Questions tagged [portfolio-management]
The professional management of an investment portfolio of various securities (shares, bonds and other securities) in order to meet specified investment goals. The process includes the specification of investment objectives and constraints, choice of asset mix, formulation of portfolio strategy, selection of securities, execution, revision, and evaluation.
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How to change the covariance matrix for a parallel-shift of the efficient frontier?
I'm trying to obtain a parallel shift in my efficient frontier based on the Merton 1972-parameters. As i think a picture tells you more than 1000 words here is what i tried:
The setting of my problem ...
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equities hedging betas for a cross-sectional risk model
This question is on equities risk models. I would like to know how to define betas when using a cross-sectional regression approach, rather than the time series approach. My goal is beta hedging of a ...
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portfolio weights based on past returns
In the academic paper Industries and Stock Return Reversals by Hameed and Mian (JFQA,2015) (see picture below), the authors describe a trading strategy based on reversal, which essentially buys past ...
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Linear programming and factor models vs M-V optimization?
I have been recently researching about portfolio optimization problems and it is unclear to me what is currently the state of art modeling choices when it comes to this topic.
On one hand, I've ...
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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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Principal Portfolios Prediction Matrix estimation (Bryan Kelly)
I have recently discovered Bryan Kelly's paper on Principal Portfolios (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3623983) and had some doubts about the prediction matrix $\Pi$. He defines $\...
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Definition of Market-Neutral
I'm reading Qian, Hua and Sorensen's Quantitative Equity Portfolio Management and one part in section 2.3.2 (page 44) states that:
"For a long-only portfolio managed against a benchmark, the ...
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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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Portfolio factorization for portfolio optimization
I am looking to do some basic portfolio constructions as an experiment to learn more about it. I have been researching a bit and what I have found is that one of the purposes of factors models (Fama-...
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Active risk management of private assets
It seems incredibly difficult to not only come up with a list of options for active risk of private assets (Private Equity, Private Credit, Infrastructure, Real Estate, etc.) but also get senior ...
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Average drawdown and average drawdown length in Python
I'm trying to use Python to give me more information about drawdowns than just the max drawdown and the duration of the max drawdown. I would like to determine the number of drawdowns that have ...
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Shortcut for cutting portfolio volatility
When calculating the portfolio's historical volatility, do I need to factor the volatility of each asset individually and then do a covariance calculation or can I get away by measuring the volatility ...
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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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Rebalancing delta hedges has an implied gamma. Is there a good way to estimate an "effective gamma" from a rebalancing strategy?
Intuitively, if we hedge delta and rebalance that delta hedge periodically, we are effectively hedging a bit of gamma with each rebalance. I feel that this would depend on the rebalancing limits and ...
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Contribution to Drawdown?
I am trying to learn about the contribution to drawdown as a risk measure. While it is common to look at volatility and VaR/CVaR contributions, I have never seen the contribution of each portfolio or ...
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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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Calculate fund size given risk limit?
I was listening to a podcast and this guy mentioned the following (literally):
The entire group is probably running 800 million at risk. So I'm going
to say like call that like a, if you think of ...
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Why do better-performing index funds not get a higher weight? [closed]
Most financial advisors recommend to inexperienced investors to put a large part of their investment in broad index funds (e.g. SPY). They will usually reiterate that most actively managed funds ...
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Does it make sense to have an allocation to short term fixed income and a leveraged or unfunded position?
This may sound like a basic question but I have seen many large institutional investors have this as part of their asset allocation and am wondering why they do this?
Does it make sense to have a ...
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Quick simple way to aggregate sharpe ratio for a portfolio with derivatives
Suppose I have a portfolio with a mix of long short equity, some bonds, as well as derivatives such as options. Is there a quick way to aggregate sharpe ratio on a portfolio level? I would imagine ...
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Existence of an upper bound for risk-factor betas/coefficients
Theory:
Based on Hansen/Jagannathan, the set of means and variances of returns is limited. With $R^f$ as the risk-free rate, $R_i^e$ as the return of stock $i$ in excess of $R^f$ and a stochastic ...
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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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Minimizing ex ante tracking error of an equities long only portfolio if correlations aren't stable
My understanding is that minimizing tracking error is similar to mean variance optimization except it uses excess returns vs. the benchmark instead of an expected return.
For a long only portfolio of ...
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Industry best practice for minimizing tracking error [closed]
Lets say I have an alpha generating model that forecasts expected returns for SP500 stocks. I formulate a portfolio with 100 stocks having the highest expected return. What is the simplest way of ...
