220 research outputs found
An empirical behavioral model of liquidity and volatility
We develop a behavioral model for liquidity and volatility based on empirical
regularities in trading order flow in the London Stock Exchange. This can be
viewed as a very simple agent based model in which all components of the model
are validated against real data. Our empirical studies of order flow uncover
several interesting regularities in the way trading orders are placed and
cancelled. The resulting simple model of order flow is used to simulate price
formation under a continuous double auction, and the statistical properties of
the resulting simulated sequence of prices are compared to those of real data.
The model is constructed using one stock (AZN) and tested on 24 other stocks.
For low volatility, small tick size stocks (called Group I) the predictions are
very good, but for stocks outside Group I they are not good. For Group I, the
model predicts the correct magnitude and functional form of the distribution of
the volatility and the bid-ask spread, without adjusting any parameters based
on prices. This suggests that at least for Group I stocks, the volatility and
heavy tails of prices are related to market microstructure effects, and
supports the hypothesis that, at least on short time scales, the large
fluctuations of absolute returns are well described by a power law with an
exponent that varies from stock to stock
The long memory of the efficient market
For the London Stock Exchange we demonstrate that the signs of orders obey a
long-memory process. The autocorrelation function decays roughly as
with , corresponding to a Hurst exponent
. This implies that the signs of future orders are quite
predictable from the signs of past orders; all else being equal, this would
suggest a very strong market inefficiency. We demonstrate, however, that
fluctuations in order signs are compensated for by anti-correlated fluctuations
in transaction size and liquidity, which are also long-memory processes. This
tends to make the returns whiter. We show that some institutions display
long-range memory and others don't.Comment: 19 pages, 12 figure
The virtues and vices of equilibrium and the future of financial economics
The use of equilibrium models in economics springs from the desire for
parsimonious models of economic phenomena that take human reasoning into
account. This approach has been the cornerstone of modern economic theory. We
explain why this is so, extolling the virtues of equilibrium theory; then we
present a critique and describe why this approach is inherently limited, and
why economics needs to move in new directions if it is to continue to make
progress. We stress that this shouldn't be a question of dogma, but should be
resolved empirically. There are situations where equilibrium models provide
useful predictions and there are situations where they can never provide useful
predictions. There are also many situations where the jury is still out, i.e.,
where so far they fail to provide a good description of the world, but where
proper extensions might change this. Our goal is to convince the skeptics that
equilibrium models can be useful, but also to make traditional economists more
aware of the limitations of equilibrium models. We sketch some alternative
approaches and discuss why they should play an important role in future
research in economics.Comment: 68 pages, one figur
An empirical behavioral model of price formation
Although behavioral economics has demonstrated that there are many situations
where rational choice is a poor empirical model, it has so far failed to
provide quantitative models of economic problems such as price formation. We
make a step in this direction by developing empirical models that capture
behavioral regularities in trading order placement and cancellation using data
from the London Stock Exchange. For order placement we show that the
probability of placing an order at a given price is well approximated by a
Student distribution with less than two degrees of freedom, centered on the
best quoted price. This result is surprising because it implies that trading
order placement is symmetric, independent of the bid-ask spread, and the same
for buying and selling. We also develop a crude but simple cancellation model
that depends on the position of an order relative to the best price and the
imbalance between buying and selling orders in the limit order book. These
results are combined to construct a stochastic representative agent model, in
which the orders and cancellations are described in terms of conditional
probability distributions. This model is used to simulate price formation and
the results are compared to real data from the London Stock Exchange. Without
adjusting any parameters based on price data, the model produces good
predictions for the magnitude and functional form of the distribution of
returns and the bid-ask spread
The price dynamics of common trading strategies
A deterministic trading strategy can be regarded as a signal processing
element that uses external information and past prices as inputs and
incorporates them into future prices. This paper uses a market maker based
method of price formation to study the price dynamics induced by several
commonly used financial trading strategies, showing how they amplify noise,
induce structure in prices, and cause phenomena such as excess and clustered
volatility.Comment: 29 pages, 12 figure
The dynamics of the leverage cycle
We present a simple agent-based model of a financial system composed of
leveraged investors such as banks that invest in stocks and manage their risk
using a Value-at-Risk constraint, based on historical observations of asset
prices. The Value-at-Risk constraint implies that when perceived risk is low,
leverage is high and vice versa, a phenomenon that has been dubbed pro-cyclical
leverage. We show that this leads to endogenous irregular oscillations, in
which gradual increases in stock prices and leverage are followed by drastic
market collapses, i.e. a leverage cycle. This phenomenon is studied using
simplified models that give a deeper understanding of the dynamics and the
nature of the feedback loops and instabilities underlying the leverage cycle.
