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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Unwinding a Portfolio

I have a portfolio ${\mathbf P}$ made up of positions $n_i$ in each of $N$ securities, which I'm assuming are jointly normally distributed with means $x_i$, and covariance matrix ${\mathbf M}$. ...
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How can one quantify the incremental value of better covariance matrix modeling in portfolio optimization?

Let's say we have two estimators of the covariance matrix, $\hat{C}_1$ and $\hat{C}_2$, and the latter is an improvement on the former. Is there any measure of the improvement that can be sensibly ...
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Shrinkage Estimator for Newey-West Covariance Matrix

I like to apply the Newey-West covariance estimator for portfolio optmization which is given by $$ \Sigma = \Sigma(0) + \frac12 \left (\Sigma(1) + \Sigma(1)^T \right), $$ where $\Sigma(i)$ is the lag ...
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Benefits of Diversification and Rebalancing with negatively skewed leptokurtic return distribution?

I am missing tools to investigate this issue. I am trying to solve this question here. What kind of issues should you acknowledge over the naive diversification/rebalancing with normal distribution? ...
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Is there a clear mathematical statement of what problem Hierarchical Risk Parity is solving?

Prado's paper is really just an algorithm for solving some inverse problem. Has anyone seen a clear statement of that inverse problem? Or do you know how to write it simply? The first step is just a ...
mathtick's user avatar
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Budget Constraint in Duffie's book

On Page 5 of Duffie's Dynamic Asset Pricing Theory, the budget-feasible set is defined as: $$X(q,e) = {e+D^T\theta \in R_+^s:\theta \in R^N, q\theta \leq 0}$$ Compared to Kerry Back's presentation of ...
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How to calculate Turnover Ratio of a scaled Portfolio

I want to calculate the Turnover of my scaled Momentumportfolio (Barroso und Santa-Clara 2015) They described Turnover Ratio with the following formula: While i understand the general concept (...
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Parametric VaR of a portfolio of a stock and an option on that stock

I understand how to calculate the parametric VaR of a stock and an option separately. But I don't understand how one can calculate the VaR of a portfolio of a stock and an option on that stock using ...
Jammie Dodger's user avatar
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How to calculate the estimation error of portfolio variance using propagation results?

I am trying to find a conservative approximation for the propagated estimation error of a investment portfolio's variance (comprising two assets), given we know the estimation error for the variance ...
AndrewLong's user avatar
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Ledoit-Wolf portfolio weights calculation

I am trying to implement the Ledoit-Wolf minimum variance portfolio strategy on a real-world stock dataset. ...
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How to correctly construct a value- and equally weighted portfolio consisting of property-types?

A problem of which I couldn’t find the answer on the forum is about the construction of equally-weighted and value-weighted portfolio. I want to compute the equally-weighted property-type portfolio ...
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Optimal weights in portfolio after rebalancing

I have a quite simple question but while looking for answers in research papers I couldn't find anything. The question can be summarized as : if you expect a shock on an asset, why don't you rebalance ...
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Intuition behind portfolio weights with lower RMSE but higher variance

I have recently encountered a phenomena in portfolio optimization that has baffled me for days. I was experimenting with different ways of transforming a covariance matrix to get a stable minimum ...
Jay's user avatar
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Reinvesting the dividends of a dividend paying stock

Suppose we have a dividend paying stock that has the following dynamics: $$dS_t=S_t((\mu-q)dt+\sigma dW_t)$$ With a continuous dividend yield $q$. What is the portfolio $Y_t$ that results out of ...
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Marginal Risk Contribution Implementation Questions

Sorry if this is too obvious to you. The marginal risk contribution mentioned here is the same as in this post Marginal Risk Contribution Formula . I understand the concepts and derivation on the ...
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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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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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Assumptions of the CAPM

As to my understanding, the CAPM assumes that all investors behave as described in the portfolio theory. Consequently, all investors hold a combination of the risk-free investment and the efficient ...
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Finding a PDE for an option $V(t,r(t),S(t))$

I have 2 approaches in my mind for finding a pde of an option that depends both on the short rate as well as the stock price- $V(t,r(t),S(t)$. Are these equivalent? Find a hedging portfolio by ...
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Vega for long long-term ATM call and short short-term ATM call

You are long a long-term ATM call and short a short-term ATM call. The ratio is adjusted to make the total vega zero. If before expiry of the short-term option, spot is again at the strike price. ...
Victor's user avatar
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Which performance evaluation measure to assess "Connectedness Matrix" based porfolios?

1. Question Which performance evaluation measure would be best to assess the portfolios built on 'connectedness matrix'? The connectedness matrix is the concept introduced in the academic paper "...
Eiffelbear's user avatar
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When does funding cost of a portfolio enter into the portfolio's present value?

This question comes from some confusion when reading Hull's book and from the general concept of no-arbitrage/self-financing portfolios in stochastic finance books. I am not fully seeing the ...
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Why Do Universal Portfolios Work?

I've been reading up on universal portfolios, but I haven't been able to find an intuitive explanation as to why they have the theoretical guarantees that they do, especially that they track the best ...
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How to ascertain/establish certainty of a portfolio rebalancing strategy?

I created a portfolio rebalancing strategy, that I am currently paper trading with. It is, primarily, based on mean-reversion principle with a few rules in place, and geared towards cryptocurrencies, ...
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Portfolio of single stock short put options: which correlation structure preferrable?

