Questions tagged [portfolio]

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28
votes
12answers
17k views

What is the reference python library for portfolio optimization?

Does anyone know of a python library/source that is able to calculate the traditional mean-variance portfolio? To press my luck, any resources where the library/source also contains functions such as ...
17
votes
5answers
2k views

is beta of a portfolio always meaningful?

Consider the following strategies: a stat arb strategy with no overnight exposure, but significant market exposure intraday. a market timing model which is always long or short the market. etc is it ...
16
votes
3answers
5k views

How do I find the most diversified portfolio, or least correlated subset, of stocks?

I have a trading system that chooses top 10 stocks in Nasdaq 100 ranked on relative strength and some other factors. However, I'd like to take positions in only 5 of these 10 stocks based on how ...
15
votes
2answers
4k views

Modelling with negative interest rates

For a project, I am interested to model the impact of recently negative interest bonds on the portfolio. The literature on modelling negative interest rates is limited, and the only theory I could ...
15
votes
2answers
3k 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 ...
14
votes
3answers
15k views

Is there a step-by-step guide for calculating portfolio VaR using monte carlo simulations

I am trying to determine a step-by-step algorithm for calculating a portfolio's VaR using monte carlo simulations. It seems to me that the literature for this is extraordinarily opaque for something ...
14
votes
2answers
984 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 ...
12
votes
4answers
2k views

Are these steps correct to calculate Value-at-Risk with a Monte Carlo simulation?

I have a problem calculating VaR with the Monte Carlo Simulation. I followed the next steps and would like know if it is a right way to calculate VaR or if I need something more? The steps Generate ...
11
votes
3answers
515 views

Portfolio construction in reality?

There are various models for portfolio selection in literature, like, Harry Markowitz (HM) model ( Mean-Variance Model) [well known model] Konno and Yamazaki (1991) model: minimizes the sum of ...
10
votes
4answers
2k views

How can I select the least correlated portfolio of assets?

Can anyone explain the process and the calculations needed to select a portfolio of liquid futures assets with the least correlation? Given a set of returns for a series of assets, how do I select the ...
8
votes
4answers
8k views

Calculate Average Price, Cost, (Un)Realized P&L of a position based on executed trades

We have built an algorithmic trading software and need to calculate the following parameters for each position in our portfolio. Average Price Cost Realized Profit & Loss Unrealized Profit & ...
8
votes
2answers
4k views

How do Return.portfolio and Return.rebalancing work in Performance Analytics in R?

I have a question about the function Return.portfolio/Return.rebalancing from the Performance Analytics package in R. I take ...
8
votes
1answer
9k views

What is a self-financing and replicating portfolio?

I try to understand the derivation of the Black-Scholes equation based on the "constructing a replicating portfolio". From mathematical point of view it looks simple. We assume that: Stock prices is ...
8
votes
2answers
597 views

How to interpret beta meaningfully?

Although this is probably a basic question, this is probably also the right forum to post it in :) I thought I understood beta, but know I am really confused... The beta between my portfolio (weekly ...
8
votes
2answers
655 views

Completeness and Hedging Question

A question in some private notes I'm struggling to work through (exam. prep.). (iii) is where I hit a wall with my understanding & I'm lost thereafter. Any help/clarification gratefully received. ...
7
votes
5answers
2k views

portfolio optimization from empirical return distributions

I'd like to do a portfolio optimization of a set of ETF's but want to avoid traditional problems with normality assumptions in returns etc. Are there techniques that let me sample 'draws' from the ...
7
votes
5answers
2k views

How to fit probability density function from sample moments?

If I have calculated the sample mean, variance, skew and kurtosis of a set of data, how would I go about fitting a probability distribution to match these moments (i.e. choosing a probability ...
7
votes
3answers
465 views

What is smart beta, alternative index, factor investing?

What is smart beta, alternative index, factor investing? Are they basically the same thing? Construct a benchmark index using schema other than market cap?
7
votes
2answers
1k 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)} = ...
7
votes
3answers
226 views

Where to find good notations to teach investment portfolio maths?