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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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Confusion about the proof of Fundamental Law of Active Management in Grinold & Kahn (2000)
I'm reading Grinold & Kahn (2000) for the proof of the Fundamental Law of Active Management.
I can't understand formula (6A.20) on page 168, which says:
Finally, by assuming that all the signals ...
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Fama French Model; 5 Factors yield higher alpha than 3 Factors [closed]
I am currently running some Fama French regressions for a number of specified portfolios, consisting of US stocks (for a university level course). The regressions are conducted in R, using the lm ...
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How to deal with benchmark timing in quantitative portfolio management?
In Grinold & Kahn (2000), the authors emphasized the separation of stock selection and benchmark timing in active portfolio management. So if we avoid benchmark timing, the optimal portfolio's ...
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Portfolio construction for almost identical assets
The problem I am looking at concerns the treatment of almost identical assets in portfolio construction.
Let us assume that we have two assets, both with a standard deviation $\sigma=0.2$ and a ...
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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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Determine if stocks are hurt by rates or recession fear
Looking at a portfolio of growth stocks which traded at high multiples until end of last year.
Stocks have been underperforming (no surprise there) but I'm trying to find ways to determine, ...
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Why are monthly active returns averaged? Should they not be multiplied?
I'm looking at this video: https://www.youtube.com/watch?v=fZmuJ2A9TC8 @4:43 but the issue is more general.
Here the speaker is taking monthly active returns and averaging them
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Using the Fama-French 5 factor model in Panel Data
I have a question regarding the use of the FF5 Factors in an industry-fixed effects model. In order to clearify my question I'll post an example of my dataset
Note that this is just an example, the ...
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Simple ways to size position without doing an optimization [closed]
Without doing portfolio optimization, how do long short portfolio managers size their positions?
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Leveraged Porfolio Hedging
What is the right approach to hedge debt of 1 dollar who's value changes based on a basket composed of:
32 cents of short Asset A
26 cents long Asset B
43 cents long usd
The debt is leveraged by 2....
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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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How to incorporate ESG in Portfolio Optimization?
I currently have a potential investment universe of several thousand stocks and would like to calculate an optimal portfolio that incorporates ESG criteria as well as risk and return. The model should ...
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Markowitz portfolio with factor/position constraints
General Markowitz-style optimization (problem objective of $w^T \mu - \lambda w^T \Sigma w$) yields simple optimal weights policy $w \propto \Sigma^{-1} \mu$.
However, I would like to add a series of ...
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How to correctly use Fama-French factors (from investment portfolio perspective)?
I have several questions regarding Fama-French and other (for instance, BAB) equity return factors for practical purposes (portfolio construction, portfolio risk analysis, portfolio return analysis). ...
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How to calculate portfolio return and risk based on given scenario [closed]
I am interested to invest Rs. 1 lacks in security market. I have securities A and B for this ...
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Unexpected Inflation and Asset Allocation
If asset allocation decisions were made prior to the news of unanticipated inflation, how should asset allocators incorporate the fact the inflation is now 5% higher than the 2% inflation target?
It ...
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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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mean-variance optimization === max sharpe ratio portfolio?
Noobie here. I just wanna ask a simple question:
in the context of portfolio optimization, is Mean-Variance optimization the same as the max sharpe ratio portfolio?
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Sample Variance of Portfolio
Let $w$ denote a vector of portfolio weights, $r_i$ denote the $i$th return vector, $\Sigma$ denote the Covariance matrix of $r_i$ and let $\hat{\Sigma}$ denote the sample covariance matrix of $r_i$.
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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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What are the quantitative requirements to distinguish between asset classes?
What are the quantitative criteria to distinguish between asset classes? I ask this as many institutional investors are undergoing strategic and tactical asset class decisions at the moment. How ...
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adjusting treasury futures exposure using micros
I want to decrease my exposure to a 10-year note futures by using 10-year micro futures after volatility-adjusting them. I've calculated that the difference in volatility in the micro has 5.125x the ...
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Fx futures pairs
I want to setup a pairs trade with the Japanese yen as the quote currency and Mexican peso as the basis currency. (long MXP vs JPY)
2 /M6J contracts, notional is 1,250,000 JPY = 10966.5*2 = 21933 USD ...
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characteristics of factor portfolios
In the paper Characteristics of Factor Portfolios (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1601414), when it discusses pure factor portfolios, it says that simple style factor portfolios ...
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