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

Filter by
Sorted by
Tagged with
23 votes
5 answers
15k views

Portfolio optimisation with VaR or CVaR constraints using linear programming

I would like to optimize a portfolio allocation (maximizing the exposure or the expected return), but with VaR or CVaR contraints. (some parts of my portfolio cannot exceed a certain VaR) How can I ...
user avatar
  • 1,993
20 votes
4 answers
14k views

Why shrink the covariance matrix?

I'm trying to understand why it's useful to shrink the covariance matrix for portfolio construction or in fact general. Think I missing something. I know if you have 5,000 stocks it's a lot of ...
user avatar
  • 347
19 votes
3 answers
3k views

Hedging Covid-19 and other low probability high loss risks

Covid-19 and similar risks are low probability, high loss events. Does it make sense to utilize options to provide hedges for such events? For example, should one utilize long positions in deep out-...
user avatar
  • 5,325
17 votes
2 answers
930 views

Current industry standard for (active/passive) portfolio optimizations

By reading multiple research papers online. I realized the current portfolio optimization (industry standards) involves building factor models, perform (conditional) value at risk optimizations, (...
user avatar
  • 207
16 votes
1 answer
563 views

Are there references about liquidation, transaction, market impact costs in portfolio optimization

I am looking for some references treating of what I would call liquidation cost market impact cost transaction cost(*) in the usual "portfolio optimization problem under linear constraints". Let ...
user avatar
  • 1,248
16 votes
2 answers
2k views

Real world application of stochastic portfolio theory

There is a branche of stochastic portfolio theory (see also this question). Fernholz and Karatzas have published research in this field (e.g. "Diversity and relative arbitrage in equity markets") and ...
user avatar
  • 13.3k
15 votes
4 answers
3k views

Why is Markowitz portfolio optimisation so popular considering it is worse than an equal weighted portfolio?

The original paper by Markowitz from the '60s has ~20,000 citations (definitely popular). However several papers I came across show that a $\frac{1}{n}$ asset allocation gives higher Sharpe ratios (...
user avatar
15 votes
1 answer
2k views

Optimization: Factor model versus asset-by-asset model

In portfolio management one often has to solve problems of the quadratic form $$ w^T \Sigma w + w^T c \rightarrow \min_{\omega} $$ with portfolio weights $w \in \mathbb{R}^N$ a constant $c \in \mathbb{...
user avatar
  • 13.3k
12 votes
1 answer
214 views

portfolio optimization averaging weights, what are benefits?

I'm playing around with different portfolio optimization techniques. Amongst others I was also looking at the resampling method, especially the one described in Meucci. I have two general questions ...
user avatar
  • 1,638
10 votes
3 answers
9k views

Application of Control Theory in Quantitative Finance

I have recently completed an MSc in Control Systems from a top university. It seems to me that control theory must have an application within quantitative finance. I would like to apply my degree ...
user avatar
10 votes
1 answer
2k views

Minimum Variance and Minimum Tracking Error portfolio as second order cone program

The quadratic optimization (min variance) $$ w^{T} \Sigma w \rightarrow \text{min}, $$ where $w$ is the vector of portfolio weights and $\Sigma$ is the covariance matrix of asset returns, is a well ...
user avatar
  • 13.3k
10 votes
3 answers
413 views

SDF as an affine transformation of the tangency portfolio

I'm studying this paper. In the formulation of the theoretical setup they state: Our goal is to explain the differences in the cross-section of returns $R$ for individual stocks. Let $R_{t+1, i}$ ...
user avatar
10 votes
2 answers
2k views

Hierarchical Risk Parity with allocation constraints?

In the really interesting paper by Marcos Lopez de Prado a variation of risk parity is applied whereby the underlying assets of the portfolio are first split in 'correlation clusters' and the ...
user avatar
  • 441
9 votes
1 answer
5k views

cvxpy portfolio optimization with risk budgeting

I'm trying to do some portfolio construction in cvxpy in Python: ...
user avatar
  • 470
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 ...
user avatar
  • 13.3k
8 votes
3 answers
5k views

Maximum Sharpe portfolio (no short selling restrictions)

Suppose we have $n$ assets whose expected return vector is $r$ and is positive, and whose covariance matrix is $\Sigma$. Is there a closed form or quasi closed form (like the eigenvector of a matrix ...
user avatar
  • 921
8 votes
2 answers
2k views

Random Portfolios vs Efficient Frontier

I understand the concept of the efficient frontier and am able to calculate it in Python. But even when generating 50'000 random 10 asset portfolios, the single portfolios are not even close to the ...
user avatar
8 votes
2 answers
4k views

Portfolio Optimization : Shrinkage of Covariance Matrix when data is available

It seems that shrinking the covariance matrix is especially useful if the number of individual stocks is greater than the number of data points. However is there any special gain if you're not ...
user avatar
8 votes
2 answers
662 views

Utility Theory and portfolio optimization - Proof of a lemma

I have a question on the following problem from chapter 9 of D. Luenberger, Investment Science, International Edition: (Portfolio Optimization) Suppose an investor has utility function $U$. There are ...
user avatar
  • 147
8 votes
3 answers
352 views

Portfolio Theory: Why is so much effort put into the reduction of estimation errors?

