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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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Optimal active risk

Can someone help me prove the statement or share a link of the proof - "The optimal amount of active risk is the level of active risk that maximizes the portfolio’s Sharpe ratio. This optimal ...
Stannis John's user avatar
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1 answer
310 views

How to set a fixed return for mean-CVaR portfolio optimization?

I'm using the timeSeries and fportfolio package in R to minimize the CVaR with different constraints for a given portfolio. Everything is working out so far. However, I can't manage to set a fixed ...
ironymike's user avatar
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1 answer
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Maximum Sharpe ratio and mean-variance optimization

I want to understand why this holds: $argmax_w ( \frac{\mu^T w}{\sqrt{w^T\Sigma w}})=\Sigma^{-1}\mu $ I just found this post: Derivation of the tangency (maximum Sharpe Ratio) portfolio in Markowitz ...
Valentin's user avatar
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100 views

Which Times Series Database framework for Python is best for portfolio optimization project?

I am starting to build a portfolio optimization algorithm in Python and want to structure a database to manipulate financial data. Although I have Python experience, I have never used SQL or such ...
Brasilian_student's user avatar
1 vote
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127 views

factor hedging erodes portfolio alpha

I am hedging a long-short equity portfolio for statistical factors, and finding an improvement in sharpe but not surprisingly an erosion of portfolio alpha (ex ante and ex post). No one factor is ...
Henry's user avatar
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Is this an Example where Maximum Adverse Excursion (MAE) is not useful for a Stop-Loss?

Below is an attached screenshot of a scatter plot of a long position Percentage Return of a Asset Security on the Y-axis, and the Maximum Adverse Excursion (MAE) Percentage on the X-axis. Green dots ...
Calculate's user avatar
  • 109
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48 views

Weight of asset has to be smaller than b% in the portfolio(Portfolio Optimization)

Given a certain portfolio with y assets, calculate the weight of each asset in the portfolio based on the asset position. The weight for each asset is calculated by (yn is the position of a certain ...
Lukas Müller's user avatar
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62 views

zero-beta portfolio $z$ solves optimization problem

Consider a market with $p$ risky assets with expected return $\mu \neq k 1$ and positive definite covariance matrix $C$. Let $z$ be a zero-beta portfolio w.r.t the market portfolio $x_M$. Show that z ...
Alex's user avatar
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1 answer
110 views

relation between risk averson coefficient and maximum Sharp ratio in Black-Litterman context

BL model compute the implied returns based on the reverse optimization where the objective is: $${\underbrace U_{{\rm{investor's \ risk \ utility}}} \buildrel \Delta \over = {\bf{w}}_M^T{\bf{\Pi }} - \...
sci9's user avatar
  • 123
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158 views

Calculation of Long-Short-Portfolio returns for different holding periods

I have monthly stock returns I want to invest in according to my trading signals. Now I want to figure out the optimal holding period of the long-short-positions. (The same time for both positions). I ...
OneNewBee's user avatar
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1 answer
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Testing severity of VaR by changing portfolio component weights

Let's assume that I have a portfolio with two components:$$\omega_i = 0.3$$ $$\omega_j = 0.7$$ I also have two P&L vectors, $v_i$ and $v_j$ each containing 1000 P&Ls. I would like to play ...
AK88's user avatar
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4 votes
1 answer
367 views

PortfolioAnalytics and regime switching issue

I've been playing around with the R package PortfolioAnalytics and I have spent more time than I'm willing to admit to try and resolve this issue: When I follow the regime switching example with the ...
AtoZ's user avatar
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Is this generalization of the Kelly Criterion valid and already known in the literature?

The classic case of a stock and bond Well known in the literature is the Kelly-Criterion in terms of Merton's portfolio problem with log-utility. To recall the specific framework, let $S_t$ be a ...
Nap D. Lover's user avatar
2 votes
0 answers
97 views

Expected returns and Fama-French Factor Model

It is my understanding that for any given stock, the sample mean of historical returns is not a good proxy for the stock's expected return. In fact, the return on a stock needs to be estimated via ...
John Paris's user avatar
2 votes
2 answers
4k views

Best books on portfolio construction?

I am a master of finance student and although I understand the basics and the theory of portfolio construction I am still struggling when it comes to the practical side of things, i.e. building a real-...
John Paris's user avatar
3 votes
2 answers
781 views

Find k of n assets that "minimize" the correlation matrix

I'm trying to find an efficient way to select $k$ from $n$ risky assets that are the least correlated with each other. I know that I can perform a brute-force search of all $k$-sized combinations of ...
geofflittle's user avatar
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1 answer
168 views

Portfolio Optimization constrained to maximum N% of short selling portfolio weights

For mean-variance portfolio optimization with short-selling allowed, but restricted to a certain percentage of the portfolio weights (lets assume N), we can constrain it in the follwoing way: (from j=...
Joquim's user avatar
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Correct way of making sharpe optimized portfolio?

