the VIX has ...
lehalle's user avatar
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1 vote

Asset Management (Inverse Matrix, MVP,TP etc)

From what I understand of your questions, they are related to f) and g). f) Can you list your workings for this question? ChatGPT is famously known to be unreliable. From what I understand, you ...
KaiSqDist's user avatar
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1 vote
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Calculating the Minimum Variance Hedge Ratio

Hedging is when you are long one thing and short another thing, with the hope that the overall portfolio will be stable, it will not change much in value. Here the hedge position is: long 1 unit of S ...
nbbo2's user avatar
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1 vote

Why is there a $\frac{1}{2}$ in front of the portfolio variance formula?

A lot of things we use in economics and financial economics in particular are inconsequential, but practical. If you have a quadratic program, include this fraction conveniently gets rid of pesky ...
Stéphane's user avatar
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1 vote

How do i find the covariance between two portfolios?

It does not matter whether you measure covariance of two portfolios or two securities, the formula is the same. Simply instead of returns and expected values for securities, put those for portfolios.
Martin Vesely's user avatar
1 vote

is it possible to get minimum variance line having only covariance matrix?

The Frontier is a hyperbola (it’s underlying problem is a quadratic one). To fully define it, we need at least two of its points.
Kermittfrog's user avatar
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1 vote
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Portfolio Optimization with Monte Carlo Simulation - How to do it with Excel?

Yes, the assumption in MPT is normal distribution for returns. You can programme yourself in R or Excel, following elementary linear algebra. Eric Zivot (U Wash) has a spreadsheet solution here: ...
rrg's user avatar
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1 vote

How to evaluate minimum-variance strategies against perfect information mvp

Just to save you some time, there is a non-existence proof for this class of problems. The models assume perfect information, what has been missed is that there are no estimators that converge to the ...
Dave Harris's user avatar
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