Let's say you want to have a equally-weighted (in terms of the option price) portfolio of short put options on various stocks with the same maturity. Running Monte-Carlo simulations, it seems that ...
PureVega's user avatar
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232 views

Liquidity Adjusted Asset Pricing Model

I have a data set with 4000 companies and I have calculated a liquidity measure of each of the company in the dataset as Where, Turnover is the monthly average ratio of daily volume to shares ...
Aquarius's user avatar
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289 views

Behaviour of out of sample efficient frontier

I am comparing the efficient frontier of a set of portfolios that are in and out of sample. The first period is from 1991-01-03 until 1992-10-03 and the second one from 1992-10-03 until 1994-03-03. I ...
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Portfolio optimised for diversification and regular yield. How to hedge?

Here is a portfolio optimisation for equity dividend and yield designed to diversify holdings and produce regular monthly returns using only ETFs complete with R code. http://prescientmuse.blogspot....
Emir's user avatar
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Sharpe Ratio for loans

I am trying to calculate the sharpe ratio for a set of loans. These loans have already matured and I know if they were good or not: grades are the different grades of the loans. interest rate is the ...
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What happened to Mountain View Analytics?

I stumbled over Thomas Cover's work on algorithmic portfolio selection; apparently, an outfit called "Mountain View Analytics" attempted to implement the suggestions from Cover's research. ...
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Portfolio insurance with a coherent risk measure (CVaR)

I would like to analysis of portfolio insurance under a coherent risk-measure method (CVaR), How can I achieve that? Is there a way to turn the problem into a linear programming problem? or to ...
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137 views

Calculating stock weight for SEC13F filers

I am trying to evaluate weight of stocks in portfolio for an investor. For this purpose I use SEC13F filings for particular quarters and historical prices from Yahoo. There are stocks in portfolio ...
Tamara's user avatar
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Claim-augmented market is arbitrage-free

Suppose we have a no-arbitrage market with a risk-free rate $r$ and $d$ risky assets with prices $(S_t)_{t \in \{0,1\}}$. Let's introduce a claim with payout $Y$, and assume that there exists a price $...
John David's user avatar
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How can equilibrium weights be found for momentum factor in Black-Litterman model?

I have a momentum factor which consists of going long in three rising ETFs and going short in three falling ETFs. I want to use this factor as part of my portfolio for Black-Litterman model, however I ...
Karina's user avatar
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Discuss how you would allocate your budget between the two assets if their correlation is 1, 0, or -1

An asset A is expected to yield a $2\%$ return with a standard deviation of $1\%$, and another asset B is expected to yield a $1\%$ return with a standard deviation of $1\%$. Discuss how you would ...
LeFo's user avatar
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How to express the process of number of stock (nt) in a portfolio using ito's lemma

We have a regular self-financing portfolio $W_t$: $$dW_t = n_t dS_t + (W_t − n_t S_t) r dt$$ Where $W_t$ is total wealth, $n_t$ is amount of stock, $S_t$ is stock price, $r$ is the risk-free rate. And ...
nearhome's user avatar
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Basket variance with correlation 1

I'm reading the famous nuclear phynance primer on dispersion trading and finding difficulty in understanding the author's simplification for the variance of a basket with correlation 1. See below: I ...
eslate's user avatar
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How to predict a portfolio's reversion?

Sorry if this has been asked before. I've been baffled by a question I'm facing. Assuming I know there are some certain demands for some stocks in near future, and I put them in a basket as a ...
inf's user avatar
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How to use coherent risk measure for evaluating price?

Coherent risk measures are defined by number of axioms (see e.g. Coherent Risk Measure) but a question that does not seem well studied is how to use them. Let's take a coherent risk measure $\rho$ and ...
Mathieu Dutour's user avatar
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How do you cross-sectionally standardize a variable?

i am doing research on a so-called carbon beta where I made a portfolio that takes a short position in 'green' stocks and a long position in 'brown' stocks, from a period of 2005 until 2020. So from ...
Edgar Bloemendaal's user avatar
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78 views

Constructing a Replicating Portfolio : Regression on Individual Constituents or their Average?

I would like to replicate a portfolio of stocks $S_1, \cdots, S_n$ using other instruments, $X_1, \cdots, X_m$. Using the letters above with a subscript $t$ to denote the forward returns over some ...
rubikscube09's user avatar
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99 views

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 <...
Quastiat's user avatar
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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, ...
ameyashete's user avatar
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116 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 ...
Dr. Paprika's user avatar
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188 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 ...
Orif's user avatar
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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 ...
Paulo Rocha's user avatar
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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 ...
John's user avatar
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Calculating portfolio weights for Black-Litterman model

I am attempting to construct a portfolio using the step by step Black-Litterman model. My idea is to have a portfolio of, say 10 ETF's (equity based) in one sector and then add some uncorrelated asset ...
Ali khan's user avatar
1 vote
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73 views

How to calculate portfolio returns from assets with different valuation frequencies and return methdologies?

I have a situation in which I'd like to calculate a total portfolio return for a portfolio made up of funds with different valuation frequencies and return methodologies. As an example, say I have a ...
kforce's user avatar
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There are several ways optimize portfolio, why use Black Litterman rather than Mean variance

I know there are two ways to optimize portfolio. What are the limitations and advantages by using Black Litterman over Mean variance.
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