# 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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### 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}\...
976 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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### Non-redundant asset?

I've been solving many exercises with three assets that have two possible payoffs each, one payoff per possible future state. The question is always the same, i.e. is any asset redundant. After ...
48 views

### No risk free security?

Imagine market without a risk free security. How is security market line constructed? How is it interpreted?
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### How to calculate Information Ratio?

In the book titled "Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk" by Grinold & Kahn, the information ratio is defined as "the ratio of ...
2k views

### Value at Risk - Long/Short position

I have a simple question on the VaR for a portfolio that consists of a long and short position. Say I have a portfolio consisting of the following positions: long 1000 shares of stock X short 1000 ...
175 views

### Problems with Performance Attribution Analysis

I am using the typical Brinson Model formula, but it doesn´t work, I think that is explained because of the compound effect and rebalancing... when I look my portfolio's YTD return and multiply by the ...
250 views

### Why is it better to use evolutionary algorithms than OLS for solving index tracking problem?

I am currently using different optimization algorithms for finding constrained portfolio that best replicate choosen index. So i have a optimization task to minimize tracking error. I wonder why every ...
789 views

### Absorption Ratio

I'm actually trying to implement Mark Kritzman's absorption ratio (Principal Components as a Measure of Systemic Risk by Kritzmam, Li, Page and Rigobon, 2010, SSRN 1633027) using Python, but I'm not ...
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### Trading 3 stocks X Y Z where X cointegrated to Y, Y to Z, but no other cointegration is available

Suppose you have 3 stocks, say X Y Z. You also know that X is cointegrated to Y using some test (say ADF) and Y is cointegrated to Z. However, no transitivity, and no threesome cointegration ...
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### Given multiple strategies with their ER, volatility, how would I calculate the combined Sharpe?

Without knowing the actual daily returns, I have a table something like this: ...
156 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 ...
648 views

### Max allowable return in Markowitz model

The Markowitz model solves the following problem: The portfolio with the smallest variance among attainable portfolios with expected return µV. Here we have to choose µV to get the optimal portfolio ...
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### Geometric Sharpe ratio

I'm computing different metrics for mutual fund performance. I want to use classic Sharpe ratio, but I also got to know there is geometric Sharpe ratio. Unfortunately I didn't find enough info about ...
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### Predicting portfolio returns

I suppose there are roughly two approaches to predict portfolio returns. Either predict the returns of all underlying stocks and aggregate all individual stock predictions, or predict the portfolio ...
1k 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 ...
131 views

### Optimal investment mix of equity and debt in a single company, HY vs IG

What is the optimal mix of equity and debt that an investor should invest in a single company? If an investor invests in both the debt and equity of a company, they are in effect de-levering the ...
834 views

### Book recommendation on portfolio managment

I have a BSc degree in pure mathematics and i am graduate student in Operations research. I will have a course on "portfolio management". I am looking for some book/lecture notes/online course ...
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### Non-parametric estimator - CVaR / Expected shortfall

Is the estimation of the CVaR using known non-parametric methods (histogram, kernels) different than the estimation of any other R.V.? If the answer is yes, I am interested to know whether there are ...
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### Why can't I take the Value at Risk "VaR" as a a risk objective in PerformanceAnalytics? (it does work for "ES)

I am currently playing around with PortfolioAnalytics package in R and some data and I am aiming to create different portfolios with different VaR. However, I am struggling first of all, add.objective(...
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### Can we get the portfolio size approximation from the PnL? [closed]

Im wondering if we can get the portfolio size approximation, if we have the volatility and -/+ pnl of the portfolio ? Is there a method or a formula ? Example the annual volatility of 3% and daily ...
103 views

### Maximum Diversification Strategy without risk free asset

I am currently dealing with the Maximum Diversification Strategy and I am trying to understand the synthetic universe approach from Choueifaty et al.(https://www.tobam.fr/wp-content/uploads/2014/12/...
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### Portfolio volatility - Real life application

Given that a portfolio consists of Stock=USD 30, High-yield bonds(duration=5 years,spread duration=5 years) =USD 40 , Commodity = USD 30.
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### What is the "characteristic" associated with the MMI portfolio? How would you find it?

