Questions tagged [portfolio]

A portfolio is a collection of financial instruments. We often collect instruments together to represent the complete holdings of an investor and to analyze the overall risk (which may be lower due to diversification, i.e the portfolio holding multiple instruments).

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12 views

Optimization algorithm for maintaning portfolio weights

I'm writing an algorithm that outputs the number of stocks I have to buy for each product in order to get as close as possible to my target weights. I was thinking at this minimization problem: $$\...
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Incorporating market cap after Hierarchical Risk Parity (HRP) Portfolio Optimization. Using Black Litterman?

Hello financial experts :) I recently got interested in portfolio optimization. I'm still learning. As I'm familiar with python I started experimenting a little in JupyterNotebooks with riskfolio. I ...
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How to combine compound calls and puts such as to have a guaranteed fixed payoff at expiration?

Let there be 2 European vanilla options: Call; Put; Both options expire at time T2 > T1 > t=0. We also have 4 additional options available to us: Compound call on call; Compound call on put; ...
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43 views

How do you hedge a portfolio against a factor using index Futures?

How do you hedge a portfolio against a factor using index Futures? I constructed a long/short portfolio and dynamically hedge against an index, beta hedge. I realized that my portfolio is highly ...
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Pricing of factors - portfolio sorts

if I read that someone is using portfolio sorts to determine whether a factor is priced in the cross section ( risk premium ) is it the two-pass Fama-MacBeth regression? Is there a material that would ...
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108 views
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compounding component contributions

Say I have a portfolio which contains two components, A & B. Below are the daily contributions to performance (0.02 equals 2%), where the overall portfolio return is equal to the sum of component ...
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How to simply calculate future value of periodic contributions to an index fund account?

So, for the sake of simplicity, ignoring taxes, expense ratio, volatility or anything else other than known values for the following five variables: Starting contribution (dollars) Annual ...
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101 views

Can I invest in the market portfolio of modern portfolio theory? [closed]

According to the theory, the market portfolio is composed of all assets weighted by their market capitalization, and this is the portfolio one should own. Is there a way to build a portfolio close to ...
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60 views

Why does the 2nd Principle Component of a portfolio explain lots of variance in the data but has a low R^2 to portfolio?

I have used QQQ (nasday etf)holdings and weights data in a PCA model to see what components drive the daily returns of QQQ. What I found was PCA 1 explains 52% of the variance and PCA 2 explains 19% ...
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59 views

Calculating average portfolio volatility

I have a question regarding calculating portfolio volatility. In my "problem", there are six portfolios. Five that have a holding length of one year and one that has a holding length of 200 ...
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Literature about optimal number of stocks in a diversified portfolio

Is there any recent paper on how many assets one should consider for portfolio optimization techniques? I found: – https://www.jstor.org/stable/2330969?seq=1#metadata_info_tab_contents – https://...
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Turnover Constraint ignores initial weights of Portfolio

I am trying to perform a standard portfolio optimization, but with a constraint to how much the final weights of the portfolio are allowed to deviate from a set of initial weights. I do this with the <...
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How can I calculate the annual Standard Deviation for Sharpe Ratio of Daily Portfolio Returns?

I'm somewhat confused with regards to calculating the annual standard deviation and Sharpe ratio for my portfolio of daily returns. I have daily data ranging from 1960-2020 and use Excel to make some ...
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Does random outperform naïve investment?

Randomly pick a (long only) portfolio from all possible portfolios over the S&P 500. The expected performance of this portfolio should equal the actual performance of the S&P 500. In contrast, ...
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21 views

What are some tools to help optimize size of an ABS portfolio with many constraints?

What are some tools (python preferred) used in the ABS industry to optimize the size of a credit portfolio, given many constraints? Constraints can be things like Weighted Average Credit Metric (e.g. ...
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How the spread portfolio t-test is calculated?

within my master thesis I am calculating the Pastor and Stambaugh (2003) liquidity factor (https://static1.squarespace.com/static/5e6033a4ea02d801f37e15bb/t/5f629437c9d51c5d00ad3ff3/1600295992687/...
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Why additivity assumption holds in CAPM and factor models? (Screenshot of a textbook included) [closed]

All the excerpts are from the book investment, written by Bodie. At the bottom of this post, I attached pages of the the book that show a related part of my question. Question 1. Why the variance of ...
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35 views

Unitise an options portfolio

Suppose I have a portfolio of European index options (long call, short put) and risk free assets (buy bank bills) to create a synthetic long index position. I wish to unitise this portfolio to ...
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127 views

python portfolio tracker

any recommendations for a portfolio tracker that updates from csv ( or websocket but that would need to come with an active github and hopefully a man page). New to python, mainly creating charts from ...
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2answers
218 views

Black-Scholes Portfolio

In the black-scholes model, the hedging portfolio is given (in some textbooks) by $$\Pi_t = V_t - \Delta S_t,$$ i.e., the portfolio consits of a long position in the option $V$ and $\Delta$ units of ...
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62 views

transforming a model to long short instead of long-only

I am currently trying to adapt a model to a long short portfolio strategy. The model is stated here: A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem by Jiang, Xu,...
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35 views

