macrocephalopod on Twitter: "known to behave *really* badly (recommending nonsense portfolios) when there is noise in the covariance matrix. You get noise when you try to estimate too many parameters from too little data, so using a factor model to reduce the number of parameters to estimate"

Country	Code	For customers of
United States	40404	(any)
Canada	21212	(any)
United Kingdom	86444	Vodafone, Orange, 3, O2
Brazil	40404	Nextel, TIM
Haiti	40404	Digicel, Voila
Ireland	51210	Vodafone, O2
India	53000	Bharti Airtel, Videocon, Reliance
Indonesia	89887	AXIS, 3, Telkomsel, Indosat, XL Axiata
Italy	4880804	Wind
3424486444	Vodafone
» See SMS short codes for other countries

macrocephalopod‏ @macrocephalopod 2 Feb 2021

Or you can get more esoteric, e.g. a factor representing all stocks that have recently been upgraded by analysts, or a factor representing stocks that are highly shorted.

1 reply 0 retweets 7 likes

Show this thread

macrocephalopod‏ @macrocephalopod 2 Feb 2021

The return of stock i on day t is modeled as a linear combination of the unknown factor returns plus an unknown residual, where the dependence of stock i on factor j on day t is given by the *known* exposure X(i, j, t)pic.twitter.com/CbdvNRGura

1 reply 0 retweets 6 likes

Show this thread

macrocephalopod‏ @macrocephalopod 2 Feb 2021

If we understand that r, f and epsilon are vectors and X is a matrix then we can drop all the subscripts and write it in matrix notation which is much easier. It's important to understand that the exposures X are known in advance, and its the factor returns f that are unknownpic.twitter.com/uKK7PuGjuQ

1 reply 0 retweets 6 likes

Show this thread

macrocephalopod‏ @macrocephalopod 2 Feb 2021

Now you have a set of linear equations on each day, and you can solve the linear equations to get the vector of factor returns for each day using the normal equation -pic.twitter.com/YwVkUzSM69

1 reply 0 retweets 5 likes

Show this thread

macrocephalopod‏ @macrocephalopod 2 Feb 2021

What's the point of this? The factor models tells you how the covariance matrix of stocks is related to the covariance matrix of factors - it's the sum of the covariance due to factor exposures - Σ_f - and the covariance of the residuals Ω which is normally assumed to be diagonalpic.twitter.com/H7ruwNaEtR

1 reply 0 retweets 7 likes

Show this thread

macrocephalopod‏ @macrocephalopod 2 Feb 2021

Now instead of estimating the ~2 million parameters of a 2000 x 2000 stock covariance matrix, you just need to estimate ~800 parameters of a 40 x 40 factor covariance matrix -- your risk model just got a whole lot simpler.

1 reply 0 retweets 9 likes

Show this thread

macrocephalopod‏ @macrocephalopod 2 Feb 2021

Even more interestingly, if you are not just a risk manager but a quant equity pm, you can take expectations and get a model for the expected return (or alpha) of each stock in terms of the expected returns on each factor --pic.twitter.com/JflXE3Qj8V

1 reply 0 retweets 6 likes

Show this thread

macrocephalopod‏ @macrocephalopod 2 Feb 2021

If you're doing this you would normally treat some factors as "risk" factors which have zero expectation (i.e. you want to hedge them to minimise risk) and some factors as "alpha" factors which have positive expectation, as well as risk --

2 replies 0 retweets 4 likes

Show this thread

macrocephalopod‏ @macrocephalopod 2 Feb 2021

you want exposure to the alpha factors, but you want *more* exposure to the ones which have higher expected return given the risk, and your factor model gives you a structured way to express that.

1 reply 0 retweets 4 likes

Show this thread

macrocephalopod‏ @macrocephalopod 2 Feb 2021

The vector of alphas, and the stock covariance matrix, are the key inputs to a portfolio optimizer (along with transaction costs, financing costs, position and turnover constraints, risk constraints etc). One particularly important fact is that portfolio optimizers are

1 reply 0 retweets 4 likes

Show this thread

macrocephalopod‏ @macrocephalopod 2 Feb 2021

known to behave *really* badly (recommending nonsense portfolios) when there is noise in the covariance matrix. You get noise when you try to estimate too many parameters from too little data, so using a factor model to reduce the number of parameters to estimate

3:05 PM - 2 Feb 2021

7 Likes

2 replies 0 retweets 7 likes

1. Show replies

Loading seems to be taking a while.

Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.

Tweets

macrocephalopod