I have monthly returns of about 977 securities of past 10 years. If I keep the returns as it is i.e. I do not multiply by 100 and keep the returns as 0.1, 0.2 , -0.3, 1.2 then I get different results ...
Stupid_Intern's user avatar
1 vote
1 answer
224 views

How is target return optimized, in practice?

Suppose we have $A$ a $T \times N$ matrix of daily returns for an asset universe of $N$ items, $b$ a $(T,)$ vector of daily returns for a target asset, $x$ a $(N,)$ weighting vector. We want a ...
ejang's user avatar
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2 answers
241 views

Black-Litterman Weights Don't Change for Assets Without Views

I am using Idzorek 2002 (https://faculty.fuqua.duke.edu/~charvey/Teaching/BA453_2006/Idzorek_onBL.pdf) as a reference to implement the BL model in R. I have specified the model in its standard form, ...
Leo Hsia's user avatar
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What does negative proportion mean in sharpe optimization model?

Using the last 20 days of market return and some stocks return I made sharpe optimial portfolio and following were the stock names and investment proportion to be made. ...
Stupid_Intern's user avatar
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78 views

Can I use Sharpe optimization model for short term portfolios?

I wanted to know if there are any mention of what is optimal lookback period i.e. how many days, weeks, months or years of return data I should consider for constructing sharpe optimal portfolio and ...
Stupid_Intern's user avatar
0 votes
1 answer
301 views

Active portfolio management - characteristic portfolios derivation

In the book Active Portfolio Management by Grinold and Kahn, on page 30, when it derives the characteristic portfolio $h_a$ for some characteristic vector $a$, the problem is set up as $$\min h^TVh$$ ...
Xiaohuolong's user avatar
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194 views

Black-Litterman for quant portfolio

I have seen a lot of research around the Black-Litterman approach and I think theoretically, it is a nice framework. However, it appears that its main strength is from a practitioner's point of view, ...
Jim's user avatar
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0 answers
71 views

Black-Litterman Weights for Intersecting Asset Classes

I'm trying to implement Black-Litterman for an arbitrary selection of assets some of which might be subsets or intersect with others. For example, one portfolio might be US Equities (VTI) A global ...
jtanman's user avatar
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2 votes
0 answers
153 views

Backtesting of outperformance of a benchmark using the Deflated Sharpe Ratio

I want to test whether, let's say, strategy A outperforms strategy B. In Marcos López de Prado's book Advances in Financial Machine Learning he presents the following statistics: The Probalistic ...
tuffah12's user avatar
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0 answers
364 views

Sharpe ratio differs from Tradingview

I tried to backtest a simple strategy on TradingView, it made 6 trades with these results: Now I want to calculate Sharpe ratio using definition provided by TradingView. So, my daily returns(...
konstantin_doncov's user avatar
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1 answer
381 views

Mixed-integer programming approach for index tracking

Suppose you currently own a portfolio of eight stocks. Using the Markowitz model, you computed the optimal mean/variance portfolio. The weights of these two portfolios are shown in the following table:...
statwoman's user avatar
  • 123
3 votes
0 answers
66 views

Interaction between raw position signals and portfolio optimisation methodologies [closed]

I'm trying to get my head around how the various aspects of constructing a final position generally interact and wonder whether anyone could expand on my (tentative) understanding currently. As I see ...
Mithra's user avatar
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1 vote
1 answer
1k views

Optimise the Sharpe ratio of a portfolio of uncorrelated assets

Given a portfolio of $n$ assets, mean returns vector $\mu$, covariance matrix $K$, one can calculate the portfolio weights $w^*$ that maximise the portfolio Sharpe ratio, by solving: $$w^*=\text{...
elemolotiv's user avatar
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1 answer
736 views

Black-Litterman model with only positive weights

I'm trying to realize Black-Litterman Model for my stocks portfolio, but under optimization, I get a subset of weights with negative values. I want to get only positive weights. IS it possible to add ...
Dmitriy's user avatar
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2 votes
2 answers
206 views

How to evaluate Asset Allocation skill?

There have been studies that show that Asset Allocation can explain 90% of the variance of returns on a portfolio. If true and Asset Allocation is the primary driver of return risk, how can you ...
AlRacoon's user avatar
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52 views

Minimize Composite Dispersion

Let's say that we have a composite of 10 fixed income portfolios, each with the same benchmark, the US Aggregate. Additionally, let's say that each portfolio has a position in Corporation ABC. The ...
Wadstk's user avatar
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1 vote
0 answers
79 views

Value of continuously rebalanced stock portfolio

I'm thinking about what a theoretical continuously re-balanced stock portfolio could look like, in which the portfolio is uniformly distributed over a selection of stocks at all times. For example, if ...
JMC's user avatar
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1 vote
0 answers
160 views

