9 votes
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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 ...
Jean-Paul's user avatar
  • 333
9 votes
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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 ...
Matthew Gunn's user avatar
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8 votes
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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 ...
MGL's user avatar
  • 516
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 ...
Matthew Gunn's user avatar
  • 6,934
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 ...
Alex C's user avatar
  • 9,372
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 ...
nbbo2's user avatar
  • 11.2k
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)\...
JejeBelfort's user avatar
  • 1,219
5 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: ...
mde's user avatar
  • 221
5 votes
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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 \} = ...
RRL's user avatar
  • 3,630
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 ...
develarist's user avatar
  • 3,000
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 ...
demully's user avatar
  • 5,071
5 votes

Why is a smaller portfolio norm better?

Norm constraints are motivated by regularisation in regression analysis. L1 and L2 norm are similar to Ridge and Lasso Regression. The author who first introduced this method argued that it will ...
Dhruv Mahajan's user avatar
5 votes

Best books on portfolio construction?

In addition to classical texts by Grinold and Kahn, and the sources cited in the previous answer, I can't help mentioning my book. It has a chapter on Portfolio Construction which includes alphas at ...
Michael Isichenko's user avatar
5 votes
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Information Coefficient (IC) Formulae Differences

Paraphrasing some quote: "they are different but same but still different" In reality the number of correct bets $N_c$ is the number of times the analyst was correct predicting the ...
emot's user avatar
  • 876
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, ...
NBF's user avatar
  • 1,068
4 votes

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

This is a commonly seen problem, and also relates to situations in which one is dealing with some less-liquid underlyings. I will describe a method that you could think of as "stochastic backfilling" ...
RiskyScientist's user avatar
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 ...
Mike O'Connor's user avatar
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 ...
nbbo2's user avatar
  • 11.2k
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 ...
Enrico Schumann's user avatar
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' (...
rbm's user avatar
  • 745
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 ...
nitin23's user avatar
  • 61
4 votes

% Drawdown on Stock Portfolio to hit Margin Call

Define CoL = cash or loan (cash if positive, loan if negative) MVL = market value of long positions MRP = Maintenance Margin Requirement fraction (=0.3) NetLiq = liquidation value (aka total ...
Alex C's user avatar
  • 9,372
4 votes
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How to calculate "portfolio cumulative return" from individual price data and weight of them?

These answers are missing the idea of path dependency. Your weights are only updated monthly. That means your weight on t0 is w0 and weight on t1 is w0*(1 + r1), weight on t2 is w0*(1+r1)*(1+r2) where ...
mperlow's user avatar
  • 446
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 ...
Matthew Gunn's user avatar
  • 6,934
4 votes

Calculating Correlation of Two portfolios?

You may be over-thinking it. It is a straightforward calculation using matrices, as easy as turning the crank of a sausage-making machine. The standard deviation matrix is ...
Alex C's user avatar
  • 9,372
4 votes
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Why annualizing sampled covariance matrix changes stock weight vector?

Q1. Calculating the GMVP involves three operations: Inverting the covariance matrix $\Sigma$ Multiplying the inverse by a column vector of 1's on the right: $x=\Sigma^{-1} \mathbf{1}$ Normalizing ...
Alex C's user avatar
  • 9,372
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 ...
Pleb's user avatar
  • 4,241
4 votes
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Show that the following result holds true for the variance of the return of a portfolio of shares

The variance part is correct. For the covariance part we can observe the following: There are $n$ variance terms in the $n \times n$ covariance matrix. This implies that there must be $n^2-n$ ...
Pleb's user avatar
  • 4,241
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, ...
Pleb's user avatar
  • 4,241
4 votes

How to set a fixed return for mean-CVaR portfolio optimization?

I don't use fPortfolio but when I run your code example, I first get an error: ...
Enrico Schumann's user avatar

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