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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64 views

Why additivity assumption holds in CAPM and factor models? (Screenshot of a textbook included)

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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27 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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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
164 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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56 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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33 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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34 views

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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34 views

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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64 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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131 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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117 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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37 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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113 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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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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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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54 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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332 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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38 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
67 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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201 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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49 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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57 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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36 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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76 views

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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118 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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51 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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56 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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54 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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107 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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28 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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54 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
80 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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55 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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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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159 views

Statistical methodology for proving the stability in time of asset allocation weights

I am comparing the set of weights obtained by the classical Markowitz allocation process with those of another asset allocation technique I have devised. Markowitz's weights are unstable, as the ...
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43 views

Proper way to measure portfolio returns

I have a peculiar trading strategy and I can't seem to be able to find a proper way to measure its performance. Background: The strategy consists of buying certain stocks and then selling them in ...
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1answer
49 views

How to Calculate weekly Turnover

I am trying to calculate the weekly turnover of a portfolio consisting of 5 assets .The portfolio rebalances every week an I have calculated the weights and portfolio returns for each week. Is there a ...
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1answer
93 views

Error in has.Ad(x) : object 'BRK' not found

I am trying to merge a list of adjusted closes of a multitude of firms for my research on ESG, in relation to risk/reward. None of the firms seem to have a problem, except for the Berkshire Hathaway ...
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1answer
109 views

How to compute a portfolio PnL and Sharpe?

I understand this is quite the common question but I haven't been able to understand this concept through the previous posts. My situation is that each day, I'm interested in buying/selling one ...
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1answer
123 views

Monthly rebalancing portfolio of daily returns

Tried to ask this already, but I am still a bit unsure on how to proceed. What I wonder is how to handle the returns and weights of the stocks in a portfolio after rebalancing monthly, so within the ...
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146 views

How to properly annualize portfolio volatility

I have a portfolio consisting of several assets and I'm using daily data to calculate various portfolio metrics, including historical returns and volatility. In order to compare portfolio performance ...
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1answer
61 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. ...
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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 ...
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1answer
92 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 ...
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247 views

Strategy of replicating a portfolio with payoff $\int_0^T \frac{dS_t}{S_t}$

Given the asset price $S_t$ which is defined as follows $$\frac{dS_t}{S_t}= r_tdt+\sigma_tdW_t$$ where $r_t$ is not necessarily deterministic. What is the strategy of replication of the portfolio with ...
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69 views

Arbitrage portfolio example

Can you give me a concrete example of a self financing portfolio which gives arbitrage opportunity in the two-dimensional Black-Scholes model? By the two-dimensional Black-Scholes model I mean $$dS_{1}...
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2answers
183 views

Replicating momentum strategies (UMD/MOM, SUE and CAR3) in R

I am writing my Master Thesis on momentum strategies including price momentum (UMD/MOM) and two fundamental momentum strategies (SUE and CAR3). Right now I'm trying to create the three momentum ...
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35 views

Examining individual portfolio allocation changes over time

I am currently working with a pretty large panel dataset containing the investment holdings of many individuals over time (i.e., for each individual I know the positions per stock over time). I was ...
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1answer
82 views

Optimal Portfolios with Skewed and Heavy-Tailed Distributions

I am learning about portfolio theory and been using Markowitz. I wondered, however, if I can use distributional and asymmetric information of the returns to solve the problem. For instance, I have a ...
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52 views

How to implement a buy and hold strategy?

Cheers, I am measuring the impact of a particular variable on a sample of stocks. To accomplish this, I am ranking stocks into decile portfolios based on this variable and then estimating the ...

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