测度羊群效应
Often in financial markets, as in our daily life, we imitate the decisions of predecessors, instead of analysing available information and making our own decisions. This decision imitation could lead to collective hysteria, and investment calls may be influenced by these panicked situations.
Imagine that you’re looking for a place to have dinner, and find a street with two restaurants. Both look good, but they’re empty because it’s still early. You decide on a whim to enter restaurant A. The moment you’re seated, a couple arrives – also intending to have dinner. Since restaurant A already has a customer (you), they decide to go for that one.
After all, since it has a customer, that one ought to be better, right? Anyone else who comes along looking for dinner will likely also reach the same conclusion. As a result, restaurant A will be full, while B will remain empty, although in principle either is equally good.
This is an everyday situation. How many of us go to a certain dentist, hairdresser or handyman because we’ve been recommended to do so by a friend who’s already used their services, even though there are others who look just as good? Personal information may be useful, but sometimes we’re more influenced by others.
The same thing happens in financial markets. Each investor receives information (signals) about how they should act. They also know the decisions of their predecessors, although they don’t know the signs they received. Using this knowledge, each investor makes their own decision. But this ignorance of previous signals can sometimes cause investors to ignore the signals they receive in the here and now, and instead adopt the same decisions as their predecessors.
This effect on the economy is known as the ‘Herd Effect’. Many consider this phenomenon to be a main starting cause of collective hysteria or panic (as seen in bubbles and crashes), that have occurred throughout history.
Definition
A Herd Effect exists in the financial market when a group of investors ignores their own information and instead only follows the decisions of other investors.
Some studies (such as Herd Behaviour in Financial Markets, or Daring to be Different) treat this effect as an intraday phenomenon, which intuitively makes sense. Investors are much more likely to imitate others than to interpret the information they receive when they have little time to make investment decisions. In recent years, this effect has been studied based on the information cascade model.
According to this model, investors receive an imperfect signal regarding the future value of an asset (V) indicating that the price will rise (S) or fall (B).
Investors know their own signal, and while they don’t know what signal has been received by others –they can observe their actions. Investment decisions are made sequentially, so decisions of previous participants are crucial when making the subsequent choices.
The scheme
The first investor (I#1) has taken the decision to observe their own signal and act accordingly (green line indicates that price will rise (S), red line indicates that price will fall (B)). The second investor (I#2) will then have two types of information: the signal they have received, and the action of I#1. If I#1 bought and the information received by I#2 is S, the second investor will also buy. If the signals are contradictory, it follows that the probability benefit is 0.5.
In this case, I#2 will make the decision to invest (or not) by chance in the most uncertain of possible situations. (Similar to the random choice you made at the start of this post when choosing the restaurant).
Suppose the first two investors have reversed. When the third (I#3) has to make their decision, they will infer the signal of I#1 was S, and although the signal of I#2 could have been either S or B, it was probably also positive (S). Therefore, I#3 will invest even if their personal signal is B.
The next investor (I#4) won’t get any additional information from the decision taken by I#3, since their investment wasn’t based on information, but on the actions of I#1. They will be in the same position as I#3, and will, therefore, invest regardless of their personal signal.
The same will happen for every following investor. A purchase cascade has begun. A waterfall in the opposite direction (B), would start the same way if both the first investor (in taking the decision) and the second (in following), do not invest.
If this phenomenon occurs and investors begin to ignore their beliefs in favour of the observed actions of others, we would expect to find longer sequences of purchases or sales throughout the session that would be expected if there were no such cascades and each investor followed their own information.
How do we quantitatively measure this phenomenon?
The first step is to look at whether the transactions have been initiated by the buyer or the seller. Two of the most commonly used methods provide similar results:
Tick-Test: A transaction is classified as buyer-initiated (up-tick) if the price is set higher than the previous transaction. A transaction is seller-initiated (down-tick) if the price is lower than the previous transaction. If the price does not change at all, a third group (zero-tick) is distinguished.
Read and Ready Algorithm: Using bid and ask prices as precedent, transactions are classified as buyer-initiated (up-tick) if they occur at a price above the mid-point of the spread, or initiated by the seller (down-tick) if performed underneath. If it’s the same price as the mid-point itself, they are considered zero-tick transactions.
We sequence sets of successive transactions belonging to the same type.
Let x(I,j,t) be sequence type I (rise, fall, zero) of the asset j at the date t.
ri: number of type i sequences (rise, fall or zero).
n: total number of transactions carried out on asset j on date t.
?: parameter adjustment for discontinuity.
pi: probability of finding sequence type I (a priori pi= 1/3)
x(I,j,t) is distributed asymptotically as a normal with zero mean and variance:
Conclusion
If the investors imitate, the actual number of sequences started will be lower than expected, and therefore the statistic values should be negative and significant. The more negatives, the greater the likelihood of herding.