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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The use of L2 Regularization in portfolio optimization
In portfolio optimization, the goal is to calibrate the weights of assets in a portfolio according to a stated objective (mean-variance, minimum-variance, risk parity etc.). Often, mean-variance or ...
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Discrepancy in Ulcer Index calculation with the Riskfolio-Lib library
I am using the Riskfolio-Lib Python library to calculate the Ulcer Index. When I run the function, the values I get are on the order of hundredths (for example, 0.0X).
My issue is that, based on other ...
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good practices for computing expected returns for portofolio construction [closed]
I am currently studying portofolio construction and am trying to construct one using an extended Markovitz setting, which will give me the weights after solving.
My problem is the computation of ...
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CVaR/VaR-based Sharpe ratio calculation problems
guys.
Currently I'm trying to realize one portfolio allocation model. I have n-1 risk assets and 1 fully unrisk asset.
So, at i ...
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Stock clustering as a part of portfolio diversification
I have a research hypothesis and now I'am trying to look at it from different angles.Now I am a bit puzzled.Maybe someone is also interested in machine learning application(especially clustering) in ...
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Clarification regarding solution to Call-Options Arbitrage question
I'm having a hard time understanding the solution to the following problem from Dan Stefanica's book "A Primer for the Mathematics of Financial Engineering":
Call options with strikes 100, ...
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Comparing optimal strategies in Black-Scholes model with python
Consider the 1-dimensional Black-Scholes model
$$dS_t = S_t(\mu dt + \sigma dW_t)$$
$$dB_t = rB_t dt$$
Given a maturity time $T$, by martingale method the optimal discounted portfolio at the maturity ...
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How to perform a long short risk budget optimization?
In their paper titled "Trend-Following meets Risk-Parity" UBS proposed an optimization algorithm for performing risk budgeting for long short portfolios. The formulation was as follows:
$$ ...
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Advanced utility functions that distinguish risk from uncertainty
During my reading of Investments by Bodie, Kane & Marcus (a textbook in finance), in section 5 (Risk Tolerance and Asset Allocation) of chapter 6 (Capital Allocation to Risky Assets), I found this ...
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Treynor and Black (1973) Equation 13 usefulness
Equation (13) in Treynor and Black How to Use Security Analysis to Improve Portfolio Selection (1973) gives the optimal weights using the formula:
In practice, I have seen the rightmost fraction ...
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Transforming portfolios when transforming factors
This should be a relatively simple, mostly linear algebra question. It starts with factors, let's say 50 of them. Each factor has a time series of returns, let's say 250, and an associated portfolio ...
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Bond portfolio optimization with Python reaching iteration limit
I am using scipy to optimize a hypothetical bond portfolio for maximum yield by choosing from a list of bonds in the portfolio's investable universe while adhering to portfolio constraints such as ...
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risk parity portfolio from scenario optimization
would like to ask how we could use simulated asset returns (a matrix $R\in\mathbb{R}^{s\times d}$ from scenarios, row per sample and col per asset) to construct a risk parity portfolio (RPP).
by ...
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Excess Return Evaluation Bias
Im currently working on a Alpha and Risk Model for constructing portfolios. From what Ive read on books and here, they are constructed in a different way and produce differents results. My Risk Model (...
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Why minimum variance portfolio is used to construct factor models
I am reading Tsay's classic "Analysis of Financial Time Series" and I have seen him using minimum variance portfolio
Relevant passage on the minimum variance portfolio here (Chapter 9, Page ...
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Setup for proving equation 3.4 from Grinold
I'm studying from Grinold's Active Portfolio Management right now, and used the below equation to answer one of the exercises:
.. let us assume that the correlation between the returns of all pairs ...
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Proof of weights maximizing sharpe of a portfolio
Given a portfolio of $n$ assets with mean vector $\mu$ and correlation matrix $\Sigma$, the optimal weights $w$ on the $n$ assets to maximize overall sharpe is found by
$$\max_{w:||w||=1}{\dfrac{\mu^T ...
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Scenario in portfolio optimization
I'm very confused in various formulations of "scenario" in portfolio optimization related articles. Can somebody describe me what exactly is scenario in this case?
I see different approaches ...
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Stochastic optimization for day trading
Suppose we have a forecast of price changes for a set of assets and we want to day trade based on it. I'm guessing this would involve some kind of stochastic optimization - with presumably a decision ...
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Reverse Optimization: finding the returns that satisfy specific weights given one known return
Here is the premise: I have a three asset portfolio, I know the assets covariance, the client's risk aversion and the expected return of one of the assets. I also have a desired set of weights.
So, 1) ...
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How do I reformulate this max GMV ratio constraint in convex way?
Let $n$ be the number of stocks in my portfolio. I would like to have the following inequality constraint in my optimization problem
$$ |x_i| \le \alpha \sum_{j=1}^n | x_j | $$
where $\alpha$ is known,...
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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 ...
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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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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 ...
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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 ...
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