I don't know whether this question is in order here. I do a bit of teaching and I am preparing my own notes but I thought that his should not be necessary. In which book/pdf on the web can we find a ...
7
votes
2answers
216 views

Portfolio returns with unequal asset return histories

Using the package PerformanceAnalytics in R, I am trying to calculate the return of an equal-weighted portfolio that contains 30 assets. However, these assets do not have the same starting point in ...
6
votes
2answers
769 views

What is the intuition of a spread portfolio and how exactly is it constructed?

In a lot of papers spread portfolios are constructed, like in Harvey and Siddique (1999), Table IV, or in Fama and French (2005 from SSRN), page 15. First, why is it important to construct such ...
6
votes
2answers
333 views

Mean Variance Portfolio theory and real-world problem?

There are many assumptions on mean-variance portfolio theory and they seem to be very unrealistic, for example 1) investors have the same information at the same time: calculating expected returns ...
6
votes
3answers
491 views

Jegadeesh and Titman 1993 Power of their test

I am reading this classic paper(http://www.business.unr.edu/faculty/liuc/files/BADM742/Jegadeesh_Titman_1993.pdf) and got confused by one of their arguments on their overlapping portfolio strategy to ...
6
votes
0answers
744 views

Shrinkage Estimator for Newey-West Covariance Matrix

I like to apply the Newey-West covariance estimator for portfolio optmization which is given by $$ \Sigma = \Sigma(0) + \frac12 \left (\Sigma(1) + \Sigma(1)^T \right), $$ where $\Sigma(i)$ is the lag ...
5
votes
2answers
294 views

Portfolio Optimization to include ALL Securities?

I'm currently optimizing portfolio weights for an investment team with N stocks. We buy stocks with a conviction it will generate a return and it is up to me to determine weighting. However, with ...
5
votes
3answers
1k views

Calculating the right portfolio(position size for each leg) in a Long/Short Strategy

For a Long/Short Strategy, I have two stocks with different volatilities. How can I calculate the right position size for each leg? *The pair trading is not coming from co-integration but more as a ...
5
votes
1answer
451 views

How modern portfolio theory(MPT) and CAPM are related?

1. Question In what sense Capital Asset Pricing Model(CAPM) is related with Modern Portfolio Theory(MPT)? Why do we need to check whether the current price of assets is overvalued or undervalued ...
5
votes
2answers
351 views

Comparing Returns on a Sector Basis

I'd like to compare the returns of a portfolio segregated by groups to the returns of those groups in total. So say for example I have a portfolio with 40% Industrials and 60% Technology, then over ...
5
votes
1answer
588 views

analyze strategy performance with given matrix of weights/time and weekly returns in R

I have a matrix of 259 weekly returns, 50 assets and a portfolio composition for each of the 259 weeks. I would like to test the performance of the portfolio during 52 weeks, rebalancing every 12 ...
5
votes
3answers
273 views

How to work out weights for a portfolio based on an inverse ratio with positive and negative values?

I am trying to work out how to determine weights for the assets in order to form a portfolio. The ratio I am using is EV/EBIT, hence the smaller the better. The problem is I don't know how to handle ...
5
votes
2answers
4k views

Equity option portfolio greeks with underlying

I'm curious about how to construct the five basic greeks for an equity option portfolio when there are shares of the underlying in the portfolio. For example, a portfolio of 100 call options and 100 ...
5
votes
1answer
342 views

RMT (Random Matrix Theory) issue with callibrating MP distribution -

I am seeing an issue when callibrating an MP distribution. Assume a log return series for the SP500 with the following dimensions dim(xts.sp500.ret.stocksonly) ==> [1] 1133 478 ...
5
votes
1answer
300 views

Simple mean reversion strategy portfolio construction

I had a quick idea I wanted to test, but am not sure of the correct way to size bets. Basically, I think that for a given index (say S&P), I want to be long under performers and short over ...
5
votes
1answer
258 views

