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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Portfolio construction in the real world [closed]
Good day. I am looking to understand how the portfolio construction process is actually done in the industry. Now, I do not know if there are too many resources on how things are currently being done (...
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Constraints in a Mean-Variance Optimization Case
Might be a repeat question, feel free to close if it is.
I am trying to perform a mean-variance optimization (maximizing the Sharpe ratio) for lets say 5 assets. Besides the weights of the assets ...
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Calculation of break-even correlation for diversification effect in N-assets case?
I'm thinking about a generalization of the following case: for 2 assets, there is a diversification effect as soon as i obtain a positive weight for the minimum-variance portfolio in the asset with ...
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Backtesting on factor model residual returns
I've heard in quantitative equity strategies, people backtest signals on residual returns. How does this work in practice? Do people find signals that forecast residual returns and then run the full ...
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When you have negative weights in the context of portfolio construction, what is the correct way normalize them?
For context, I am building an eigenportfolio following the conventions of Avellaneda and Lee Statistical Arbitrage in the U.S. Equities Market (2008), and I get negative weights for eigenportfolios 2,...
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Subportfolio optimisation and asset clustering with maximum cluster cardinality constraint
Assume that $N \in \mathbb{N}$ assets are given, but the portfolio optimisation algorithm can only compute portfolios with $m<N$ assets. To compute a portfolio, I would like to cluster the $N$ ...
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Maximising sharpe of portfolio with equal weights
I want to maximise $\frac{w^T\mu}{\sqrt{w^T\Sigma w}}$ with $w_i$ either 0 or $\frac{1}{\#\text{nonzero weights}}$.
This is the same as maximising $\frac{\tilde{w}^T\mu}{\sqrt{\tilde{w}^T\Sigma \tilde{...
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How to adjust an assets position to target volatility in a long-short portfolio?
I have a portfolio of weights $\mathbf{x}$ where some positions in $\mathbf{x}$ are short s.t. $\Sigma_i x_i=0$ (dollar neutral).
The standard way to estimate the volatility contribution per asset is ...
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What do the existence and parameters of an efficient investment tell you about the value of a risk-free return?
I'm working on an unassessed course problem,
Consider the following risky investments \begin{matrix}
\text{name} & \text{expected return} & \text{standard deviation of return} \\
A & 9\% &...
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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 ...
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Are there known benchmark examples where Cover universal portfolio performs better than naive uniform CRP and Split-and-Forget?
I am investigating the performance of Cover universal portfolios cf. https://en.wikipedia.org/wiki/Universal_portfolio_algorithm (and references therein).
I would like to know if there are any ...
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Reliability of R Package on Covariance Matrix Shrinkage
I recently used a R package CovTools in R with the command CovEst.2003LW(X), where X is your sample covariance matrix as an input, to compute the shrunk covariance matrix (an estimate that is closest ...
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Combining many trading strategies in an efficient
I have a lot (>50) of back tested (and naively "validated") trading strategies. They trade different ETFs, mostly equities, but also others (like GLD, USO, ...). These are all strategies ...
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Calibration of Covariance Matrix for a Cumulative Period Return
I am trying to compute optimized weights (minimum-variance portfolio) for a cumulative return over a period (weekly or fortnightly). In a daily return setting, it is quite simple, I just compute a ...
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Portfolio construction: Over/underweighting assets with a given active risk budget
I am trying to refresh my knowledge of portfolio risk calculation but would like to get a second opinion on the best approach.
I have a set of 10 assets that together make up the benchmark and I have ...
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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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Interpretation of optimal weights in portfolio for risk-adjusted return maximization
To start, I'm not an expert in portfolio management. My research involves examining the effects that one financial asset has on another, specifically looking at the spillovers between cryptocurrency ...
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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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PCA for portfolio optimization (Markowitz)
Suppose that I've used the spectral theorem of linear algebra to completely decompose the covariance matrix. I now know the largest and smallest eigenvalue, which corresponds to the largest and ...
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Maximizing the expected log utility
Let's assume that we have a self-financing portfolio made by $\delta_t$ shares and $M_t$ cash, so that its infinitesimal variation is:
$$
dW_t = rM_t \, dt + \delta_t \, dS_t
$$
We define $\alpha_t$ ...
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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 (...
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What do we know about "overconfidence" w.r.t asset characteristics and how can the overconfidence bias be implemented in a Markowitz portfolio modell?
Disclaimer: I have a simnilar question already in quora with some answers which are good but not really satisfying (they were taken from Wikipedia or ChatGDP).
If I break down overconfidence into ...
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Portfolio risk of correlated assets using Mahalanobis distance
I am trying to understand if there is an agreed methodology to measure the total risk in a portfolio of correlated assets.
I am taking a simple model of stock prices following geometric Brownian ...
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How to find the expression for the SDF and solve this exercise?
I'm struggling to solve point a and b of this exercise, while in point c I got a very close result to the reciprocal of the relative risk aversion. If you can help me and explain how to do it, it ...
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Maximising skewness for a portfolio
I am trying to recreate the Mean-Variance-Skewness-Kurtosis-based Portfolio Optimization work done by Lai et Al. (2006) (link).
I reached the part where in order to run the PGP model, you need to feed ...
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Static Multiperiod Optimal portfolio
I am interested in optimal portfolios in a multi-period setting
To be more precise, say I have an investment horzion over $T$ periods and the market consists of $N$ assets. I simulated future asset ...
