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16
votes
6answers
7k views

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 ...
12
votes
5answers
1k 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 ...
11
votes
3answers
2k 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 ...
11
votes
2answers
984 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 ...
6
votes
5answers
665 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 ...
6
votes
1answer
2k 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 ...
6
votes
2answers
210 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 ...
5
votes
4answers
993 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 ...
5
votes
5answers
898 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 ...
5
votes
1answer
217 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
407 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 ...
5
votes
0answers
470 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 ...
4
votes
3answers
458 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 ...
4
votes
2answers
286 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 ...
4
votes
2answers
317 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)} = ...
4
votes
1answer
807 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
161 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 ...
4
votes
0answers
290 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 ...
3
votes
1answer
140 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 ...
3
votes
1answer
327 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 ...
3
votes
2answers
718 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 ...
2
votes
1answer
78 views

Correlation of asset to portfolio, given certain variables

Ultimately I'm trying to calculate stdev contribution, but I've hit a hurdle. What I have: 20x20 correlation matrix for various assets Standard deviations for each asset Returns for each asset ...
2
votes
1answer
111 views

Is the volatility of a trader's wealth equal to the volatility of the underlying assets traded?

Assume that a trader trades in several stocks with different volatilities. The return of the trader's portfolio would be the weighted average of returns and the risk would be a function of the the ...
2
votes
1answer
511 views

Using alpha to evaluate trading strategy

I have a trading strategy that generates returns $R_{t}$. I want to test the strategy by looking at the alpha: $R_t - R_{f,t} = \alpha + \beta (R_{m,t} - R_{f,t}) + e_t$ I compare my alpha against ...
2
votes
0answers
117 views

What happened to Mountain View Analytics?

I stumbled over Thomas Cover's work on algorithmic portfolio selection; apparently, an outfit called "Mountain View Analytics" attempted to implement the suggestions from Cover's research. ...
2
votes
1answer
55 views

Why does my posterior mean differs from Idzorek's results?

I have implemented two different expressions (Idzorek p.6, Walters p.51) of a posterior mean return calculation within a Black-Litterman framework. My results are the same, irrespective of the ...
2
votes
0answers
75 views

Portfolio insurance with a coherent risk measure (CVaR)

I would like to analysis of portfolio insurance under a coherent risk-measure method (CVaR), How can I achieve that? Is there a way to turn the problem into a linear programming problem? or to ...
2
votes
0answers
408 views

How to correctly construct a value- and equally weighted portfolio consisting of property-types?

A problem of which I couldn’t find the answer on the forum is about the construction of equally-weighted and value-weighted portfolio. I want to compute the equally-weighted property-type portfolio ...
2
votes
2answers
121 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 ...
2
votes
0answers
126 views

Calculating stock weight for SEC13F filers

I am trying to evaluate weight of stocks in portfolio for an investor. For this purpose I use SEC13F filings for particular quarters and historical prices from Yahoo. There are stocks in portfolio ...
1
vote
1answer
128 views

Given a correlation martrix, calculate portfolio's correlation with its assets

Find correlation vector like $[ d e f ]$ where d, e and f represent correlation of P(portfolio) with its assets A, B and C respectively. The assets A, B, C can be another portfolio. In order for ...
1
vote
2answers
145 views

Statistics of difference between two GBMs

if I have two asset prices modeled separately as geometric brownian motions. How do i go about calculating the expected statistics of their difference? Like given the sigmas and mus of both processes, ...
1
vote
2answers
49 views

Calculate alpha (CAPM) in “cross country-portfolio”

Assume I wanted to compute the alpha (in CAPM sense, i.e. $r_i - r_f = \alpha_i + \beta_i(r_m - r_f) + \epsilon_i$) of a stock. So I take, say, monthly returns of a stock $i$ for 1 year. Subtract the ...
1
vote
2answers
209 views

Risk management of options

Your client would like to buy a digital call option. the digital call option pays the buyer in one years time (i.e at maturity ) N=1m SGD, if the SGD USD spot rate at maturity is above a prescribed ...
1
vote
1answer
68 views

Arbitrage Strategy Proof in Bjork

In Tomas Bjork's Arbitrage Theory in Continuous Time (or here), $\exists$ this proposition Proposition 2.9 Suppose that a claim X is reachable with replicating portfolio h. Then any price at t=0 of ...
1
vote
1answer
95 views

Greeks of self-financing portfolio

I would like to learn more about the Greeks of portfolios of options: In textbooks and websites, I commonly encounter the unqualified claim that "The Greek measure of a portfolio is the sum of the ...
1
vote
1answer
319 views

Portfolio software that shows 'total return' for each investment

I'm a high school technology teacher and sponsor for the Charity Student Investment Project. Currently our students track our investment portfolio via a google spreadsheet ...
1
vote
1answer
417 views

derivation of formula for portfolio skewness and kurtosis

Where can I find derivation of formula for portfolio skewness and kurtosis? I can find formulas everywhere, but not their derivations? For example, the portfolio variance formula is well known and I ...
1
vote
2answers
1k 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 & ...
1
vote
1answer
148 views

Resampled efficient frontier length of simulation

I was provided with a VBA program from my lecturer that applies the resampled efficient frontier. We have an investment horizon $T$ (6 years) and he uses a multivariate normal distribution with ...
0
votes
2answers
197 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 ...
0
votes
1answer
132 views

How to get permanently growing chart within PCA

I looked onto different questions and answers about application of PCA on this site and found this interesting article : ...
0
votes
1answer
146 views

How do I simulate stock prices for a 10 asset portfolio, over a period of 10 years in MATLAB? [closed]

If I have given vectors for return and volatility (i.e. I have two 1x10 vectors), and I assume at first that their correlation is 0 (meaning my covariance-variance matrix is just diagonal), how do I ...
0
votes
0answers
16 views

Portfolio Optimization

I've just started reading up on Portfolio Optimization models and have come across the use of exposure bounds to mitigate the sensitivity of the optimized model solution, owing to parameter estimation ...
0
votes
0answers
58 views

Option payoffs and replicating payoffs

I've come across the below question which has no answers to it and I was hoping someone could provide some help. I know it quite a long question and I appreciate any help with this. An investment ...