Full Kelly portfolios having same weights as tangency portfolios

I'm currently comparing empirically the differences between Markowitz and Kelly portfolios. I calculated the Kelly weights for monthly return observations over 10 years for a sample of 50 stocks from ...
4
votes
2answers
2k views

Portfolio Risk Decomposition - different methodologies

I understand that there are several methods for decomposing contributions to risk (be it variance, std dev, etc.) in a portfolio of assets. For example, a response in this post indicates that there ...
4
votes
1answer
181 views

How do I model risks for specific short-term short calls in a portfolio with limited data?

I'm trying to do some risk analysis on a portfolio of bonds, currency, stocks and short calls. The short calls expire in approximately 15-30 days and I've only got around 20 days of pricing data on ...
4
votes
1answer
3k 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 ...
4
votes
1answer
145 views

Calculating portfolio weights of derivatives

A rather simple question. You have a portfolio of USD100 in cash. You now take USD10 and buy a derivative that gives you exposure of USD200 to something. What is the weighting of cash in the ...
4
votes
2answers
122 views

When would dedicated portfolios do better than 'immunized' portfolios?

We just learned about cash-matching through dedicated portfolios (using risk free bonds) in my class that concerned mathematical programming. However, in an aside one of the notes said: It should be ...
4
votes
1answer
843 views

Portfolio optimization with Portfolio CVaR Constraint

I wanted to optimize a portfolio based on a portfolio-wide CVaR constraint (i.e. $CVaR_p \leq 0.08$). Unfortunately, I only find solution that minimizes the entire CVaR of the Portfolio. Do you mind ...
3
votes
2answers
763 views

Basic question on Portfolio Theory

I was revising my stuff about portfolio theory and I noticed that every single time, expected return and corresponding variance or covariance are given! (not calculating ourselves). So I'm just ...
3
votes
3answers
357 views

Is there a way to meaningfully generate daily returns from monthly?

I have a set of 7 investments in a portfolio and I need to optimize the weightings based on some exposures to various markets/styles/economic factors. I was hoping to do some sort of simple exposure ...
3
votes
1answer
989 views

How to compute the variance of a Long-Short Equity Portfolio?

I am calculating the historical portfolio variance of various long-short equity portfolios. For simplicity, assume the portfolio is long stock A with weight 1.0 and short stock B with weight -0.5. ...
3
votes
1answer
2k views

How to compute the forward price using a replicating portfolio?

I post this question here as I didn't receive an answer in the Mathematics community. I am trying to understand how replicating portfolios can help us determine fair prices. Suppose we have a 3-year ...
3
votes
2answers
1k views

Dmat argument in solve.QP R function: Cov or 2*Cov?

Background My final objective is to find a portfolio located on the efficient frontier from a choice of 100 stocks from a stock index (eg. S&P500). This efficient portfolio will be such that ...
3
votes
1answer
233 views

Should a backtester have ability to run multiple strategies simultaneously?

At the moment the backtester has a portfolio; a portfolio is associated with one strategy. The backtester is used to test different strategies one at a time, giving their return, Sharpe, drawdown. But ...
3
votes
1answer
196 views

Why are there two expressions for the Black-Scholes hedging portfolio

I am new to derivatives pricing and am trying to understand why there are two different expressions for the Black-Scholes hedging portfolio. The first approach, used in books like Hull, stipulates ...
3
votes
1answer
856 views

How to choose a tangency portfolio without a risk-free rate

How do you choose an optimal portfolio from the efficient frontier if no risk-free rate is given? I know that if there exists risk-free asset, then you would combine a portfolio from the efficient ...
3
votes
1answer
108 views

How to distinguish true negative eigenvalues from small negative eigenvalues due to floating point error?

Floating points have rounding errors so algorithm to find eigenvalues may report tiny negative eigenvalues but in reality thsee could actually be 0 if we had full precision. Any way to tell ? I have ...