Questions tagged [markowitz]

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158 views

Solving a system of two equations with non-convex matrix multiplication for MV optimization

Scenario: I am trying to do a variation of the MV optimization for a portfolio. In this instance, I already have a vector of mean returns ($\mu$), a vector of ones, a covariance matrix ($\Sigma$), and ...
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1answer
225 views

Solving a Markowitz problem with restrictions (lower and upper bound) to the weights vector

I would like to find a step by step solutionfor the following Markowitx problem. It is a standard markowitz problem. The unique detail (wich is why I am posting this question here) is that there is a ...
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1answer
92 views

Understanding portfolio weights and purchasing stock in modern portfolio theory

Recently I've been learning about the markowitz algorithm. It's pretty interesting, but I'm curious how we apply this in practice. Lets say I have some optimal portfolio: $R_p = x_aR_a + x_bR_b$ ...
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1answer
44 views

Spot Rates on Treasuries

I am trying to find the spot rates for 1mo, 3mo, and 6mo tbills. This would just be their yields as listed on the treasury website, correct or am I missing something?
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99 views

Can simple risk management outperform portfolio optimization like this, or is there most likely an error?

I am using a simulation approach to compare the performances achievable by simple risk management and portfolio optimization for portfolio selection. My problem is that my results indicate that simple ...
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0answers
32 views

fPortfolio specify our constraints for efficientPortfolio [closed]

I am working on the library fPortfolio in R and I have a question. How can we fix for a portfolio the sum of weights equal to 1 ? When I study the code, I see that we cannot choose which constraints ...
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66 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 ...
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0answers
67 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^{} ...
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1answer
116 views

Markowitz expected return time

This is perhaps a rather silly question for the more experienced people in the community but it has been puzzling my mind for a while. Let's say we have a portfolio of 10.000 dollar. We will apply ...
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1answer
129 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 ...
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1answer
46 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 ...
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156 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 ...
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0answers
63 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 ...
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0answers
126 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 ...
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0answers
477 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(...
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1answer
458 views

Portfolio Optimisation/Covariance Estimation on a large scale

When using Markowitz Portfolio Theory, e.g. for finding an optimal portfolio composition, one needs to have estimates of the returns, but most importantly of the covariance matrix. If our universe of ...
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1answer
42 views

how to relate risk aversion and sharpe ratio in optimisation

I am trying to optimise the following: U(w)=w′μ−λ/2w′Σw which is the typical risk aversion problem. I would like to set lambda in order to have the max sharpe but I cannot find in literature what is ...
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1answer
181 views

Prove that a determinant in markowitz method derivation is greater than zero

I want to prove that the following determinant, that appears in the markowitz method of portfolio allocation is greater than zero. ($\mu$ is the vector of returns and $\sum$ is the covariance matrix)
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1answer
693 views

R optimization using OPTIM

I have a covariance matrix and vector of expected returns as my inputs. I have used optim to solve for the weights that maximize the portfolio's return/volatility. I like optim as you can create your ...
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1answer
135 views

Mean-Var optimisation of Monte Carlo simulated model

I have a problem which involves optimisation of a portfolio containing one stock and multiple call options written on it, with the same maturity and different strikes. In order to use optimisation ...
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1answer
75 views

Which riskfree rate to use for Maximum Sharpe Ratio Portfolio?

I am conducting out of sample backtests of the MV framework. But how exactly do I derive the Maximum Sharpe Ratio portfolio for this? The standard forumula of the Sharpe Ratio is given by: $$\frac{(...
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1answer
954 views

optimal portfolio with different lending and borrowing rates

I have 4 risky securities (have returns and var-cov matrix for monthly data), and I can lend at 1% per annum, but borrow at 5% per annum. If i wish to obtain the s.d. of 5%, what is the optimal ...
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2answers
83 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 ...
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36 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 ...
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43 views

financial markets

Let's suppose the following model of financial markets : Market-Maker : the sell financial derivatives, the hedge all the risk after calculating their sensibilities to market risk factors. Thus ...
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288 views

Mean-Variance Optimization Techniques with Multiple Asset Classes

Why does it make sense to use single-period Markowitz mean-variance optimization techniques when we're trying to figure out asset allocation across multiple asset classes (bonds, stocks, REITs, etc)? ...
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107 views

Show that two formulations of Markowitz problem are equivalent

I would like to solve (as mathematically and formally as possible) that the following Markowitz problems are equivalent. The big point is: I want to show that it is equivalent to constrain the return ...

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