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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 Optimization Maximizing Sharpe Ratio Allowing Shorts [closed]

hope you find all well I'm currently exploring portfolio optimization techniques aimed at maximizing the Sharpe ratio while allowing for short selling. My constraints are upper bound of 0.5 and a ...
WatchMeScale's user avatar
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Excess Return Covariance Matrix is Singular - Cash return and risk free rate are the same [closed]

I've created a three asset excess return covariance matrix. The assets are; equity, bonds, and cash. However, my cash return is the same as my risk free rate ( i.e. 3 month Euribor). This is leaving ...
Farrep7's user avatar
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Reverse optimization: How to generate the expected portfolio returns given the weights and a series of constraints on those weights?

I have the below function in Python. My objective is to back out the expected returns associated with certain portfolio weights given a series of assumptions. From this I want to generate the expected ...
Farrep7's user avatar
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How to construct a delta-neutral portfolio containing stocks using correlations?

I’m aware of the mean-variance framework where we construct a portfolio such that we attempt to minimise the variance and maximise returns. What if instead we’re in a scenario where the main goal is ...
Xerium's user avatar
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Bonds in a zero interest rate environment

I've been looking at Pension Fund asset allocations. Why would they have any allocation to bonds in an zero interest rate environment? To make the point, let's assume the interest paid on these bonds ...
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How to prove that the feasible set of a two-asset portfolio is a hyperbola?

The question comes from ‘Mathematics for Finance: An Introduction to Financial Engineering’ by Marek Capiński (Author), Tomasz Zastawniak. The book does not give a complete proof, and I did not find a ...
bokabokaboka's user avatar
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Conic form of maximizing Sharpe ratio with long-short constraints

I read the blog post of mosek software package and learn how to transform the original form of maximizing the Sharpe ratio to the conic form. We consider the following optimization problem $$ \max_{x\...
Simon Pun's user avatar
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Portfolio optimization with Scipy in Python

I performed Scipy portfolio optimization in two scenarios: 1) when I cannot lend or borrow at the risk-free rate; 2) when I can lend and borrow at rf=1.5%. Now, optimal risky portfolio weights anyway ...
Maurizio Marinaro's user avatar
2 votes
1 answer
220 views

When optimizing a portfolio for risk parity, can any portfolio weights turn negative?

As the title reads, when performing risk parity optimization (equal risk contribution amongst all assets to the portfolio volatility), is it possible for weights to turn negative? I understand that in ...
KaiSqDist's user avatar
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Robust or Stochastic Optimization Approach for Maximizing Profit with Limited Price Information

I am tackling a linear maximization problem where I need to select the optimal product among several options over a series of weeks, given certain constraints, in order to maximize future profit. The ...
anasse's user avatar
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If an option is undervalued, how does shorting a portfolio generate profit?

I am reading Hull's Options book. He introduces a one-step binomial model and a no-arbitrage argument, using the example shown in the picture below: Consider a portfolio consisting of a long ...
user546106's user avatar
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Multifactor model assignment problem

Consider the following two-factor model for the returns of three stocks:. Assume that the factors and $e_{j}$ have a zero mean, that all the factors have a variance of 0.01 and are uncorrelated, and ...
Aradhana Saha's user avatar
2 votes
1 answer
149 views

Optimal weights in portfolio after rebalancing

I have a quite simple question but while looking for answers in research papers I couldn't find anything. The question can be summarized as : if you expect a shock on an asset, why don't you rebalance ...
krauuuus's user avatar
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How to calculate historical returns and variance for a non-BAH trading strategy?

Suppose i have a strategy that is not buy-and-hold type of strategy. It can have unique entry timing and unique exit timing for a single asset and both long and short positions will be allowed, and ...
Kevin Kim's user avatar
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Question about marginal risk contribution / portfolio volatility decomposition

I am trying to understand the rule where you add a new asset to a portfolio if its Sharpe ratio is greater than the product of the portfolio sharpe ratio and the correlation between the portfolio and ...
Steve R's user avatar
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55 views

Measure of hedge efficacy or other means to compare hedging strategies?

Is there a measure of hedge efficacy or another means to compare hedging strategies? I have seen Institutional Investors take very different approaches to tail hedging. On one extreme, I have seen ...
AlRacoon's user avatar
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Application of Leverage in Different Interest Rate Environments to an Efficient Portfolio

I have read that some Institutional Investors are utilizing leverage. According to Modern Portfolio Theory, to apply leverage one would: a) find the tangency portfolio on the efficient frontier from ...
AlRacoon's user avatar
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Constructing a Corporate Bond portfolio?

Is it possible to create a corporate bond portfolio such that its yield is 100bps higher that its benchmark, while still outperforming the benchmark (BBG Corporate bond Index)? I guess my question is ...
the_brass_bottle's user avatar
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Analytical solution to short-sale constrained portfolio

Say that we want to find the efficient mean-variance portfolio (i.e. minimize variance given that weights sum to 1 and given a set target return) and impose a short sale constraint such that $w_i \geq ...
Mr Entscheidung's user avatar
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What is Ei in paper "How to Combine a Billion Alphas" by Zura Kakushadze? [closed]

I am reading paper "How to Combine a Billion Alphas" by Zura Kakushadze. In the paper, it has Ei which are the expected returns for alphas. It also has Ri hat as follows. I wonder what the ...
Li Mike's user avatar
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Why not inequality constraint in mean-variance portfolio optimization?

