# 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 ${\mathbf M}$. ...
859 views

### 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 ...
209 views

### 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? ...
38 views

### 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 ...
251 views

### 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 ...
54 views

### 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 ...
218 views

### Ledoit-Wolf portfolio weights calculation

I am trying to implement the Ledoit-Wolf minimum variance portfolio strategy on a real-world stock dataset. ...
1k views

### 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 ...
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 ...
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}... 0answers 74 views ### 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 ... 0answers 259 views ### 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 (... 0answers 148 views ### 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. ... 0answers 40 views ### 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 "... 0answers 61 views ### 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, ... 0answers 83 views ### 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 ... 0answers 196 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 ... 0answers 253 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 ... 0answers 44 views ### 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 ... 0answers 70 views ### 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.... 0answers 183 views ### 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 ... 0answers 289 views ### 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. ... 0answers 157 views ### 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 ... 0answers 136 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 ... 0answers 78 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, ... 0answers 71 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 ... 0answers 52 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 ... 0answers 117 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 ... 0answers 32 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 ... 0answers 33 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 ... 0answers 93 views ### 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 ... 0answers 60 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 ... 0answers 65 views ### 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. 0answers 81 views ### Momentum strategy with Entropy Pooling i'm currently trying to implement a ranking based on momentum indicators into my Entropy Pooling approach. Basically, the idea behind Entropy Pooling is to incorporate views into a reference model (... 0answers 41 views ### Relationship between risk and return for GBM and riskless bond Suppose we have S, a stock following geometric Brownian motion (dS_t = S_t (\mu dt + \sigma dZ_t) for Z = Brownian motion) and B, a zero coupon bond with rate r, i.e. dB_t = rB_t dt. In ... 0answers 50 views ### Relation between CAPM and Portfolio Theory can any of you explain to me in simple terms how CAPM and portfolio theory are related to each other? To my understanding: Portfolio theory helps to select the "right" stocks under risk/... 0answers 348 views ### Portfolio Performance Attribution Using Carino Smoothing I'm trying to conduct portfolio performance attribution using Carino smoothing, but it seems that the active returns do not match and I don't know why. Here is the example I use: \begin{array} {|r|r|r|... 0answers 84 views ### Option Based Portfolio Insurance OPBI Simulation Excel I want to simulate an example of OBPI in Excel. I can't find any example online with random figures that show how to simulate it. I tried to understand the appendix of Perold (1995): Dynamic ... 0answers 99 views ### How does negative performance of a portfolio constituent affect its weight? This is an easy question, I hope. Suppose we have a swap A with a long position, which, originally, has a weight of 30%. Over time, it has a positive performance of 3%, meaning we have a multiplier ... 0answers 80 views ### CVaR portfolio optimization with risk aversion parameter I'm trying to implement the Rockafellar's function described in this paper http://past.rinfinance.com/agenda/2009/yollin_slides.pdf with a risk aversion parameter for my thesis. The function to ... 0answers 32 views ### Time and asset weighted rate of return of a portfolio If I have a portfolio with 3 initial assets on day 1 (say, stock 1 with beginning market value of \100, stock 2 \150 and stock 3 \175) and after 10 days the stock 2 is sold for \200, how can I ... 0answers 45 views ### Show the expected return of the portfolio and how to derive return variance of the long-short portfolio? Show the expected return of the portfolio and how to derive the return variance of the long-short portfolio? (see picture) 0answers 88 views ### PortfolioAnalytics: Training window based on entire history before rebalancing in 'optimize.portfolio.rebalancing'? I am fairly new to PortfolioAnalytics and R in general. I am trying to do some backtesting of a minimum variance portfolio. I have weekly, monthly, quarterly and yearly return data of 3 selected ... 0answers 30 views ### Value weighted Portfolio: Include Market cap of pref shares? I got Datastream MV data for my sample and i want to exclude Preference Shares. Since Datastreams definition of MV is shares*price there are two Marketvalues, one for common stock, one for preference ... 0answers 35 views ### Given multiple strategies with their ER, volatility, how would I calculate the combined Sharpe? Without knowing the actual daily returns, I have a table something like this: ... 0answers 51 views ### Constructing Portfolio Beta Suppose I have a portfolio with securities with different history. Say some securities have 15-20 years of history and some are like Uber or Lyft, which has limited history. There are assets with 1/2/... 1answer 408 views ### Leverage constraints I am trying to complete my project on Mean-Variance Leverage Optimization, and I have found lots of helpful advice on this forum. I wanted to ask you if you have some idea on how to implement a ... 0answers 59 views ### Why can't I take the Value at Risk “VaR” as a a risk objective in PerformanceAnalytics? (it does work for "ES) I am currently playing around with PortfolioAnalytics package in R and some data and I am aiming to create different portfolios with different VaR. However, I am struggling first of all, add.objective(... 0answers 177 views ### Applying portfolio variance weight based on logarithmic returns? The expected logarithmic return of a portfolio is calculated as :$$𝐸_p = \log\left(\sum_i w_i e^{R_i}\right) Therefore, I was wondering that how can I apply weight to use with the variance based ...
I'm studying the BARRA Predicted Beta model, and the common factor covariance between portfolio $p$ and the return on the market $m$ is defined as the product of the transposed vector of the factor ...