15 votes
Accepted

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

You have the correct approach. (1) The simulation generates sampled portfolio values, $P_1,P_2, \dots, P_n$ at time $t=T$. VaR is specified as a left-tail percentile. Order the sample as $$P_{(1)} ...
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  • 3,250
9 votes
Accepted

Portfolio construction in reality?

Portfolio optimalisation depends heavily on the estimation of the moments (and therefore has HUGE estimation uncertainty). Even though it's useful for comparing and analysing different existing ...
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  • 333
8 votes
Accepted

Portfolio Risk Decomposition - different methodologies

Different portfolio risk decompositions answer different questions. Before discussing what method to use, first ask why you want a decomposition and what definition of risk are you using. Is the ...
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  • 6,334
8 votes
Accepted

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

CAPM states that the expected return of any given asset should equal $ER_i=R_f+β_i (R_m-R_f)$, with α being the error term of the previous equation. Now, as α has an expected value of zero, then only ...
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  • 496
6 votes
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Mean Variance Portfolio theory and real-world problem?

Mean-variance (MV) is a framework rather than a prescription. This framework allows one to make, discuss, and defend his investment decision. In practice, there are many ways to make adjustments to ...
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6 votes

What is smart beta, alternative index, factor investing?

In recent years there has been much attention given to defining indexes other than market-cap based indices. While market-cap based indices approximate the theoretical Market Portfolio enshrined in ...
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  • 9,462
6 votes

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

The first step is to divide a very large number of stocks into deciles (groups having 10% of the stocks) based on some ranked measure (for example book to market or liquidity etc.), then you construct ...
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  • 9,077
6 votes
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What is the intuition of a spread portfolio and how exactly is it constructed?

Does variable $x$ forecast returns? Let's say you have some variable $x$ that you think forecasts returns, and you want to conduct statistical tests of a null hypothesis that $x$ has nothing to do ...
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  • 6,334
6 votes
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Volatility of a multiple-asset portfolio

You can generalize the formula from a portfolio composed of 2 assets to a portfolio composed of $N$ assets as follows : $$ \sigma^2_{port} = \sum_{i=1}^N \sum_{j=1}^N \omega_i \text{cov} (i,j)\...
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  • 1,209
5 votes

Correlation of asset to portfolio, given certain variables

If $\Sigma$ is the covariance matrix of all assets and $w$ is the column vector of weightings of the asset in a certain portfolio. Then $$ w^T \Sigma w = VAR $$ is the variance of the portfolio. The ...
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  • 13.3k
5 votes

Are there any tools or useful algos for identifying corner portfolios?

7 years ago I had to solve the problem of a efficiency frontier under linear constraints on the asset weights and also stumbled upon Markowitz Critial Line Algorithm. I still have a directory with ...
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5 votes

Basic question on Portfolio Theory

Of course estimating expected returns is the very core of portfolio management. Finding a useful covariance matrix too. To find both fills a book. So I first thought about closing the question. But it ...
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  • 13.3k
5 votes
Accepted

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

We have weights $w_A$, $w_B$ and $w_C = 1 - w_A - w_B$ that sum to $1$. With de-meaned returns $r_A$, $r_B$, and $r_C$, the portfolio variance is $$E\{[w_A r_A + w_B r_B + (1 - w_A - w_B)r_C]^2 \} = ...
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  • 3,250
5 votes
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Widely accepted methods for coming up with the co-variance matrix of assets?

Multivariate volatility models for replacing the sample covariance matrix with in the mean-variance portfolio selection model: RiskMetrics 1996 EWMA (Exponentially weighted moving average) covariance ...
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  • 2,835
5 votes
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Sharpe Ratio and Sortino Question: Standard practice

Theoretically, Sharpe should be the average of (compounded) excess returns divided by the volatility of the same. It was designed to measure the risk-reward preferring the risk asset to riskless. So ...
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  • 4,896
4 votes

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

If you only need to pick 5 out of 10 and want equal weights then just enumerate all 252 possibilities (as pointed out above) and compute the portfolio volatility $(\textbf{1}'K^{(i)}\textbf{1})^{1/2}...
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  • 537
4 votes

What is the reference python library for portfolio optimization?

Convex Optimisation - CVXOpt and CVXPy. Textbook by Boyd & Vandenberghe Aside from CVXOPT (known for its cone programming, see http://cvxopt.org/) with extensive documentation by the authors, ...
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  • 1,018
4 votes

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

Using Andy Flury answer and bit polishing it gives following Python class for PnL calculator: ...
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  • 211
4 votes
Accepted

Geometric Return & Performance Results for Quarterly Rebalancing

Actually, neither of your two results are quite correct. As explained in the Details for the Return.calculate function, most of the PerformanceAnalytics functions use discrete returns, not log ...
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  • 404
4 votes

Jegadeesh and Titman 1993 Power of their test

Non overlapping periods would make for a far smaller sample
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4 votes
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Basic question on Portfolio Theory

Theoretically speaking (as it's done in financial textbooks at b-school level), variance and covariance are calculated on historical performance of asset classes, forward looking returns are CAPM ...
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4 votes

Mean Variance Portfolio theory and real-world problem?

It is well known that the MV-optimal portfolio has some very bad properties in practice: Backtesting: The MV portfolio performs very bad in backtesting applications Diversification: The MV portfolio ...
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  • 5,629
4 votes

how to calculate daily risk free rate using 13 week treasury bill

user233051 notes that ^IRX is indeed the official discount rate of the US Treasury. So to answer his question we need to exactly understand how the Treasury computes the discount rate. My answer is ...
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4 votes

Variance Matrix with 'nan' values

This is a common problem in covariance matrix estimation, with several possible solutions. One of the simplest involves two steps: (1) You compute each element of the covariance matrix on a 'best ...
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  • 9,462
4 votes

What is the delta of a portfolio invested in different stocks?

Strictly speaking, you cannot aggregate (i.e. sum) deltas. However, equity traders often provide their net exposure in currency units, which is a useful number. The same reasoning is possible with ...
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4 votes
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What is `1+ return` called?

It's called 'Gross return' (a.k.a. 'Gross Rate of Return'). See Zivot Course Notes Eqn. 1.8 Also, as pointed by Alex C: ... in Statistics it is called a 'link relative' or 'chain relative' (...
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  • 725
4 votes

What returns to use?

Since you're looking to summarize the performance of a monthly return series in a single number, it is best to compute the annualized return. This is the standard used in the investment management ...
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  • 61
4 votes

What does risk tolerance represent for utility-maximizing optimization with linear constraints?

You cannot eliminate the dependence of a solution on the risk aversion parameter (which this author confusingly calls $\lambda$). Perhaps a source of confusion? Typically $\lambda$ is used to denote ...
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  • 6,334
4 votes
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Active portfolio management - characteristic portfolios derivation

Below proposition 1 (In the 2nd edition at p. 28?), at the beginning of the chapter, he specifically writes: Characteristic portfolios are not necessarily fully invested. They can include long and ...
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  • 3,618
4 votes
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Best books on portfolio construction?

I can list a couple of things that are very reasonable to start off with. As written in the above comment, you will not be able to find any "secret sauce" in books and journals. You will, ...
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