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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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 ...
1 vote
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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 ...
58 views

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 ...
1 vote
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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 ...
144 views

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 ...
1 vote
337 views

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 ...
166 views

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 $\alpha_t$ ...
116 views

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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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 ...
91 views

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 ...
152 views

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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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. ...
146 views

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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