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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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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}) - ...
codeedoc's user avatar
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7 votes
2 answers
2k views

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)} = ...
Richi Wa's user avatar
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0 votes
1 answer
4k views

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 ...
sen_saven's user avatar
  • 441
7 votes
2 answers
1k 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 ...
Mahi's user avatar
  • 71
3 votes
2 answers
3k views

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 ...
user28909's user avatar
  • 498
20 votes
3 answers
5k views

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 ...
Owen's user avatar
  • 478
3 votes
5 answers
4k views

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 ...
Hiru's user avatar
  • 103
45 votes
12 answers
31k views

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 ...
nxstock-trader's user avatar
21 votes
4 answers
4k views

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. ...
17 votes
4 answers
8k views

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 ...
Pasha's user avatar
  • 171
9 votes
2 answers
4k views

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 ...
user avatar
9 votes
2 answers
1k views

Why do low standard deviation stocks tend to have superior future returns?

I've recently stumbled on something that really surprised me. These papers (1, 2) find that past standard deviation of returns is inversely related to future returns. That is, portfolio of low ...
Jase's user avatar
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7 votes
2 answers
723 views

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 ...
Stefan Voigt's user avatar
  • 1,466
6 votes
1 answer
1k views

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}\...
Alejandro Andrade's user avatar
4 votes
1 answer
1k 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?
lemontree's user avatar
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3 votes
1 answer
673 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 ...
ontic's user avatar
  • 85
3 votes
3 answers
4k views

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?.
user3481555's user avatar
2 votes
1 answer
187 views

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 ...
Wolfy's user avatar
  • 728
2 votes
2 answers
314 views

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 ...
Taylor's user avatar
  • 554
24 votes
4 answers
19k views

Why shrink the covariance matrix?

I'm trying to understand why it's useful to shrink the covariance matrix for portfolio construction or in fact general. Think I missing something. I know if you have 5,000 stocks it's a lot of ...
user8170's user avatar
  • 387
23 votes
5 answers
16k views

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 ...
RockScience's user avatar
  • 2,003
23 votes
2 answers
2k views

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 ...
hhh's user avatar
  • 705
17 votes
2 answers
4k views

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 ...
strimp099's user avatar
  • 2,116
15 votes
1 answer
2k views

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{...
Richi Wa's user avatar
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14 votes
2 answers
1k views

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 ...
Ram Ahluwalia's user avatar
12 votes
2 answers
1k views

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 ...
RockScience's user avatar
  • 2,003
11 votes
2 answers
5k views

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-...
michael's user avatar
  • 257
10 votes
0 answers
297 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 ${\mathbf M}$. ...
StackG's user avatar
  • 3,046
9 votes
5 answers
19k views

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 ...
Carlo's user avatar
  • 143
8 votes
5 answers
11k views

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 ...
Wintermute's user avatar
7 votes
3 answers
2k views

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.
dvegadvol's user avatar
7 votes
2 answers
7k views

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 ...
Richard's user avatar
  • 87
6 votes
1 answer
4k views

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 ...
user avatar
5 votes
4 answers
2k views

How to determine what's driving the VaR?

I am given the following data: Historical (260 days) P&L vector of a portfolio. Specific P&L's for each investment in the portfolio, for the 10 days with the lowest P&L. The question ...
Mkch's user avatar
  • 151
5 votes
2 answers
12k views

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 ...
codeedoc's user avatar
  • 245
4 votes
4 answers
8k views

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 ...
forstenn's user avatar
4 votes
3 answers
525 views

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 ...
AlRacoon's user avatar
  • 6,632
3 votes
1 answer
3k views

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 ...
Stefan Voigt's user avatar
  • 1,466
3 votes
4 answers
577 views

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 ...
Mayou's user avatar
  • 662
3 votes
1 answer
4k views

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 ...
JungleDiff's user avatar
3 votes
1 answer
682 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 ...
Jan Sila's user avatar
  • 732
3 votes
2 answers
1k views

Construct a butterfly interest rate portfolio to eliminate PCA exposures

I have data from 2012 to 2016 for interest rates whose term range from 2 month to 30 years, a total of 10 Principal components can be calculated. Then I want to construct a portfolio, $$WFLY = w_1 *5Y ...
Qing's user avatar
  • 95
2 votes
2 answers
4k 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-...
John Paris's user avatar
2 votes
1 answer
1k views

Minimize overall portfolio turnover under constraints

Assume I have M portfolios, each of them can be represented as a T by N matrix, where N represents number of stocks traded and T represents number of days. For each portfolio matrix, each row is under ...
Warren's user avatar
  • 145
2 votes
3 answers
2k views

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 ...
Richi Wa's user avatar
  • 13.7k
2 votes
3 answers
2k views

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 ...
Hiru's user avatar
  • 103
1 vote
1 answer
165 views

Reverse optimization: How to generate the expected portfolio returns given the weights and a series of constraints on those weights?

I have the below function in Python. My objective is to back out the expected returns associated with certain portfolio weights given a series of assumptions. From this I want to generate the expected ...
Farrep7's user avatar
  • 21
1 vote
1 answer
3k views

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: ...
4thSpace's user avatar
  • 167
1 vote
1 answer
307 views

Naive question: how do factor models inform portfolio construction?

I have read plenty on the topic of factor modelling, but, in the end, after one has decided upon the factors to include in a model, how do all the Betas how tell one how to weigh each asset in a ...
Coolio2654's user avatar
1 vote
1 answer
181 views

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{\...
Monolite's user avatar
  • 367