# Questions tagged [mean-variance]

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### Find variance of Asset with lesser return to make a pure portfolio of it the min-variance portfolio [duplicate]

I need to solve the question mentioned above. For an asset with a worse payoff than another, I need to determine a variance for which the minimum-variance portfolio only consists of this asset. There ...
1 vote
101 views

### Closed form solution for Mean-Variance optimization without short-selling

So I am writing my bachelor thesis about the naive portfolio vs mean-variance portfolio and I am currently a bit stuck at the part about describing the mean-variance portfolio. I know that if there ...
1 vote
46 views

### 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 ...
79 views

### Evaluating estimate of covariance matrix

I am testing out different methods / shrinkages to estimate a covariance matrix and I am wondering what is the best method of comparing the estimated covariance matrix to the true covariance matrix (...
52 views

### How to change the covariance matrix for a parallel-shift of the efficient frontier?

I'm trying to obtain a parallel shift in my efficient frontier based on the Merton 1972-parameters. As i think a picture tells you more than 1000 words here is what i tried: The setting of my problem ...
67 views

### How to construct the behavioral efficient frontier

I just stumbled across an interesting chart in Meir Statman's book "Finance for Normal People" where he introduces his behavioral portfolio theory. There, he also provides the following ...
53 views

### If Kelly and tangent portfolios have the same weights, do they differ only empirically?

I studied Kelly portfolio and tangent portfolio and found that they have the same weights. But the empirical studies that I have seen so far show that Kelly portfolio has a smaller number of stocks ...
88 views

### Markowitz Optimization with 2 assets

Suppose there are only two risky assets and we want to optimize our portfolio. Constraints are that we have a minimum return $\overline{r}$ and we can only invest $w_1 + w_2 = 1$. Is it possible that ...
70 views

### Beyond the mean-variance framework, can expected returns be HIGHER for an individual due to a HIGHER risk aversion?

In the mean-variance framework, the only way to get a higher expected return is to be exposed to a higher beta, and the more risk-averse an agent, the lower the beta of their portfolio (lending ...
112 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 ...
91 views

### Comparing the performance of portfolio optimization methods

I am trying to compare the performance of the compositions of a single portfolio determined by unconstrained mean variance optimization, minimum variance optimization (expected returns equal to 0 in ...
1 vote
173 views

### Alternative form of mean-variance optimization that uses standard deviation

I'm curious about an exercise found in Optimization Methods in Finance. Exercise 8.2 (pg 143) explores a variant of the more commonly used form of MVO. When I refer to the more common variant I'm ...
1 vote
224 views

### Maximizing Mean+Variance in a Portfolio

Mean-Variance optimization trades off expected returns with portfolio variance. The idea is that excess variance is not desirable. But what if you weren't averse to high variance and you wanted to ...
389 views

### Efficient frontier portfolio's analytical solution for a given expected return $r$
$$\begin{equation} \boldsymbol{w}(r) = \frac{r\mathbf\Sigma^{-1} \boldsymbol{\mu}}{\boldsymbol{\mu}^{\top} \mathbf{\Sigma}^{-1}\boldsymbol{\mu}} \end{equation}$$ is the closed-form analytical ...
How can an asset's variance, $\sigma_i^2$, be shown to contribute to portfolio variance, $\sigma_p^2$? I was thinking of taking the derivative (first order conditions \$\frac{\partial L_{\sigma_p^2}(w,\...