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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5k views

Calculating alpha and its meaning

According to wikipedia, CAPM model is described by: $E(R_{i})=R_{f}+\beta _{{i}}(E(R_{m})-R_{f})$ And according to website such as http://investexcel.net/jensens-alpha-excel/, $\alpha = E(R_{i}) - ...
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Average correlation of index/portfolio

We try to analyze the average correlation of a portfolio as it can be found here in section 2 b), the same formula which is also used by the CBOE to calculate implied correlations: $$ \rho_{av(2)} = ...
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What books should any quantitative portfolio manager or risk manager have as reference? [closed]

I'm interested to know what are the critical reference texts you rely on for portfolio or risk management? I mean those texts that you come back to because they are chock full of insight and know-how. ...
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Why do expected return models and risk models use different factors?

This is a question responding to weekly topic challenge. I happen to see an interesting question from SYMMYS by Michael Kapler. I always approached expected return and risk modeling as separate ...
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Choosing the right statistical test for Mutual Fund Performance Evaluation

How do you suggest I do this? I would like to perform a statistical test to check if: the aggregate alpha of all funds equals 0. the aggregate beta of all funds equals 1. Data Sample of 1000 mutual ...
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706 views

Delta hedge value formula

When we delta hedge with implied volatility, and dynamically adjust every day, I believe the PnL theoretically is $$PnL = 0.5 \Gamma S^2 (\sigma_r^2 - \sigma_i^2)dt$$ where $\sigma_r$ is realized ...
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How to calculate the annual contribution of a fund to a portfolio of funds?

let's assume I have a portfolio of two funds (call them F1 and F2), where, by convention, there is a monthly compounding of the returns. On a monthly basis, the contribution of each fund will just be ...
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Why does the minimum variance portfolio provide good returns?

I've been a researching minimum variance portfolios (from this link) and find that by building MVPs adding constraints on portfolio weights and a few other tweaks to the methods outlined I get ...
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Comparing MVO with Resampled Efficient Frontier

My question: How can I compare the Resampled Frontier (REF) to the standard MVO frontier when I have been provided with $\mu$, $\Omega$, and don't have access to true future data to test real out of ...
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How do I calculate the skewness of a portfolio of assets?

I need to calculate the skewness of a portfolio consisting of 6 assets. I know that for that I would need the co-skewness matrix between the assets. Does anybody know the formula for co-skewness or ...
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Maximum Certainty Equivalent Portfolio with Transaction Costs

Out of curiosity I tried to compute the portfolio weights of a maximum certainty equivalent allocation, however, by incorporating (quadratic) transaction costs. However, my result is not as intuitive ...
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1answer
863 views

Finding arbitrage opportunity

Find an arbitrage opportunity in this market. Can anyone explain how to mathematically solve this exercise with for example solving a system of linear equations?
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Handling Missing values in stocks returns when estimating the co variance matrix

What is the best way to handle missing values when stocks did not exist for the entire historical period?.
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Rockafellar-Uryasev mean-CVaR optimiztion

In Rockafellar-Uryasev 2001 paper the mean-CVaR optimization can be written as a linear programming optimization problem as: $$P_{\text{CVaR}} = \arg \min_w \text{VaR}_\alpha+\frac{1}{(1-\beta)S}\...
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1answer
380 views

target market correlation for long / short equity portfolio

Given a long / short equity portfolio, I want to have some net long market exposure. My portfolio volatility is fixed to a target, so I don't think it makes sense to target market beta. I think I ...
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Efficient frontier doesn't look good

Hi I'm trying to draw an efficient frontier. Below is what I used. returns parameter consists of 9 column returns of portfolio. I selected 10,000 portfolios and this is how my efficient frontier ...
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1answer
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Value of a perfect hedge

Background Information: The price of a portfolio at time $t$ ($t = 0 ,1$) is $$V_t(\pi) = \phi S_t + \psi B_t$$ The portfolio $\pi$ is a perfect hedge for the claim $X$ if $V_1(\pi) = X$ a.s. as ...
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name of this portfolio optimization strategy

I have come across a portfolio selection strategy that buys in equal amounts the top decile of expected earners, and simultaneously short sells the lowest decile in a similar fashion. What is this ...
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Portfolio optimisation with VaR or CVaR constraints using linear programming

I would like to optimize a portfolio allocation (maximizing the exposure or the expected return), but with VaR or CVaR contraints. (some parts of my portfolio cannot exceed a certain VaR) How can I ...
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Diversification, Rebalancing and Different Means

I have found many financial authors making generalizations about the geometric mean (GM) and arithmetic mean (AM) but they are wrong in certain circumstances. Could someone explain their reasoning? My ...
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Optimization: Factor model versus asset-by-asset model

In portfolio management one often has to solve problems of the quadratic form $$ w^T \Sigma w + w^T c \rightarrow \min_{\omega} $$ with portfolio weights $w \in \mathbb{R}^N$ a constant $c \in \mathbb{...
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Are there any tools or useful algos for identifying corner portfolios?

Let's say I am performing mean-variance optimization subject to some weight constraints. I'd like to identify the set of corner portfolios so that I can interpolate the entire efficient frontier. A ...
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What is the intuitive reason why the Gamma and the Theta tend to have the opposite sign?