Interpretation of rebalance and reconstitute in equity portfolios of different weighting methods

What are the portfolio construction differences between equal-weighted and capitalization-weighted with regard to terms like reconstitution and rebalancing? Reconstitution seems very straightforward. ...
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Efficient frontier plot including Mean-Variance and Mean-CVaR frontiers

I am trying to compare the outcomes of a Mean-Variance and Mean-CVaR Optimization approach. I succeeded in plotting the efficient frontiers + tangency portfolios for both cases. Does anyone know how ...
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Motivation/intuition behind the following portfolio selection problem

I am developing a Reinforcement learning algorithm for the optimal portfolio selection, using stochastic control approach. I have a market with risky and risk free assets. However becouse of some ...
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84 views

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 ...
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1answer
148 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 ...
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1answer
179 views

Information Coefficient (IC) Formulae Differences

I am learning about Fundamental Law of Active Management, and there seems to be two different Information Coefficient (IC) formulae presented. Though I myself am not a CFA candidate, these appear to ...
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44 views

Ideal daily leverage assuming Laplace distribution

Assumption; Laplace distribution is a reasonable representation of an index daily change. Starting out with index historical annualized CAGR and standard deviation. I find the Laplace distribution ...
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0answers
117 views

Introduction to volatility targeting, scaling, timing

I am a finance student, but I am quite new to the field of asset management and quantitative Finance. I have to write a literature review about volatility targeting and I am looking for good resources ...
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47 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 ...
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94 views

What are some advanced portfolio rebalancing strategies?

Want to write some portfolio rebalancing code but have found only simple portfolio rebalancer strategies like calendar and threshold. I want to rebalance a portfolio with different asset groups (EQ, ...
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1answer
56 views

structural model - exposure estimation

The following example is from the book Active Portfolio Management by Grinold and Kahn. Suppose we have the factor returns and want to estimate the exposures/factor loadings. Say the factor returns ...
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2answers
525 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-...
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53 views

Geometry of Efficient Frontier of Portfolios

I have been reading about Portfolio Theory, and though the algebra of it seems quite intuitive, I am having a hard time understanding it's geometry. For the sake of simplicity, I will only talk about ...
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1answer
124 views

Carhart 4-Factor Model intercept interpretation

I've been following studies such as Kempf & Osthoff (2007) and Statman & Glushkov (2009) in building a methodology measuring ESG portfolio performance centred around the Carhart 4-Factor Model....
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1answer
408 views

Bloomberg Get ETF Constituents

I used the PortfolioDataRequest aspect of the Bloomberg API in C++; however, when attempting to request the portfolio of the TAIL US EQUITY (an ETF), it returns an invalid symbol. I also tried using ...
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55 views

Show that the following result holds true for the variance of the return of a portfolio of shares

Start with a portfolio $p$ of $n$ shares, each with weight $x_i = \dfrac{1}{n}$ (for $i$ ranging from $1$ to $n$, discretely). Its return is given by: $$R_p=x_1R_1+\ldots+x_nR_n=\sum_{i=1}^{n}=x_iR_i\...
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59 views

Consensus expected excess return from Active Portfolio Management

In the book Active Portfolio Management, when discussing components of expected return (page 92 in edition 2), the authors mention that the consensus expected excess return $\beta_n\mu_B$ is the ...
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37 views

Construct portfolio with assets having expected negative returns

I have been asked to select a n stocks among N stocks, to construct a portfolio. Some of them have have negative weekly returns on average. If I want to select these n stocks by constructing an '...
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OLPS in real conditions

The Online Portfolio Selection problem has been extensively researched over the years, and various models have been implemented in open-source projects on GitHub. However the theoretical frameworks of ...
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1answer
126 views

Optimal portfolio with only n assets (with n less than total assets)

Given a time series of a set of N assets (let's say 100), how can I find the optimal portfolio, with the constraint that only n<N assets (let's say 10) can be in the portfolio? With 'optimal ...
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52 views

How to model when to buy and sell a stock? [closed]

Given a set of historical data and volatility of price in each day, how is it possible to determine a price to purchase a stock at each day? For example, I want to find a price like $125 and receive a ...
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2answers
111 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, ...
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62 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 ...
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1answer
118 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 $$\min h^TVh$$ ...
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36 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 ...
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62 views

Calendar time portfolio construction

I am writing my master's thesis about analyst star-rankings and whether their recommendations have investment value. For these purposes I am trying to construct calendar time portfolios as it was made ...
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1answer
99 views

Portfolio returns, volatility and weights of capital

I would just like to check if I've done these questions right, I feel like I might have used the complete wrong methods to get my answers. I've been given information on 3 stocks: I've filled in the ...
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60 views

Problem from Stochastic Portfolio Theory Textbook

I'm trying to do the following problem from Robert Fernholz's textbook Stochastic Portfolio Theory: The assumptions mentioned are: and my attempt is as follows: I have no idea how to deduce that ...
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1answer
46 views

Confused in regards to calculation of delta of one share including one call and one put [closed]

Q:My investment portfolio has one share of one call and one put, what would be the delta of my portfolio ? delta of call:0.45 delta of put: -0.14 My thought process: To begin with since im dealing ...

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