Questions tagged [portfolio-optimization]

Questions related to mathematical methods used for searching of optimal portfolio structures. Also related to questions on optimal structure of portfolios from both strategic and tactical point of view

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4 votes
2 answers
948 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 ...
1 vote
2 answers
272 views

text books or online courses for a math student to learn asset pricing [closed]

I just got my bachelor degree in math and statistics and will take a mathematical finance master degree. I have not learned any financial courses and want to teach myself asset pricing. I have seen ...
0 votes
1 answer
75 views

Algorithm / formula / method to determine optimal weightings given expected return, % of volume and slippage

Please bear with me - I know I'm supposed to do this with a bunch of Greek letters but I don't know how so I'll just describe the data I have and what I am trying to do. I have an expected return for ...
5 votes
2 answers
162 views

Help guessing the solution to an optimal control problem

I am considering an investor facing a discrete-time multi-period minimization problem $$ \min_{\{v_t\}_{t=0}^\infty}\Bigg[\sum_{t=0}^\infty(1-\rho)^{t+1}\bigg(\frac{1}{2}v_{t}\Omega_{t+1}v_{t}'\...
1 vote
0 answers
54 views

Have more complex MVA-style models become obsolete?

Just reading a book about about portfolio optimisation. You hear left and right that MVA (Mean Variance Analysis of Markowitz) is out of date, creates suboptimal portfolios in practice and so on ...
2 votes
2 answers
325 views

Kelly Criterion applied to portfolios vs Markowitz MVA

I have recently watched two videos about Kelly Criterion for portfolio optimization, however one seem not to deduce it correctly (as people commented) and the another just don't show any deductions at ...
1 vote
2 answers
201 views

Is optimising for the Final Wealth is the same as optimising log of growth rate in Kelly Criterion?

A direct, brute force approach could be used to find the Optimal Portfolio. Consider simple play. There's a biased coin with 55% probability of win. The simulator play as a single person with 100$ ...
1 vote
2 answers
108 views

Can I apply the Kelly criterion directly, without fitting any distributions?

Problem I want to apply the Kelly criterion to asset returns, so that I know how much to hold of each, ideally (and how much I should keep as a cash reserve). As far as I understand the Kelly ...
0 votes
1 answer
83 views

efficient frontiers are equal

I created 3 different efficient frontiers with 3 different risk factors(sharpe ratio, ulcer performance index and serenity ratio) and I wanted to find both MSR and GMV(and their equivalent for the ...
1 vote
1 answer
132 views

Why the portfolio return is defined as a weighted return?

After reading the modern portfolio theory, I am wondering why the portfolio return is defined that way. Suppose there are $n$ assets in a portfolio, the simple return of an individual asset $i$ at ...
9 votes
1 answer
327 views

The optimization problem of the equal risk contribution portfolio

I try to understand the equal risk contribution (ERC) portfolio as described in On the Properties of Equally-Weighted Risk Contributions Portfolios by Teiletche and Roncalli. For a given covariance ...
0 votes
1 answer
87 views

What is industry best practice to combine alphas?

Say I have 100 different alphas that all have statistically significant returns in-sample. Is the best practice to use historical covariance matrix plus Markowitz portfolio theory to create an optimal ...
2 votes
0 answers
96 views

Portfolio construction for almost identical assets

The problem I am looking at concerns the treatment of almost identical assets in portfolio construction. Let us assume that we have two assets, both with an expected return $\mu=0.1$, a standard ...
0 votes
0 answers
52 views

How to incorporate "correlation neglect" in a M-V-Framework?

at the risk of boring you with another behavioral finance question, i found a bunch of papers on a phenomenon dubbed correlation neglect, where economic agents misperceive the correlation structure of ...
0 votes
2 answers
249 views

How can I measure returns such that the average is useful?

If I measure daily returns by simple percent change, a -50% day then a +50% day (or vice versa) results in a true -25% total change, but the average makes it look like you would expect a total 0% ...
0 votes
0 answers
69 views

For mean-variance portfolio optimization, shouldn't all the allocations sum to 1?