Quoting Hull's book: When gamma is positive, theta tends to be negative. The portfolio declines in value if there is no change in S, but increases in value if there is a large positive or ...
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Risk Budgets with Target Portfolio Volatility

I'm working through the implementation of a risk budgeting approach as described in the recent Roncalli paper. The idea is that the portfolio manager sets a contribution of total portfolio volatility ...
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How to compute performance attribution between daily rebalanced strategies?

I have a daily rebalanced portfolio of several strategies. After one month, I now want to attribute the performance to the different strategies. There are several ways to do it. For instance one ...
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What is the total correlation between assets in a portfolio?

Suppose I have portfolio with 10 assets, each one of them with a weight of 10% from the total portfolio (equally weighted). It's well known how to measure from historical prices->returns a variance-...
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What to use as portfolio diversification measure?

Suppose that we have a portfolio of $n$ assets. A perfectly diversified portfolio is one in which each asset has equal weights, i.e. each asset has weight $\frac{1}{n}$. Of course this is usually not ...
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What position-sizing methods are used in futures trading?

Beyond optimal / partial f and a few other older methods, there's very little information out there for futures trading.
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1answer
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Michaud's Resampled Efficient Frontier - Out of Sample Simulation Testing

I will be putting ALL my account points on bounty to whoever answers this question [if your answer is crap but it's the only answer, you're getting the 165 points]. You will have to wait 2 days or so ...
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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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Asset Allocation with near zero rates

With central banks pegging interest rates to near zero rates, an argument could be made that the future distribution of interest rates and bond returns are not normally distributed. How has modern ...
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1answer
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Absorption ratio by Mark Kritzman

In Principal Components as a measure of systemic risk, the author Mark Kritzman defines absorption ratio (AR) as the fraction of the total variance of a set of asset returns explained or absorbed by a ...
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3answers
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Regularizers to compute Minimum Variance Portfolio weights

I need to compute the mimimum variance portfolio using different regularizers, to compare the results and use validation methods to find the optimal parameters. Currently my work has been performed ...
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What can I use to measure of diversification?

I have to come up with a measure of diversification for trade (this can tie in closely to diversification as regards portfolios). Are there any well known measures of portfolio diversification?
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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 ${\mathbf M}$. ...
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Calculate bond returns from yields

I have to construct and evaluate portfolio of bonds and stocks, namely I need to get return on portfolio, standard deviation and sharpe ratios. I have weekly data that contains stock prices, and I ...
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2answers
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non-subadditivity of VaR

I have been reading up on VaR and get very confused by the subadditivity concept. On wikipedia, it says "VaR is not subadditive: VaR of a combined portfolio can be larger than the sum of the VaRs ...
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1answer
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Portfolio optimization subject to transaction costs

Mean-Variance portfolio optimization attracted lots of attention in this forum so far. I am interested in the effect of incorporating transaction costs into the decision framework and I would like to ...
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What are pros and cons of mean absolute deviation portfolio optimization?

In this question a paper about mean absolute deviation portfolio optimization is mentioned and in the answer a spreadsheet with an implementation is attached. What is the use of this procedure? Does ...
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1answer
150 views

Risk minimization by investing in all assets with positive expected return

Suppose I have an amount $T$ to invest and $N$ available assets. The stochastic return per invested unit of asset $i$ is $R_i$. The variance and the expectation of $R_i$ are $\sigma^2_i$ and $\...
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1answer
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How to implement Konno's Mean-Absolute Deviation Portfolio Optimization Model using LP methods in Excel

Konno proposed a LP method for portfolio optimization using the Mean Absolute Deviation (MAD)
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1answer
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On a source for a mean-variance portfolio optimization result

In the context of a mean_variance framework consider an optimizing investor who chooses at time $T$ portfolio weights $w$ so as to maximize the quadratic objective function: $$U(w) = E[R_p] - \frac{\...
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2answers
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Calculating Portfolio Skewness & Kurtosis

I need to calculate the skewness and kurtosis of 2 asset portfolio, can someone please help me with the formulas and definition of terms? Thank you. I have been using the matrices method and I am not ...
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1answer
451 views

Expected shortfall minimization as portfolio objective

I'm trying to solve portfolio problem with minimising its Expected shortfall, assuming the returns follow a stable distribution. If I'm able to calculate MLE fit to the series, calculate expected ...
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4answers
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Portfolio Optimization using S&P Universes

Assuming a set portfolio optimization problem, if all optimization inputs are kept constant, what would you expect, in terms of results, if you run the same optimization using the S&P500 as ...
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1answer
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Calculating portfolio allocation beta with different asset classes?

I'd like to calculate portfolio allocation beta on a portfolio that has different asset classes. The portfolio may be made up of: ...
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1answer
975 views

Marginal contribution to Tracking error

I'm trying to calculate Marginal contribution to Tracking error. I would use the following formula: MCTE(asset i)=TE(excess return asset i vs.benchmark)* Beta(excess return asset i vs. benchmark AND ...
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1answer
153 views

How to measure the practicality of a market portfolio for long-term investment?

Do you believe that the composition of the market portfolio that you have found is a desirable or practical one as an investment? Explain why or why not, based on the positions of your stocks. I ...
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1answer
938 views

How does Kenneth French create the industry portfolio returns?

Kenneth Frenches Data Library includes industry portfolios. Is this done via a software of some type. I have some stock returns but I want to calculcated the returns of the industries in the ...
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1answer
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Do the wallet weights with the minimum variance need to be nonzero?

I wonder if we have n risky assets, does the portfolio with the minimum variance always have non-zero weights or can any weight be 0?