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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Constraints in a Mean-Variance Optimization Case
Might be a repeat question, feel free to close if it is.
I am trying to perform a mean-variance optimization (maximizing the Sharpe ratio) for lets say 5 assets. Besides the weights of the assets ...
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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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When you have negative weights in the context of portfolio construction, what is the correct way normalize them?
For context, I am building an eigenportfolio following the conventions of Avellaneda and Lee Statistical Arbitrage in the U.S. Equities Market (2008), and I get negative weights for eigenportfolios 2,...
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CML equation - from where does the square come from?
In his textbook Asset management Andrew Ang uses the following CML formula (chapter 6)
E(rm) - rf = y * σ^2
Where y is risk aversion factor
What is the source of square?
When I look at CML graph there ...
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Interpretation of optimal weights in portfolio for risk-adjusted return maximization
To start, I'm not an expert in portfolio management. My research involves examining the effects that one financial asset has on another, specifically looking at the spillovers between cryptocurrency ...
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Creating a Bloomberg bquant portfolio
As an ex-investment banker (salesperson to be specific) and amateur programmer, I’d like to move into quant work.
I’d like to create a coding portfolio using Bloomberg’s bquant, but as I’ve left the ...
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How do I find daily expected portfolio return that has both short and long assets?
For example, let's say we have 3 assets (A, B, C) with weights (0.3, 0.3, -0.4). Hence the portfolio is 20% net long.
Assets have daily price returns of [[0.01, -0.02], [0.03, 0.04], [-0.01, 0.03]].
i....
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How can this problem be defined formally?
Let's consider a straightforward example in which I possess a portfolio consisting of two stocks:
$
R(t) = S_{1}(t) \cdot x_1 + S_{2}(t) \cdot x_2,
$
Here, $t$ represents the time index, $R(t)$ ...
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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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Why do we need the covariance when calculating portfolio VaR?
I was recently learning about value at risk and how to calculate it, and one of the steps was to calculate the covariance of the returns of the securities making up the portofolio.
This makes sense ...
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Solving Equation for estimation risk averse parameter
Let the portfolio value follow the SDE:
$$V_t=(\mu w+r(1-w))\cdot V_t\cdot dt +\sigma \cdot w\cdot V_t \cdot dB_t $$
where $\mu$ = drift of the portfolio,
$\sigma$=standard deviation of the portfolio, ...
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Difference between the two definitions of Ulcer Index
The Ulcer Index (UI) is defined as follows on page 89 of the book "Practical Portfolio Performance Measurement and Attribution, 2E" by Carl Bacon:
$$
UI= \sqrt{\sum_{i=1}^{i=n} \frac{D_{i}^...
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Difference between Maximum Drawdown and Largest Individual Drawdown
Bacon in Practical Portfolio Performance Measurement and Attribution distinguishes between the two, specifying that "Maximum drawdown represents the maximum loss an investor can suffer in the ...
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Is the self-financing condition necessary/"useful" in practice outside of replication/valuation?
I know that the need for a portfolio/strategy to be self-financing (the purchase of a new asset needs to be funded by selling of an older one/ones) is very helpful when attempting to price derivatives ...
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Why reduce number of short contracts to reduce beta, and take long positions to increase it?
My question is about chapter 3 in the ninth edition of "Options, futures and other derivatives" by John C. Hull, subchapter 5 under the heading "Changing the Beta of a Portfolio".
...
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How to express the process of number of stock (nt) in a portfolio using ito's lemma
We have a regular self-financing portfolio $W_t$:
$$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 ...
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Confusion about the formula for gain process in a financial market
In this wikipedia page, we consider the following financial market
The formulas for the stocks are given here
And the gain process of a portfolio $\pi$ is defined such that
From what I understand, ...
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calculating portfolio weight for long short
Sorry for this dumb question but what are the mathematical-finance /academic conventions for calculating portfolio weights in a long/short portfolio where the longs are fully funded by the shorts? ...
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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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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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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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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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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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