I found the above question in Grinold and Khan "Active Portfolio Management", p39 Chapter 2 Q3 of the Exercises. I presume the MMI portfolio is the Major Markets Index portfolio, but I'm struggling to ...
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### Construct a portfolio of European call options with a certain payoff function

My question is similar to Replicate a Portfolio with Given Payoff but I am not quite sure how to apply this to my problem. A portfolio of European call options on an asset $S_T$ has a payoff function ...
156 views

### Do correlated assets affect the price of a portfolio of derivatives?

I need to compute the value at risk of a given portfolio as an exercise for a class at university but I have trouble understanding how correlated assets affect the price of the portfolio. Could you ...
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### Classifying groups of stocks beyond Market Cap/Industry/Sector

I'm monitoring margin values for a portfolio and I want to classify the stocks in my universe using different metrics/information. Just for the sake of making analysis/inferences on the data I have. ...
4k views

### robust portfolio optimization re-balancing with transaction costs

The optimal re-balancing strategy takes account of factors including i) objective function, ii) current portfolio weights, iii) expected return vector containing updated views/alpha forecasts, iv) ...
83 views

### Spot trading: exact mathematical definition of the positions for a portfolio

Let us say that I want to spot trade a portfolio constituted of a pair of two stocks of respective prices (for example in USD) $S^1_t$ and $S^2_t$, and suppose for example that they co-integrate ...
3k views

### calculate portfolio return with one long position and one short position

I was trying to learn how to work out the performance of a portfolio where you are long one stock and short another. I found an example below. The NAV is calculated by adding the value of the long ...
512 views

### Most significant research articles for practical investors with research perspectives

I am an applied mathematician and recently I have decided to study the portfolio management theory. As a final objective, I want to manage my own portfolio and to try make some money on it using my ...
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### Black Litterman: Is it possible to have multiple views (from different sources) on the same asset?

From the basics of Black Litterman I understand that each view on a stock is implemented via the pick matrix P with the expected value of the views in Q. I have read several papers where each stock ...
2k views

### R: Calculating cumulative return of a portfolio

I've downloaded adjusted closing prices from Yahoo using the quantmod-package, and used that to create a portfolio consisting of 50% ...
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### Co-variance of Portfolio A with Portfolio B

I'm trying to calculate the correlation between two separate portfolios. I've used A*COV(AB)*B to calculate the co-variance of each portfolio where: A = Array ...
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### Which performance evaluation measure to assess "Connectedness Matrix" based porfolios?

1. Question Which performance evaluation measure would be best to assess the portfolios built on 'connectedness matrix'? The connectedness matrix is the concept introduced in the academic paper "...
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### Compare portfolio variance using different regularizers

I'm given a question like below. Using the 48_Industry_Portfolios_daily dataset: characterize/describe the dataset and focus on the global minimum variance portfolio. Compare the portfolio variance ...
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### Rebalancing order on trading pairs

I'm working on a program to rebalance my portfolio among a set of crypto assets. Though I'm a bit confused on how to best order the buys in sells among the various pairs. Consider the following ...
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### How to check if a portfolio has momentum bias

I am wondering what methodology exists to check if a fund/portfolio is having momentum bias or chasing the past performance, assuming you have their full returns and full portfolio holdings for past ...
130 views

### Correct beta weighted delta options formula?

Is this the correct formula for beta weighted delta: http://www.nishatrades.com/blog/beta-weighted-delta I've seen this What is the formula for beta weighted delta and gamma? but they seem to be ...
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 ...
608 views

### portfolio information ratio calculation on daily returns including hedged strategy results interpretation

I am tasked with calculating the portfolio information ratio on ~15 years of daily portfolio returns and I am finding several approaches online which is quite confusing. The first approach simply ...
I have a time series of adjusted returns for two companies, A and B. I have created a portfolio consisting of these two time series with equal weighting (sum of weights must equal 1): $w_a = w_b=0.5$...