# Questions tagged [mean-variance]

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### 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 ...
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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
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
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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 ...
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### 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 (...
685 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 ...
443 views

### Cover's universal portfolio vs. Markowitz's mean-variance model

Cover's universal portfolio maximizes the wealth growth rate Markowitz's mean-variance model minimizes portfolio variance Both allocate assets based on historical returns. How do these two models ...
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 ...
1 vote
778 views

### Leverage constraints

I am trying to complete my project on Mean-Variance Leverage Optimization, and I have found lots of helpful advice on this forum. I wanted to ask you if you have some idea on how to implement a ...
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 ...
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 ...
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### 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 ...
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### 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 ...
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 ...
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### 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 ...
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### Closed form solution for Mean-Variance optimization under constraint

Is there a closed form solution for the vector weight $w$ for the following mean-variance optimization problem? $\max_w w'\mu - \frac{\gamma}{2}w'\Sigma w$ s.t. $w'z\geq \bar{z}$ where $w, z$ are N ...
1 vote
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### Mean-EVaR efficient frontier

Entropic Value-at-Risk (EVaR) is an alternative and more efficient risk measure than conditional Value-at-Risk (CVaR). EVaR serves as an upper bound to both VaR and CVaR. Below is a graph of the mean-...
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### Questions about Merton's derivation of the security market line

In Merton's "An Analytic Derivation of the Efficient Frontier" (PDF), he derives the security market line for the CAPM using the definition of the tangency portfolio. He writes: Here, $m$ ...
1 vote
238 views

### Is this quadratic form the Sharpe ratio?

I'm reading Merton's An Analytic Derivation of the Efficient Portfolio Frontier. In section IV, he derives the efficient frontier with a riskless asset. Let $\mathbf{w}$ be a vector of portfolio ...
936 views

### Why the market portfolio is the tangency portfolio in the Mean-Variance Optimization model?

I read in an explanation that the tangency portfolio has all securities with weights proportional to their market value because supply equal’s demand. But I can't understand why supply equals demand ...