In MPT, very much effort by researchers is put into developing methods and techniques to handle the rather poor performance of the estimated means, variances and covariances. There are shrinkage ...
user avatar
8 votes
1 answer
949 views

What's the importance of duality theory in portfolio optimization?

I'm interested in portfolio optimization and there's a lot of modelizations out there using duality theory. Since I didn't study that yet, I searched around the net to understand what it means and ...
user avatar
  • 287
8 votes
1 answer
597 views

How can I simulate portfolio risk (diversification) with a 'Wheel of Fortune' like investment options/returns?

Say I have 6 possible investment options with the following probability of success and the corresponding returns: ...
user avatar
  • 185
8 votes
1 answer
472 views

Overview of robust/regularized portfolio selection

I am looking for either a review paper or individual papers on portfolio selection using robust statistics or regularization (e.g. LASSO, Ridge, etc.) I.e. a review on methods along the lines of: M ...
user avatar
  • 125
7 votes
2 answers
892 views

how to choose top n assets?

I have m assets, and have estimated their future returns and covariance matrix. I would like to invest in an evenly weighted n product basket from this universe, where 0<n<m. How do i find the ...
user avatar
7 votes
2 answers
638 views

Maximum Certainty Equivalent Portfolio with Transaction Costs

Out of curiosity I tried to compute the portfolio weights of a maximum certainty equivalent allocation, however, by incorporating (quadratic) transaction costs. However, my result is not as intuitive ...
user avatar
  • 1,436
7 votes
2 answers
2k views

On learning the bayesian approach to portfolio optimization

I am required by my course to write a small paper on the Bayesian approach to portfolio optimization, I am following Applied statistical decision theory [by] Raiffa, Howard. Which can be consulted ...
user avatar
  • 357
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 ...
user avatar
  • 71
7 votes
1 answer
1k views

Why maximize expected growth rate?

It seems to me that the optimality of the Kelly Criterion relies on the assumption that it is in an investor's best interest to maximize his portfolio's expected growth rate. Why would he care what ...
user avatar
  • 537
7 votes
2 answers
2k views

Factor Model - Minimum Variance Portfolio [Complete Proof]

Can someone check my proof? I think there is something not quite right. I have found limited resources online for this as well so I think it might benefit others to get this on the internet. Assume ...
user avatar
  • 1,049
7 votes
1 answer
319 views

Question about quadratic form of f* in the Continuous Kelly Criterion

I am trying to follow the Optimal Kelly derivation on Wikipedia for two continuous assets: one risky and one risk-free. The derivation begins by assuming that the risky assets follows a GBM (a ...
user avatar
7 votes
1 answer
174 views

Finding a minimum variance portfolio when using a regulariser?

I am aware that the minimum variance portfolio of a market with $n$ securities can be shown to be: \begin{equation} w^* = (1^T_n\Sigma^{-1}1_n)^{-1}\Sigma^{-1}1_n, \\ s.t. \ \ 1^T_nw = 1 \end{...
user avatar
7 votes
2 answers
2k views

Beta Constrained Markowitz Minimum Variance Portfolio - Closed Form Solution

This question is related to recent rule changes in the Quantopian Open. I am trying to figure out a closed form solution to a beta constrained minimum variance portfolio problem but it doesn't seem ...
user avatar
  • 1,049
7 votes
1 answer
326 views

Stochastic control (HJB) for wealth process involving stopping times

Given a wealth process that evolves as $$d w_t = r w_t dt + \theta_t ( \sigma dW_t + (\mu-r) dt) - c_t dt.$$ where $\theta_t$ is the worth of holding at time $t$ and $c_t$ is the consumption stream. ...
user avatar
  • 632
7 votes
1 answer
2k views

Sharpe Maximization under Quadratic Constraints

When doing Sharpe optimization $$ \max_x \frac{\mu^T x}{\sqrt{x^T Q x}} $$ there is a common trick (section 5.2) used to put the problem in convex form. You add a variable $\kappa$ such that $x = ...
user avatar
  • 1,561
7 votes
0 answers
2k views

How good is the inverse-volatility portfolio?

