Posts Tagged ‘mean reversion


Paper: Volatilidad y largo plazo

Are Stocks Really Less Volatile in the Long Run?


According to conventional wisdom, annualized volatility of stock returns is lower over long horizons than over short horizons, due to mean reversion induced by return predictability. In contrast,we find that stocks are substantially more volatile over long horizons from an investor’s perspective. This perspective recognizes that parameters are uncertain, even with two centuries of data, and that observable predictors imperfectly deliver the conditional expected return. Mean reversion contributes strongly to reducing long-horizon variance, but it is more than offset by various uncertainties faced by the investor, especially uncertainty about the expected return. The same uncertainties reduce desired stock allocations of long-horizon investors contemplating target-datefunds.

Link al Paper


Paper: La reversion a la media “garpa”

Mean Reversion Pays, but Cost


A mean-reverting financial instrument is optimally traded by buying it when it is sufficiently below the estimated ‘mean level’ and selling it when it is above. In the presence of linear transaction costs, a large amount of value is paid away crossing bid-offers unless one devises a ‘buffer’ through which the price must move before a trade is done. In this paper, Richard Martin and Torsten Schoneborn derive the optimal strategy and conclude that for low costs the buffer width is proportional to the cube root of the transaction cost, determining the proportionality constant explicitly.

Link al Paper


Finanzas 101: Modelar la volatilidad

El blog Quantitative Research and Trading propone una serie de posts sobre volatilidad y pricing de opciones. Asi mismo, linkea una presentación la cual vale la pena mirar.

En esta primera entrega ofrece algunos conceptos claves sobre volatilidad como este:


Mean Reversion vs. Momentum
A puzzling feature of much of the literature on volatility is that it tends to stress the mean-reverting behavior of volatility processes.  This appears to contradict the finding that volatility behaves as a reinforcing process, whose long-term serial autocorrelations create a tendency to trend.  This leads to one of the most important findings about asset processes in general, and volatility process in particular: i.e. that the assets processes are simultaneously trending and mean-reverting.  One way to understand this is to think of volatility, not as a single process, but as the superposition of two processes:  a long term process in the mean, which tends to reinforce and trend, around which there operates a second, transient process that has a tendency to produce short term spikes in volatility that decay very quickly.  In other words, a transient, mean reverting processes inter-linked with a momentum process in the mean.  The presentation discusses two-factor modeling concepts along these lines, and about which I will have more to say later.



Paper: Ruido de Microestructura

Modeling microstructure noise with mutually exciting point processes


We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2(for a pair of assets). The construction is based on marked point processes and relies on linear self and mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process withthe positive and negative jumps of an asset price. By coupling suitably the stochastic intensities of upward and downward changes of prices for several assets simultaneously, we can reproduce microstructure noise (i.e. strong microscopic mean reversion at the level of seconds to a few minutes) and the Epps effect (i.e. the decorrelation of the increment sin microscopic scales) while preserving a standard Brownian diffusion behaviour on large scales.More effectively, we obtain analytical closed-form formulae for the mean signature plot and the correlation of two price increments that enable to track across scales the effect of the mean-reversion up to the diffusive limit of the model. We show that the theoretical results are consistent with empirical fits on futures Euro-Bund and Euro-Bobl in several situations.

Link al Paper


Una nueva “Normal” y reversión a la media

Via FT, me cruce con un post de James Montier en el cual explica porque la posición de la troupe de PIMCO sobre las estrategias de reversión a la media es un poco prematura; a pesar de la existencia de una nueva Normal (distribución).

In a recent article [1] Richard Clarida and Mohamed El-Erian of PIMCO argued that the ‘New Normal’ offered at least five implications for portfolio management.

I. Investing based on mean reversion will be less compelling

II. Risk on/risk off fluctuations in sentiment will continue

III. Tail hedging becomes more important

IV. Historical benchmarks and correlations will be challenged

V. Less credit will be available to sustain leverage and high valuations

Implications IV and V seem pretty reasonable to me. However, reports of the death of mean reversion are premature. I fear that the authors are confusing the distribution of economic outcomes with the distribution of asset market returns. The distribution of economic outcomes may well turn out to be flatter, with fatter tails than we have previously experienced.

However, asset markets have long suffered such a distribution; it has proved no impediment to mean reversion based strategies. In fact, the fat tails of the asset market have provided the best opportunities for mean reversion strategies.


Pair Trading – Cointegration Testing

Ese es el nombre de un post muy interesante del blog Trading with Matlab.

Cointegration technique is sometimes used to do Pairs trading. By checking if a pair of stocks are cointegrated, one could go long on one stock and short on the other (multiplied by Hedge Ratio). We are thus trying to be market neutral.

Asi mismo, ofrece una check list para saber rapidamente si dos acciones estan cointegradas y dos papers para interiorizarse más en el tema.

Como grand finale, el codigo de Matlab.


Como primer post en el blog, dejo el paper que presente en el QFClub el pasado viernes 18 de diciembre, MeanReversion. Es un gusto poder postear aquí, y espero no ser el único contribuidor además del amigo Besanson.
Cuando tenga un poco más de tiempo (frase típica antes de promesa a incumplir) prometo postear algo más, y contar un poco más de la presentación que armamos.
Los esperamos a todos el año que viene, queremos empezar a mover la comunidad quant en Argentina

Un saludo a todos



Newton y Estrategias

Kid Dynamite´s World tiene un post que relaciona La Primera Ley de Newton con el movimiento que tuvieron las acciones este año.

Lo más interesante es la explicación que hace de la diferencia entre dos tipos de estrategias: mean reversion strategies y momentum strategies. La fuente de dicha explicación es una presentación de Jeff DeGraaf (ex- Lehman Brothers).

Now, Degraaf’s presentation illustrated distribution curves showing return profiles for each strategy.  Each curve looked nearly  normal in shape (a bell curve), but there were two key differences.  First – in the mean reversion strategy, the mode (most common result – the peak of the bell curve) of the return distribution was slightly positive – mostly your trades make a little bit of money.   On the momentum strategy, the mode of the return distribution was slightly negative – the bell curve was centered slightly to the left of zero – most of your trades actually lose a little bit of money.

Fun & Finance


Fun & Finance Rollover

"It is hard to be finite upon an infinite subject, and all subjects are infinite." Herman Melville

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July 2020



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