We introduce a flexible leverage regulation policy in which it is possible to
continuously tune from pro-cyclical to countercyclical leverage. When the
policy is sufficiently countercyclical and bank risk is sufficiently low the
endogenous oscillation disappears and prices go to a fixed point. While there
is always a leverage ceiling above which the dynamics are unstable,
countercyclical leverage can be used to raise the ceiling. We also study the
impact on leverage cycles of direct, temporal control of the bank's riskiness
via the bank's required Value-at-Risk quantile. Under such a rule the regulator
relaxes the Value-at-Risk quantile following a negative stock price shock and
tightens it following a positive shock. While such a policy rule can reduce the
amplitude of leverage cycles, its effectiveness is highly dependent on the
choice of parameters. Finally, we investigate fixed limits on leverage and show
how they can control the leverage cycle.Comment: 35 pages, 9 figure
How predictable is technological progress?
Recently it has become clear that many technologies follow a generalized
version of Moore's law, i.e. costs tend to drop exponentially, at different
rates that depend on the technology. Here we formulate Moore's law as a
correlated geometric random walk with drift, and apply it to historical data on
53 technologies. We derive a closed form expression approximating the
distribution of forecast errors as a function of time. Based on hind-casting
experiments we show that this works well, making it possible to collapse the
forecast errors for many different technologies at different time horizons onto
the same universal distribution. This is valuable because it allows us to make
forecasts for any given technology with a clear understanding of the quality of
the forecasts. As a practical demonstration we make distributional forecasts at
different time horizons for solar photovoltaic modules, and show how our method
can be used to estimate the probability that a given technology will outperform
another technology at a given point in the future
Leverage Causes Fat Tails and Clustered Volatility
We build a simple model of leveraged asset purchases with margin calls.
Investment funds use what is perhaps the most basic financial strategy, called
"value investing", i.e. systematically attempting to buy underpriced assets.
When funds do not borrow, the price fluctuations of the asset are normally
distributed and uncorrelated across time. All this changes when the funds are
allowed to leverage, i.e. borrow from a bank, to purchase more assets than
their wealth would otherwise permit. During good times competition drives
investors to funds that use more leverage, because they have higher profits. As
leverage increases price fluctuations become heavy tailed and display clustered
volatility, similar to what is observed in real markets. Previous explanations
of fat tails and clustered volatility depended on "irrational behavior", such
as trend following. Here instead this comes from the fact that leverage limits
cause funds to sell into a falling market: A prudent bank makes itself locally
safer by putting a limit to leverage, so when a fund exceeds its leverage
limit, it must partially repay its loan by selling the asset. Unfortunately
this sometimes happens to all the funds simultaneously when the price is
already falling. The resulting nonlinear feedback amplifies large downward
price movements. At the extreme this causes crashes, but the effect is seen at
every time scale, producing a power law of price disturbances. A standard
(supposedly more sophisticated) risk control policy in which individual banks
base leverage limits on volatility causes leverage to rise during periods of
low volatility, and to contract more quickly when volatility gets high, making
these extreme fluctuations even worse.Comment: 19 pages, 8 figure
An empirical study of the tails of mutual fund size
The mutual fund industry manages about a quarter of the assets in the U.S.
stock market and thus plays an important role in the U.S. economy. The question
of how much control is concentrated in the hands of the largest players is best
quantitatively discussed in terms of the tail behavior of the mutual fund size
distribution. We study the distribution empirically and show that the tail is
much better described by a log-normal than a power law, indicating less
concentration than, for example, personal income. The results are highly
statistically significant and are consistent across fifteen years. This
contradicts a recent theory concerning the origin of the power law tails of the
trading volume distribution. Based on the analysis in a companion paper, the
log-normality is to be expected, and indicates that the distribution of mutual
funds remains perpetually out of equilibrium.Comment: 6 pages, 3 figure
- …