Heuristic portfolio construction techniques include the equally-weighted portfolio (1/N) and the inverse volatility portfolio (IVP), which is based on the low-volatility effect. They can be assembled ...
user avatar
  • 2,835
6 votes
2 answers
586 views

Mean Variance Portfolio theory and real-world problem?

There are many assumptions on mean-variance portfolio theory and they seem to be very unrealistic, for example 1) investors have the same information at the same time: calculating expected returns ...
user avatar
  • 184
6 votes
4 answers
477 views

R: Book with extensive examples for either portfolio optimization or volatility forecasting?

I'm at a new job and there's the option to use R (you don't have to, but I'd like to). I used R years ago, so I while I'm somewhat familiar with it, I have forgotten most of it. For me, the best ...
user avatar
6 votes
3 answers
493 views

Generalized Mean Variance Portfolio

Utility based portfolio optimization deals with the problem of finding the optimal portfolio $x_T$ by maximizing the utility/objective function $O(x_T,x_0)$ where $x_0$ is the current portfolio. In ...
user avatar
  • 227
6 votes
2 answers
636 views

Portfolio Analysis Interview Question

Suppose you have a portfolio of 100 options. Then I give you a subset of trades in which you can make. The trades consist of possible buys/sells of different options from different clients. Discuss ...
user avatar
  • 377
6 votes
1 answer
760 views

Rockafellar-Uryasev mean-CVaR optimiztion

In Rockafellar-Uryasev 2001 paper the mean-CVaR optimization can be written as a linear programming optimization problem as: $$P_{\text{CVaR}} = \arg \min_w \text{VaR}_\alpha+\frac{1}{(1-\beta)S}\...
user avatar
6 votes
1 answer
12k views

Marginal Risk Contribution Formula

I am trying to understand and implement the standard 'marginal risk contribution' approach to portfolio risk and hoping to reconcile the formulae provided for its calculation in different sources. ...
user avatar
6 votes
2 answers
706 views

tail dependency for portfolio optimization

This question pops up in my head every few weeks and I'm struggling to really understand the concept / theory behind it. We all know there are different kind of measures of dependencies out there. ...
user avatar
  • 1,638
6 votes
1 answer
440 views

How can I use a more efficient volatility estimator to improve the co-variance matrix?

Using mean-variance, I need to estimate a co-variance matrix $\Sigma$ to obtain the best weights in my portfolio. However, there are other ways to compute the volatility $\sigma$ than historical ...
user avatar
6 votes
1 answer
410 views

Optimizing a portfolio whose risk is target expected shortfall

I want to maximize the return of a $n$-asset portfolio under known risk: $$\max_{\{w \in \mathbb{R}^{n}|w_{1}+...+w_{n}=1\}} \; \mathbb{E}\left[\sum_{i=1}^{n}w_{i}R_{i}\right]$$ under the constraint $$...
user avatar
6 votes
2 answers
543 views

Matlab Portfolio Optimization with bid ask spread

I'm trying to find the optimal portfolio of options and stock which minimizes the standard deviation of the portfolio returns but also taking into consideration the bid and ask prices of the assets. ...
user avatar
6 votes
1 answer
390 views

Markowitz portfolio in reality

I am in academia and begin to work on topics including portfolio optimization. I just read lots of paper discussing different extensions to the Markowitz approach, given different (possibly ...
user avatar
  • 61
6 votes
1 answer
238 views

Market Portfolio Optimization

Consider the minimization problem $$\min\left\{\frac{1}{2}x^T\Sigma x - \lambda(\mu-r_f)^Tx\right\}$$ and assume the CAPM model, i.e. $$r_i-r_f = \beta_i(r_m-r_f) + \varepsilon_i$$ Assuming $\...
user avatar
6 votes
1 answer
418 views

Simple mean reversion strategy portfolio construction

I had a quick idea I wanted to test, but am not sure of the correct way to size bets. Basically, I think that for a given index (say S&P), I want to be long under performers and short over ...
user avatar
  • 323
5 votes
3 answers
404 views

Is there an intuitive explanation for why Kelly gambling ignores odds?

I have just learned about Kelly gambling from Chapter 6 of Cover & Thomas' Introduction to Information Theory. The mathematical setup is that we have a horse race, with horse $i$ winning with ...
user avatar
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 ...
user avatar
  • 340

1
2 3 4 5
13