Reading a paper by Black and Litterman, I'm having trouble understanding the set of valid allocations in which we're trying to optimize expected returns. In Table III, the authors show two portfolios ...
5 votes
2 answers
1k views

How to derive portfolio weights from risk budget

Goal: I'm trying to frame target volatility investments given some view on what asset to overweight. For example, starting with a risk-parity allocation, tweak the marginal risk contribution of each ...
1 vote
1 answer
534 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 ...
2 votes
1 answer
144 views

Utility Theory and Mean Variance Analysis

I was wondering if it's pertinent to use this interpretation of the expected utility function given by the Taylor series expansion, $${E(U(W)}\approx{U[E(W)}]+\frac{U''[E(W)]\sigma^2_W}{2}\tag{1}$$ to ...
0 votes
0 answers
57 views

Why weigh assets by market values in CAPM?

Can anyone help me understand as to why in CAPM's market portfolio investors will always have the assets in proportion to the market value? One of the intuitive reasonings that I have read explains ...
1 vote
1 answer
133 views

Are there optimal portfolio theories than instead of the expected value they were based on the Mode of distributions

Are there optimal portfolio theories than instead of the expected value they were based on the Mode of distributions? During my engineer student days I saw the Markowitz theory for portfolio selection ...
0 votes
1 answer
117 views

Is it possible to construct an efficient frontier without the mean?

If we assume the estimator for a sample mean is biased and if the optimal portfolio weights vary with the estimated mean, is there a way (similar to the zero beta portfolio approach wrt the risk free ...
0 votes
0 answers
54 views

how can I linearize a constraint of the form sum(min(x(i),y(i))) for a linear optimisation problem?

I have an linear optimisation problem with the objective : $ max PortfolioSpread(x_1,x_2,....x_N) = ∑_{i=0}^N(x_i*s_i)/budget$ s.t. $∑_{i=0}^N x_i = budget$ (+ other constraints) $∑_{i=0}^N min⁡(x_i,...
1 vote
1 answer
718 views

how to use factor models to construct a hedging portfolio?

This is a new project for work that I am stuck on and looking for help: If i am given a factor model (e.g. barra) and a equity portfolio we're trying to hedge, how can I come up with a hedge portfolio ...
1 vote
1 answer
75 views

Hedging with peer companies and optimize the weights

I am trying to long a security that is expected to outperform its peers after certain corporate actions, but want to hedge using the same group of peers (so short ~5 names). So the goal here is to ...
1 vote
0 answers
49 views

Hedging large single asset positions

I recently came across an article that described how big market participants like GS, JPM, etc. take off large equity positions (block trades) of their clients, and putting that risk on their own ...
5 votes
1 answer
217 views

Portfolio construction: If modern portfolio theory is not good than what else?

MPT and Mean Variance optimisation do not take into account fat tails and many other things like the problema in estimating the co variances etc. Nassim Taleb has been arguing this for a long time, ...
2 votes
1 answer
111 views

Portfolio Optimization Problem

I have the following expression for which I wish to find the $\vec{w}$ which minimizes it: $$ L = \frac{\vec{w}^TA\vec{w}}{\vec{w}^TB\vec{w}} - \lambda(\vec{w}^T\vec{1} - 1) $$ The partial derivates ...
1 vote
1 answer
114 views

Is float32 enough for option pricing?

Most quantitate libraries use float64 precision for monte-carlo or other method. Some academic papers do experiments on float16 and find it has some restrictions on float16. I just wondering if ...
7 votes
4 answers
12k views

Why do we assume quadratic utility in portfolio theory?

In my text (Investments by BKM), the investor's mean-variance utility (given as $U = E[R] - \frac12A\sigma^2$) is stated to be the objective function we wish to maximize. Upon further digging, it ...
3 votes
2 answers
113 views

Is there a performance measure for the entire efficient frontier?

The Sharpe ratio is an example of a performance measure for individual mean-variance efficient portfolios, regardless if they maximize the Sharpe ratio or not. The efficient frontier, however, ...
0 votes
0 answers
23 views

Computing the highest vol for worst-of basket

I would like to ask a very general question. I am not expecting a closed-form solution to this problem so, any, help, idea or suggestion will be welcome. Suppose that we have a bunch of X stocks (10 ...
4 votes
0 answers
90 views

Why does the mean term have a higher effect than the covariance term in MV optimization? [closed]

I am trying to use the mean-variance (MV) optimization framework. When I change the mean term using future-ground-truth return (I am not supposed to do so), it has a higher effect on the MV ...
0 votes
1 answer
47 views

How to optimize two highly correlated risky assets?

