# Tag Info

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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### 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 ...
• 516
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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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• 3,700

### 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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### 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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### 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 ...

### 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 ...
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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 ...
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### How to calculate the log return of portfolio?

Now this is a farily basic question, but since I see professionals having trouble with this all the time, let us go through it Simple returns aggregate nicely (linearly) across trades but not time, ...
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### 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" ...

### 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 ...

### 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 ...
• 11.6k
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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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### 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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### % 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 ...
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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 ...
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### 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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### 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 ...
• 9,402
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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 ...
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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 ...
• 4,726
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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 $n^2-n$ ...
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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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### 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: ...
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### Literature about optimal number of stocks in a diversified portfolio

The first article on this was Fisher and Lorie "Some studies of variability of returns on investments in common stocks" JB April 1970. https://www.jstor.org/stable/2352105 The Statman ...
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### Can I invest in the market portfolio of modern portfolio theory?

This "market portfolio" is a chimera: very useful for basic reasoning and teaching, but that cannot be traded. Here are three reasons why the term "market" suggests that it is ...
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