Questions tagged [markowitz]

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1answer
134 views

Portfolio Optimization sum of weights constraint with short selling

For mean-variance portfolio optimization with short-selling allowed I have seen 2 ways to specify the portfolio constraint. In most resources I've seen, such as https://www.coursera.org/learn/...
4
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1answer
415 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 ...
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1answer
651 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 ...
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2answers
150 views

What does the concept “standard Markowitz approach” include?

Does "standard Markowitz approach" include only mean-variance approach or does it also include other approach such as minimum-variance approach?
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0answers
100 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 ...
3
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1answer
111 views

Do normal returns make the mean-variance portfolio model perform properly?

The Markowitz mean-variance model is known to suffer from estimation error due to financial returns not meeting the assumptions of a normal distribution, providing portfolio weights that underperform ...
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1answer
46 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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0answers
100 views

Transform this non-linear portfolio optimization problem into a quadratic optimization problem

I have a portfolio optimization problem similar to this question here, with a V-shape transaction costs such that we pay a fee proportionally to the sum of absolute rebalancing: $$TC(\omega) = \frac{1}...
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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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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 ...
2
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1answer
84 views

Mean-Variance optimization with no short selling

I am wondering how I can find the vector of Lagrange multipliers $\mu$ for the non-negativity constraint of the following problem: $$ L(w,\lambda, \mu) = w^{T}\Sigma w - \lambda(w -1) + \mu w $$ So ...
3
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1answer
474 views

Can a capital market line have a negative slope?

I am struggling to interpret my mean-variance / efficient frontier / capital market line results. I have no issues calculating the efficient frontier. However, I do increase the risk-free rate from ...
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1answer
81 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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0answers
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 ...
4
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1answer
195 views

Markowitz portfolio in reality

I am in academia and begin to work on topics including portfolio optimization. I just read lots of paper discussing different extensions to the Markowitz approach, given different (possibly ...
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2answers
1k views

Relationship between CML and SML

I am referring to the book Sharpe et al. (1998), Investments, 6th Edition. I am trying to wrap my head around some lines from the book, pertaining to Security Market Line. It reads: Earlier it was ...
4
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6answers
254 views

Is a more robust Covariance estimation possible?

I'm working on a mean-variance optimization problem, but instead of financial securities I'm choosing a 'portfolio' of N athletes. It is a 1-period optimization problem over one generic statistic ...
1
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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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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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0answers
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 ...
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1answer
4k views

Where to get MSCI World Index constituents (+ weights)

Where can I download The MSCI World index constituents and their weights (daily update) The current prices of the constituents plus three years of EOD (or weekly) history Corporate actions of the ...
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2answers
297 views

Max allowable return in Markowitz model

The Markowitz model solves the following problem: The portfolio with the smallest variance among attainable portfolios with expected return µV. Here we have to choose µV to get the optimal portfolio ...
2
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2answers
138 views

Estimated betas and optimal portfolio

I ran a regression on 20 assets to estimate their beta with different methods. I would like to see the differences of these estimation differences in terms of mean-variance optimal portfolio. How can ...
5
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1answer
108 views

Risk/Return Paradox in Markowitz Optimization?

It is possible that from the efficient frontier obtained varying the "lambda" parameter of the risk-appetite coefficient, in the Mean Variance Parametric Quadratic programming problem, it results that ...
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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 ...
1
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1answer
90 views

Formula in Markowitz Optimization Problem (without riskless asset)

(hope this is not too basic, I'm new to this forum) Im struggling to understand the optimization problem (global minimum variance portfolio) formula in Markowitz Theory: $$\arg\ \min\ Var(Return\ x) =...
2
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1answer
132 views

Mean-variance maximization

I denote by $W_0$ and $W_1$ the wealth of an investor at $t=0$ and $t=1$, respectively. Let $r_f$ be the risk free rate, $r$ the vector of returns of the risky assets in excess of the risk free rate, ...
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1answer
171 views

Market Portfolio Optimization

Consider the minimization problem $$\min\left\{\frac{1}{2}x^T\Sigma x - \lambda(\mu-r_f)^Tx\right\}$$ and assume the CAPM model, i.e. $$r_i-r_f = \beta_i(r_m-r_f) + \varepsilon_i$$ Assuming $\...
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0answers
68 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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1answer
110 views

Markowitz portfolio optimization and CAL [closed]

Just had some questions regarding the efficient frontier and the CAL. As i understand it the point where the CAL is tangent to the efficient frontier is the optimal mix of risky assets. However I also ...
2
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1answer
109 views

Markowitz portfolio risk with PV01 instead of variance

As the PV01 ($= dpdy \times notional$) of a bond is a measure of its risk, as well as its price return variance, could we measure the risk of a bonds portfolio with the Markovitz portfolio variance ...
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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
110 views

What does risk tolerance represent for utility-maximizing optimization with linear constraints?

Referencing Wei Jiao (2003) p. 8, formula (1.12), for $Ax = b$ set of linear constraints in a portfolio, the solution for the optimum weights to maximize the utility is: $$w^* = \Sigma^{-1}A^T \left( ...
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1answer
173 views

Markowitz optimization - can two sets of returns produce the same set of weights?

The portfolio optimization problem I have in mind is a minimum variance optimization with positive weights, formulated as below: I am trying to show that the solution is unique, specifically in the ...
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1answer
120 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 ...
3
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2answers
252 views

Markowitz; risky asset frontier w/o risk free asset

What is the intuition behind the "spanning" result in the following statement? For a fixed pair of distinct frontier portfolios $\phi_p$ and $\phi_q$, any frontier portfolio $\phi$ can be obtained ...
8
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2answers
3k views

Why does the Markowitz mean-variance model require the assumption of normality?

Given $N$ assets, the Markowitz mean-variance model requires expected returns, expected variances and a $N \times N$ covariance matrix. The joint distribution is fully defined by these measures. ...
1
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1answer
696 views

Linear Regression vs Mean Variance Optimization

Assume I have n signals, which I would like to linearly weight and combine to form an aggregate signal. Two possible ways of doing this based on historical data are:...
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2answers
5k views

Formula for Optimal Portfolio of 2 Assets when No Shorting Allowed?

I am looking for a formula to calculate the weights of two risky assets that produce the optimal portfolio (i.e highest Sharpe ratio). So far I have found the following formula from a website of ...
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1answer
955 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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1answer
47 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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1answer
160 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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0answers
181 views

Optimisation problem with bid-ask spread

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 ...
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1answer
461 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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2answers
250 views

Backtest Results needed to Model Validate my Modern Portfolio Theory model

this is my 1st post, and I hope someone can help me! I have been searching for a week now without any luck I have built a Portfolio Allocation model based on Modern Portfolio Theory (MPT). I now need ...
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0answers
157 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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1answer
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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1answer
855 views

Derivation of the efficient frontier set (markowitz problem)

I would like to find a Derivation of the efficient frontier set for the markowitz problem:
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1answer
226 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 ...
0
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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)