Strange efficient frontier, when I try to calculate BTC & ETH ratios using MPT(Modern Portfolio Theory) [closed]

The 10k Monte-carlo simulations all fall on the same line, instead of a proper scatter plot.. Not sure what I'm doing incorrect. It all works fine, if I include Monero in the mix. Any pointers ? I'm ...
PlanetUnknown's user avatar
1 vote
0 answers
55 views

Change weights of the portfolio [closed]

I have spent a lot of time finding some trading alphas. Now, I have about 10 alphas to trade Future, I also optimized the portfolio by using Markowitz's Modern Portfolio Theory (MPT) to get weights. ...
Nhân Thành's user avatar
0 votes
1 answer
55 views

Multiple Indices for CAPM model [closed]

I am new to quantitative finance so, please excuse me if the terms are not correct. I am trying to apply CAPM on a portfolio which has multiple indices (S&P 500, Russel 1000 and S&P Financials)...
user54434's user avatar
2 votes
1 answer
100 views

Optimal Portfolio Formulation

I'm currently studying Luenberg's Article "Projection Pricing" (Jrl of Optimization Theory and Applications, Vol. 109, No. 1, pp. 1–25, April 2001) and there is a claim that I can't prove. ...
Felipe Teti's user avatar
0 votes
1 answer
119 views

Sub-portfolio correlation

I am trying to reduce correlation matrices into sub portfolios. For example, I have a covariance matrix $\Sigma$ and weight-vector $w$ of two line items which I blend together into a sub-portfolio $\...
ilikemath3.14's user avatar
1 vote
0 answers
32 views

Statistical testing of out-of-time portfolio performance (measured via a custom metric)

I'm testing (out-of-time) my machine learning (ML) based strategy against a strong benchmark. As a performance metric, I'm using a custom rolling metric $M(t)$ which takes into account the portfolio ...
BGa's user avatar
  • 169
1 vote
0 answers
472 views

Deriving the tangency portfolio with a condition in Python

If there are sister-sites better suited for this question please let me know, I thought this to be the most fitting I have the covariance matrix, the return vector and some scores (ESG scores). The ...
BlackBear's user avatar
1 vote
0 answers
50 views

Best bibliography on the classic Merton portfolio problem

I am writing a small section on my thesis about the classic Merton portfolio problem. I was wondering what are the best books on the subject. I am looking for something from the beginner to the ...
Paulo Rocha's user avatar
1 vote
1 answer
361 views

cvxpy Portfolio Optimization

I am trying to understand which is the best way to construct the parameters using the cvxpy engine. I have seen this post: more of list-like way of constructing constraints etc and this post: more ...
wanna_be_quant's user avatar
1 vote
0 answers
72 views

How many principal components to use for statistical risk model?

If I use every principal component to explain total variance of my portfolio, does it still make sense in portfolio optimization? Because since alpha factors try to find out and explain unexplained ...
geonhwa's user avatar
  • 57
0 votes
1 answer
365 views

RIsk-retun of 2-asset portfolio with perfect negative correlation

Risk-retun of 2-asset portfolio with perfect negative correlation $(\rho=-1)$ is a straight line with slope of $\frac{|\mu_2 - \mu_1|}{\sigma_2+\sigma_1}$ since $\sigma_P=|\omega_1\sigma_1 -\omega_2\...
techie11's user avatar
  • 213
1 vote
0 answers
431 views

global minimum variance portfolio vs all-bond portfolio

I'm leaning portfilio theory and have got some questions. global minimum variance portfolio is defined as the leftmost point on the efficient frontier which suggest it is a all-bond portfolio if risk ...
techie11's user avatar
  • 213
0 votes
1 answer
101 views

Portfolio allocation question: is it not circular reasoning?

Is portfolio allocation not circular reasoning? Say we have a portfolio manager, Michael, and a risk manager, Vito. Michael has a portfolio and would like to determine the optimal allocation of his ...
NotMarkowitz's user avatar
0 votes
1 answer
102 views

Misconception about replicating portfolio [closed]

I am solving a problem in which following payoff is provided: With $S_0=100$ and $T=8$. Looking at the payoff it seems obvious that it is replicated with two european put options ($K=100$ and $K=150$)...
Gaussian's user avatar
2 votes
4 answers
310 views

Cant replicate minimum variance portfolio variance by simulating many random portfolios in R

I have computed the theoretical minimum variance portfolio using the 30 stocks in the Dow. The formula used is: $$\underset{N\times 1}{\omega_{mvp}}=\frac{\lambda}{2}\cdot \Sigma^{-1}\iota=\frac{\...
Emil Bille's user avatar
2 votes
2 answers
408 views

State-of-the-art MVO methods?

I learned Markowit'z mean-variance optimzation in school. Now I've been googling a bit, and to my surprise, Markowit'z is STILL being used by most people, AFAIK. Are there really not some state-of-the-...
shudup's user avatar
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