# Questions tagged [markowitz]

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623 views

### Optimal Portfolio from Efficient Frontier

I found this code on plotly site, using CVXOPT to find the efficient frontier, and then, the optimal Portfolio. The optimal function is ...
270 views

### Finding mean vector and covariance matrix for annual returns given quarterly returns

I am currently trying to calculate a vector for the mean annual returns of 4 different asset classes along with their 4x4 covariance matrix in excel. However, I am having problems since the data I ...
378 views

### Definition of sharpe ratio maximising and variance minimising portfolios

In this paper, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2226985, in the derivation of the mean variance efficient portfolio using lagrangians in the appendix, on page 29, the two portfolios ...
261 views

### Residual Covariance Matrix, and MVO for Residual Variance and Alpha

My overall goal is to find an efficient frontier using QP in terms of $\alpha$ and residual variance ($\omega^2$) for a portfolio $P$ given a benchmark $B$. We know the equation for residual variance ...
39 views

### Tangency portfolio with two additional constraints

I know that the formula for determining the weights of the Tangency portfolio is given as $w_{tan}$ = $\frac{\Sigma \mu}{\iota^{\prime}\Sigma\mu }$, but I was wondering how to derive the weights in ...
176 views

I want to optimise a static portfolio with a holding period of 90 days given 10 tradable assets. The assets are quoted in bid and ask prices. I want to minimise the risk measured by standard deviation ...
116 views

### Relation between mean and variance of a portfolio in modern portfolio theory:

I hope that this is the right place to ask my question! Let a market with $N\ge1$ risky assets and denote by $(R_i,i=1,\cdots, N)$ their returns and $R$ the vector of these $N$ returns. In addition, ...
236 views

### Behaviour of out of sample efficient frontier

I am comparing the efficient frontier of a set of portfolios that are in and out of sample. The first period is from 1991-01-03 until 1992-10-03 and the second one from 1992-10-03 until 1994-03-03. I ...
64 views

### Markowitz models with uncertain returns

I am analyzing the Markowitz models with uncertain returns as follows: after calculating the expected returns and the covariances of 30 monthly historical series of 30 stocks, I resolve the Markowitz ...
62 views

### Mean-cVaR model: How can one include transaction cost

 \min \delta CVaR - (1-\delta) \sum_i^{n} \mu_i x_i \\ \sum x_i = \sum x^{old}_i \\ Losses(s) = \sum x_i - \sum_i^{n} (R(s,i))x_i \\ VaRDev(s) = Losses(s) - VaR \\ CVaR = VaR + \frac{\sum_s^{} ...
127 views

### Markowitz w/ riskless asset & CAPM

If risk free rate ($R_0$) is bigger than expected return on minimum variance portfolio ($\bar{\mu}$), so $R_0>\bar{\mu}$. I.e. the tanget portfolio is on the risky inefficient portfolio frontier ...
152 views

### Solution for Markowitz problem with Safety-First Ratio

What is the solution for the following markowitz unconstrained problem? The sum of the entries of the weights vector $w$ should always be requied to sum one? Or if we use the risk-free asset it can be ...
62 views

### Periodicity justification in Markowitz optimization

Monthly returns seems to be the industry standard for everything. Markowitz used monthly returns in his original paper on mean-variance optimization, the efficient frontier, etc. Did he ever provide ...
124 views

### Should the number of Markowitz Optimization steps be counted as backtest trials?

I'm backtesting a strategy that involves monthly investments in a few stocks out of a given set, that is, each month some of the stocks are shortlisted from an index and a long position is taken in ...
475 views

### Tangent portfolio weights without short sales?

Consider a mean-variance investor in a world with a risk-free asset. Let $R_f>0$ be the return of the risk-free asset, $\mathbb{E}(R_i)>R_f$ the expected return of the risky asset $i$ and \$SD(...
64 views

### Can naive diversification outperform mean-variance optimization like this, or is there most likely an error?

I am using a simulation approach to compare the performances achievable by naive diversification and mean-variance optimization for portfolio selection. My problem is that my results indicate that ...
82 views

### Understanding what is 'special' about the security market line

I am trying to get my head around the CAPM model and all the intricacies of portfolio management. I have written some code to help me visualise what happens to the risk-return characteristics of my ...
30 views

### How to obtain tangency portfolio of the resampled efficient frontier in MATLAB?

I have generated the resampled frontier according to Michaud's approach. In order to compare it with the classical mean variance approach I want to invest in the respective tangency portfolios. While ...