Suppose you have two highly correlated risky assets. Correlation coefficient: 0.9 Volatility: Asset 1 price varies 2.5% /day Asset 2 price varies 5% / day What can be done to do reduce the risk and ...
3 votes
1 answer
275 views

PortfolioAnalytics and regime switching issue

I've been playing around with the R package PortfolioAnalytics and I have spent more time than I'm willing to admit to try and resolve this issue: When I follow the regime switching example with the ...
2 votes
2 answers
524 views

What's the point of resampling?

Resampling is a popular method for portfolio optimization. We repeatedly draw samples from a distribution, compute the optimal mean-variance portfolio and finally average over all allocations. However,...
0 votes
0 answers
63 views

Index Tracking Problem

I have set up a mean variance optimization problem, $$min:{W}^{\prime}{\Sigma_{\varepsilon}{W}}$$ $$s.t:{W}^{\prime}{\alpha}=R_B\;,\;\;W^{\prime}l={1},\;\;W'\beta=0,\;\;W'Z=\beta_p$$ where, $W$ is an (...
0 votes
0 answers
142 views

Sampling in Portfolio Optimization

I recently came across the following method for portfolio optimization: Let $Y$ be a random variable that describes the returns of $n$ assets. Fix a constraint matrix $A \in \mathbb{R}^{m \times n}$ ...
0 votes
0 answers
58 views

What could be a real-life example of sectors and instruments in a Financial Market in the context of this Portfolio Optimization Problem?

Recently I've been reading about mathematical models in finances and economics; however, I encountered this book chapter: Nagurney, A. (1993). Financial Equilibrium. In: Network Economics: A ...
2 votes
1 answer
110 views

How to incorporate ESG in Portfolio Optimization?

I currently have a potential investment universe of several thousand stocks and would like to calculate an optimal portfolio that incorporates ESG criteria as well as risk and return. The model should ...
2 votes
0 answers
53 views

Dynamic portfolio optimization with cumulative prospect theory

i'm new to this forum and i hope i can get some help or at least some guidance how to tackle the following problem: I'm tasked to write a VBA Macro that conducts an intertemporal portfolio ...
0 votes
0 answers
45 views

Portfolio optimisation with estimated positive and downside returns

What are the approaches to optimise a portfolio where for each security the analyst specifies expected return (10%) and downside risk (-3%)?
0 votes
0 answers
40 views

Portfolio optimization - Correlation risk stress testing - DCP

I have a script based on Python/CVXPY trying to define the portfolio with the maximum expected return, given some risk constraints. I would like to introduce a constraint that limits correlation risk. ...
1 vote
0 answers
98 views

Portfolio optimisation approach used in the industry

I was wondering what portfolio optimisation is used by professionals. I know about these 3: Mean-variance Black-Litterman Kelly Criterion Which one is preferred? Is there some other more robust ...
0 votes
0 answers
68 views

Kelly criterion for portfolio optimisation with variance optimisation

I was wondering how Kelly criterion can be used for portfolio optimisation in the case one would like to optimise the portfolio for minimum variance. I understand how the Kelly criterion can be used ...
0 votes
1 answer
59 views

Pareto comparison of return distributions

In making a choice among financial strategies, each of which has some estimated return distribution, some strategies will clearly be better than others. But many times, the choice is a question of ...
0 votes
0 answers
73 views

Why do we use half of the risk in objective function of markowitz portfolio theory

In some documents I have seen objective function of markowitz portfolio theory is as follows. minimize 1/2 * w'Σw where w is weights Σ is covariance matrix I could ...
0 votes
0 answers
118 views

Why is the Sortino ratio non convex and also non concave?

I am considering as my objective the Sortino ratio: $\frac{\mu^{\top}x-R}{\sqrt{\mathbb{E}[(min\{0,(r-\mu)^{\top}x\})^2]}}$ In my textbook they state that this ratio just like the Sharpe ratio is ...
0 votes
0 answers
72 views

Risk Factors, Portfolio Optimization

I really need help with a project that I am working on, for my university.I study in Ecuador and the research material here is very limited. Nonetheless I have tried my best to start with the basics ...
2 votes
1 answer
142 views

Unexpected Inflation and Asset Allocation

If asset allocation decisions were made prior to the news of unanticipated inflation, how should asset allocators incorporate the fact the inflation is now 5% higher than the 2% inflation target? It ...

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