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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Derivation of optimal portfolio weights using Risk Budgeting approach
In Thierry Roncalli's book Introduction to Risk Parity and Budgeting (2013), he gives an example of particular solutions to the Risk Budgeting portfolio such as for the $n=2$ asset case.
The risk ...
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How to calculate the ex-ante beta of a portfolio between several rebalancing?
I have a portfolio composed of $ N $ assets.
I know the one-year beta of these assets, I also know the past (ex-post) beta ($\beta$) of my portfolio.
My portfolio changes allocation every month. So I ...
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Optimal leverage for 5 discrete steps
I received the following problem:
Your’re to invest EUR 100 for five years in a portfolio of stocks
delivering normally distributed returns with µ = 0.05 p.a. and σ = 0.1
p.a. For each EUR invested ...
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Calculating tangency portfolio weights with the given information? (2risky +riskfree asset)
We have 2 risky and 1 risk-free asset.
E1 = 4%, STD1=10%
E2 = 5.5%, STD2 = 20%
rf=1.5%
The covariance matrix and it's inverse are given:
...
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Calculating variance of long/short portfolio
Say I have a portfolio of stocks, stock A, stock B and stock C, with the below positions:
stock A: long 100 USD
stock B: long 50 USD
stock C: short 200 USD
How do I calculate the portfolio variance ...
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PortfolioAnalytics: Out-of-sample optimization with transaction cost constraint using ROI solver does not work
I am currently trying to run an out-of-sample-optimization with the PortfolioAnalytics package in R, where the quadratic utility function of the investor also penalizes transaction costs (80bps) ...
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How to calculate Quartile (or Decile) returns
I have split the following portfolio of 20 stocks into 4 quartiles by say market cap. My main question is how would you ...
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Equity and Credit Portfolio Return
This might sound like a trivial question but would appreciate the answer.
How would you calculate the return of the portfolio consisting of only equity and credit instruments? For example, consider ...
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How to find top 10 entities who owned APPLE since the time it went public, on an yearly basis? [duplicate]
So, I want to find out, what were the top 10 people/entities/funds any type of entity basically, who have owned Apple since the time in went public on a yearly basis.
Like for example, over here: ...
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Is this equation correct for portfolio optimization for CARA normal with N risky and one riskless asset?
Suppose the consumer Solves $\max -e^{-\gamma W}$ where $W=X^T D -X^Tp R_f$ where $X$ is the vector invested in a risky asset and $D\sim N(E[D],\Sigma^2_D)$ and $R=\sim N(E[R],\Sigma^2_R)$. Then ${ X=(...
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How to create Industry Portfolios per country? [duplicate]
Regarding the industry portfolio as created by Kennth R. French like here: https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/det_17_ind_port.html I was wondering how I could do this ...
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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 ...
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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 ...
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How to calculate the portfolio risk and return if daily share prices, volume held on that day is given for all assets?
The problem is with the changing volume of assets which changes the weights. I want to use the formula for portfolio risk but cannot figure out the weights. Should taking average weight of an asset ...
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Portfolio with Put Options - VaR, Std. Dev
I did a Monte Carlo simulation to evaluate my portfolio. I used different Strikes and Weights for the Put options. Now to my problem: All statistical measures (like expected return, volatility) ...
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Derivations of the pricing PDE for the Heston-Hull-White or Heston-CIR models
Consider the hybrid model given by
$$dS=(r-q) S dt + \sqrt{v} S dZ_1$$
$$dv = \kappa_v (\theta_v - v) dt + \sigma_v \sqrt{v} dZ_2$$
$$dr = \kappa_r (\theta_r - r) dt + \sigma_r r^p dZ_3$$
with ...
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Double counting in turnover calculation
While reading Koijen's Carry paper, they states double counting when calculating the turnover, as below. I'm wondering if they are referring to buy and sell or something else.
If I liquidate all my ...
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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 ...
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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 ...
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How to calculate the log return of portfolio?
Suppose that we have five trades each day with these returns ($R_{day,trade}$) and we have 300 days in total:
$R_{1,1}$, $R_{1,2}$, $R_{1,3}$, $R_{1,4}$, $R_{1,5}$
$R_{2,1}$, $R_{2,2}$, $R_{2,3}$, $R_{...
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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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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 ...
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mean return and volatility with transaction cost
What means that 5 bps per half-turn for transaction cost?
How can I implement mean return and volatility with this transaction cost in formula or python code?
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long short portfolio sharpe ratio
What is the proper way to caluclate sharpe ratio for the long short portfolio? When I calculate daily return with no cost, I use this formula: (return for long k.mean()+ (-1)*(return for short k.mean()...
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Treasury futures and the TUT spread historical volatility
I'm doing a study at Rutgers on the TUT spread. The TUT spread is composed of 2 2-year treasuries and 1 10-year treasury per spread. I was trying to estimate the historical volatility of the spread, ...
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What is Leverage?
What would you consider leverage? I know this may sound like a basic question but I have spoken with several industry professionals with a significant amount of experience and all of them have a ...
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Correlation Matrix to Variance Covariance Matrix Portfolio STDEV
I have a correlation matrix that I wanted to convert into a variance covariance matrix. I also have the weights in a column in excel along with each assets standard deviation. What excel function can ...
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How to compute portfolio weight of forward contract
how would one formally calculate the portfolio weight of a Forward position?
Suppose I have 100 mio portfolio. I have 50mio in Tesla shares and I have 50mio in Microsoft shares, and I enter into a 1 ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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