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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34 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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79 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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52 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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1answer
249 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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36 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
58 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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93 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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47 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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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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34 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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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 ...
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114 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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48 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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53 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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53 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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98 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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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 ...
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1answer
78 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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1answer
38 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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2answers
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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39 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
40 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
94 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
110 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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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 ...
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1answer
57 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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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 ...
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1answer
77 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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241 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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64 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
159 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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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 ...
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1answer
80 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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51 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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1answer
29 views

Value at maturity of long position in money market

This should be easy, but for some reason I am struggling with it. Say you have a long position in the money market (you hold dollars), say you own a quantity of $Ke^{-r(T-t)}$ dollars at time $t$, ...
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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 ...
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1answer
80 views

Why is a smaller portfolio norm better?

If the norm of the portfolio weight vector, $\frac{1}{p}\sum_{i=1}^n |w_i|^p$ for $p=1,2$, of portfolio A is 0.6, and the norm of portfolio B is 0.4, then portfolio B is considered more attractive ...
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2answers
232 views

Portfolio Optimization - Equal Weighting Algorithm

I am trying to write an algorithm which can output the number of stocks to purchase so that it equal weights positions in a portfolio of stocks. Say we want to invest $1000 in 5 stocks with equal ...
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1answer
45 views

Calculation Expecting Credit Loss from a Portfolio

I have the following question: An investor holds a portfolio of 50 million dollars. This portfolio consists of 'A' rated bonds (30 million dollars) and 'BBB' rated bonds (20 million dollars). Assume ...
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1answer
87 views

Build a portfolio with $\beta=1$ and minimize $\sigma^2$ using CAPM

Suppose there are two stocks A and B: expected returns are $E[R_A]=0.1$, $E[R_B]=0.15$; standard deviations are $\sigma_A=0.1$, $\sigma_A=0.2$; correlation is $corr(A,B)=0.6$; their betas to some ...
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164 views

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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1answer
78 views

Criteria for excluding an Asset Class from a Strategic Asset Allocation

While historically the return, volatility and correlation characteristics justified the inclusion of Sovereign Bonds (US Treasuries, European Central Bank Debt, etc) in Strategic Asset Allocation ...
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2answers
124 views

Standard deviation formula with Short selling- Markowitz model

I have 2 fast quastions. Before I begin I want to show you that I found minus before SD of bills in the book Principles of corporate finance(1.screen). I know SD of bills is zero and minus in this ...
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2answers
125 views

PCA on the stocks

I have N stocks, and a covariance matrix that indicates the covariance of these N random variables. Now, if I run PCA on the covariance matrix, what can you tell about the principle component?
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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 ...
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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.
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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 (...

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