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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 ...
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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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Effect size for information coefficient
The information coefficient is the correlation between a signal $g(t)$ and returns $r(t)$. I’m hoping to build some practical intuition on the information coefficient.
Similar to the notion of effect ...
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Linear programming and factor models vs M-V optimization?
I have been recently researching about portfolio optimization problems and it is unclear to me what is currently the state of art modeling choices when it comes to this topic.
On one hand, I've ...
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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 ...
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negative portfolio variance? Creating a positive semi definite matrix in excel
I am attempting a portfolio optimization model and ended up generating negative portfolio variance using 2WaWbσaσbcorrel(a,b) or 2WaWb*Cov(a,b)
From reading the linked article where other users had an ...
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Information Ratio Confusion in Grinold's Signal Weighting Paper
In the procedure Grinold outlines in his 2010 paper "Signal Weighting" for optimally combinining $J$ raw alphas, $\mathbf{a}_j$, he first assumes each $\mathbf{a}_j$ has been scaled so its ...
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Question about adding new investment A to portfolio B
I've found a ton of sources that mention the classic rule of
"If the Sharpe ratio of the new asset is greater than the Sharpe ratio of the existing portfolio times the correlation of the existing ...
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Selection of Risk aversion in portfolio optimization
I have a portfolio of equities with a cross-sectional score as expected return (mean=0) and am using mean-variance optimization. However, the question is how one selects the risk aversion parameter. ...
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How can one quantify the incremental value of better covariance matrix modeling in portfolio optimization?
Let's say we have two estimators of the covariance matrix, $\hat{C}_1$ and $\hat{C}_2$, and the latter is an improvement on the former.
Is there any measure of the improvement that can be sensibly ...
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How to solve for the optimal portfolio weight with target variance?
I'm confused a bit with the following problem:
As far as i understand, the following problem where
$$\min_{w} \omega^{T}\Sigma\omega$$
$$\textrm{s.t.}\hspace{0.5cm} \omega^{T}\mu=E$$
$$ \omega^{T}\...
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Terminology: "global" in "global minimum-variance portfolio"
I am confused about the meaning of "global" in "global minimum-variance portfolio". The sources that I have encountered so far do not explicitly state what "global" means....
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"fix" a sample covariance matrix which is not positive semidefinite by using daily returns instead of monthly
In the portfolio optimization problem at hand, one of the constraints is that the tracking error should not be greater than $\gamma$.
The constraint is therefore:
$(\textbf{x}-\textbf{w})^\mathrm{T}\...
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How to derive the optimal option structure given investor views, i.e. is it optimal to buy a call option, a risk reversal or a butterfly
Optimizing a position typically requires two things:
An assumption about how prices will behave in the future
An objective function to maximize/minimize
For certain cases in finance, we have closed-...
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Markowitz Eigenvalues & PCA
I came across this passage in a book about PCA and denoising of Markowitz:
But eigenvalues that are important from risk perspective are least important ones from portfolio optimization perspective.
...
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Portfolio factorization for portfolio optimization
I am looking to do some basic portfolio constructions as an experiment to learn more about it. I have been researching a bit and what I have found is that one of the purposes of factors models (Fama-...
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Wider VaR for portfolio risk?
Is there a way to widen the 95% VaR by changing the distribution of a portfolio of stocks? When calculating 95% VaR of my portfolio using the holdings based approach (which requires the covariance ...
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How to express the process of number of stock (nt) in a portfolio using ito's lemma
We have a regular self-financing portfolio $W_t$:
$$dW_t = n_t dS_t + (W_t − n_t S_t) r dt$$
Where $W_t$ is total wealth, $n_t$ is amount of stock, $S_t$ is stock price, $r$ is the risk-free rate.
And ...
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Optimal portfolio as combination of target and minimum tracking error portfolios?
Dear Quant StackExchange
I seek some intuition for how my portfolio behaves given constraints.
In a universe of say 5 assets, I have a "target portfolio" with weights that are found from ...
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Tail Risk Hedging for Public Pension Plan
Very simplistically, ERISA rules require corporate pension plans to use market rates to discount their liabilities. If interest rates go up, the value of their pension liabilities goes down. Since ...
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Is It necessary to make each strategy's volatility almost equal before solving weight when constructing a risk parity portfolio? Or use other model?
Say I want to construct a portfolio consisting of different trading strategies (but trades same pool of assets) with cross-sectional varying volatility. It makes me feel uncomfortable since the one ...
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Faster Portfolio Optimization under rank 1 updates
I was studying Markowitz portfolio optimization and had a question on the practicality of this in the setting of high frequency trading. Optimization seems like a cumbersome process. But at each tick ...
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Is there economic/intuitive reason why the treynor-black model favour low delta instruments?
In the treynor-black model optimal instrument weights are proportional to:
$w_i = \frac{\frac{\alpha_i}{\sigma_i^2}}{\sum_j \frac{\alpha_j}{\sigma_j^2} }$.
Let Instrument 1 be a stock with $\alpha_1$ ...
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Risk Budgeting with negative covariance
Let's say I want to optimise allocations between strategies in a multi-strategy fund.
There are 3 strategies, and the CIO want me to solve the portfolio that has 50% of risk in 1st strategy, 40% in ...
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