Question 1: In Modern Portfolio Theory, the case where we minimize variance given a set return and that the weights sum to 1, why is the return set as an equality constraint, not an inequality? ...
Mr Entscheidung's user avatar
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Calculate minimum variance hedge ratio for foreign-denominated asset hedged to domestic currency

The formula for minimum variance hedge ratio (MVHR) is conceptually the correlation multiplied by the ratios of volatilities. correl (Y,X) * (STDEV Y / STDEV X) ...
sjedi's user avatar
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About the problem of maximizing Sharpe ratio [closed]

Regarding this problem, is this equivalent to optimize the standard mean variance portfolio and then comparing the Sharpe ratio of all the portfolio along the efficient frontier? Edit: Instead of ...
D H's user avatar
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Combining trading signals (equity long/short strategy)

Currently, I have developed three separate trading strategies on equity securities. All involve taking long and short positions in the top and bottom decile with respect to some measure (say, a ...
StackExchangeDisplayName's user avatar
3 votes
1 answer
301 views

Given a statistical model which predicts price, how to determine trading strategy?

Let us assume that we have a statistical model such as ARIMAX that predicts the daily closing price of an asset for the next 30 days. Assume starting capital of $1mn. The model will make new ...
MilTom's user avatar
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1 answer
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Portfolio Optimization with ETFs and Futures

I am looking to perform portfolio optimization with a single ETF (or two) and a VIX futures (with the possibility of adding an additional hedging instrument). Here are some features of my portfolio ...
KaiSqDist's user avatar
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3 votes
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Option-like behaviour of momentum strategy

this may come as rather vague question, since I do not have something very exact issue on my mind. Nevertheless, I think this is an interesting question and must have been thought by some other people ...
blizzard16's user avatar
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12 views

constrains of return distribution and risk return trade off

Suppose we have a portfolio $V$, we are only allowed to invest in one stock $S$, its price movement follows the geometric brownian motion, i.e. $dS=S(\mu dt+\sigma dW)$. We are allowed to choose ...
Mango's user avatar
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How can equilibrium weights be found for momentum factor in Black-Litterman model?

I have a momentum factor which consists of going long in three rising ETFs and going short in three falling ETFs. I want to use this factor as part of my portfolio for Black-Litterman model, however I ...
Karina's user avatar
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What is the correct method to maximize information ratio ex ante of a 150/50 portfolio against the S&P500

I have no problem forecasting and minimize ex ante information ratio for a market neutral portfolio, because the benchmark is just zero and you are just minimizing portfolio variance while maximizing ...
xxanissrxx's user avatar
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Two different ways to optimize ex-ante correlation of a long / short portfolio

Assuming I am making a long/short portfolio of S&P500 stocks and I would like to use the historical correlations to minimize ex-ante portfolio volatility. I can think of two ways of doing this: ...
xxanissrxx's user avatar
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29 views

Minimizing tracking error for a 150 / 50 portfolio against the S&P500

I am trying to minimize tracking error ex-ante for a 150 / 50 portfolio, eg. it is 150 units long, 50 units short and market exposure of 100 units. It uses all 500 stock in the S&P500. I've ...
xxanissrxx's user avatar
2 votes
0 answers
41 views

Intuition behind portfolio weights with lower RMSE but higher variance

I have recently encountered a phenomena in portfolio optimization that has baffled me for days. I was experimenting with different ways of transforming a covariance matrix to get a stable minimum ...
Jay's user avatar
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1 answer
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Volatility Tax/Variance Drag and Drawdowns/Breakevens

been reading about Drawdowns and respective returns to get back to breakeven as shown below: Many cite this as an evidence of the well publicized Vol Tax Formula (Geo Mean = Arithmetic Mean - 0.5*...
nzc's user avatar
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0 votes
1 answer
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Asset Management (Inverse Matrix, MVP,TP etc) [closed]

i just found this website and hope someone can help me. We have a midterm and we got 1 old exam but the Prof didnt want to provide the solutions and he is terrible anyway - so it kinda sucks, and i ...
user70385's user avatar
1 vote
0 answers
130 views

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 (...
rodrigo's user avatar
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0 answers
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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 ...
KaiSqDist's user avatar
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0 votes
1 answer
148 views

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 ...
T123's user avatar
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0 answers
77 views

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 ...
Michael's user avatar
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1 answer
112 views

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,...
Kenfisherman's user avatar
1 vote
0 answers
35 views

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 $N$ ...
Nick's user avatar
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1 vote
0 answers
97 views

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{...
pshhhhhttttttttt's user avatar
1 vote
0 answers
102 views

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 ...
PyRsquared's user avatar
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1 answer
86 views

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\% &...
mjc's user avatar
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0 answers
32 views

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 ...
gerscorpion's user avatar
2 votes
0 answers
33 views

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 ...
user1120695's user avatar
1 vote
0 answers
135 views

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 ...
user947967's user avatar
0 votes
0 answers
56 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 ...
KaiSqDist's user avatar
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2 votes
0 answers
64 views

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 ...
K. Leblora's user avatar
1 vote
1 answer
228 views

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 ...
soulsbornefan's user avatar

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