By: Pritha Dev
In a world where information is gold, why would anyone give it away instead of keeping it to himself and thus reaping the maximum benefits?…
What drives stock market recommendations by analysts who are also trading on their own account? That is, what propels them to share their information (often freely) in newspapers, trade magazines, online forums or television channels? In a world where information is gold, why would anyone give it away instead of keeping it to himself and thus reaping the maximum benefits? This article, based on Dev(2013), shows that there is a direct economic incentive for this transfer of information.
Strategic traders participate in the market for an asset if they believe they have an informational advantage over the rest of the market. They trade only if they have information which implies that the asset is mispriced. If they had only as much information as the rest of the market, they would have no incentive to trade since the price that they expect the market to set would be no different from their valuation of the asset. Information is crucial for the strategic traders to make any profits; as such they are generally willing to pay for it. This article considers the possibility of an information transfer from an informed strategic trader to other uninformed strategic traders.
Many authors have considered the sale and transfer of information in asset markets. The theoretical model often used is based on Kyle(1985). He considers a model with one informed trader (who knows the liquidation value), a market maker and noise traders. They trade in the asset for some periods at the end of which the liquidation value is announced and profits are realized.
Market makers are assumed to set prices equal to the expected value of the asset given their information. In a linear equilibrium, prices are linear in the total trade and the insider’s trade is linear in the liquidation value. In a series of papers on the sale of information, Admati and Peiderer (1986), Admati and Peiderer (1988), and Admati and Peiderer (1990), find that in a rational expectations equilibrium it is never optimal to let a positive fraction of the traders know the exact value of the asset, that a risk averse trader will sell information to share the risk and that indirect sale of information, e.g. through a mutual fund, is more profitable than direct sale of information.
Another reason for information release could be stock price manipulation, where the informed trader transfers a signal contrary to his information to the uninformed traders with the intent to push the price in the wrong direction and making larger profits. Alternatively, the trader might not be informed and still transfer a signal to push prices in the direction which favors his trading position. In this paper, the incentives behind the direct transmission of information are not to manipulate or to share risk, but rather to use the trade by less informed traders as a camouflage for the trade by the informed trader.
I claim that there can be transfer of information by a risk neutral trader if he transfers a noisy signal of this information. The informed trader knows exactly what the final liquidation price of an asset is going to be. Instead of giving out his information as is and letting other traders know the liquidation value, the informed trader gives out a hint regarding the liquidation value. He transfers this noisy version of his information directly to the buyer. The buyer then uses this information to trade strategically. If the informed trader regularly makes such transfers of information he has reputational concerns which ensure he transfers the information at the quality promised.
The exact setup of the market is such that all traders trade in a single risky asset and submit the quantity they wish to trade of that asset to a market maker. The market maker then sets the price of the asset according to the information available to him and at that price executes all the trades. There are two types of traders – strategic traders and uninformed noise traders. The noise traders are non-strategic traders and they trade for reasons other than to make a profit. For instance, they might have liquidity constraints which force them to trade. Noise traders trade a random amount $u$ which is normally distributed with mean 0. The strategic traders trade only if they have information regarding the liquidation value of the asset. Suppose there is single informed trader who knows the liquidation value of an asset. If he does not transfer the information, the other strategic traders stay out of the market. The other strategic traders are able to participate only if the informed trader transfers his information fully or partially to them.
The risky asset has a liquidation value denoted by the random variable v, where v is distributed normally with mean µ and variance σ2. The informed trader knows the exact realization of v and he transfers a signal s=v+ ε where ε is normally distributed with mean 0 but with positive variance. In this case, ε is the noise added to the actual information. Since the mean of the noise is 0, it must be that this noise has no bias. Note that if variance of this noise term is zero then the information is transferred as is without adding any noise. The sequence of events is as follows:
- Stage 0
- The informed trader receives accurate information, $v$, regarding the liquidation value of the stock.
- He then decides whether or not to freely transfer some of his information to other strategic traders in the form of a signal. To make the decision, the owner compares his expected trading profits with the transfer of information to the profit in the case of no transfer of information.
- Stage 1
- All traders submit market orders to the market maker. The market maker observes only the total order volume and not the individual orders.
- The market maker sets the price $p$ at which all orders are executed.
- Stage 2
- The true liquidation value is announced and all traders liquidate their positions and realize profits.
The informed trader never transfers his exact information since that leads to him losing his informational advantage completely and giving rise to an equal competitor. The competition leads to lower total profits for both the informed traders. If the informed trader transfers a noisy signal, he retains an informational advantage over the rest of participants in the market since this trader knows the true information as well as the signal. The decision to transfer information involves a tradeoff on the part of the informed trader.
On the one hand, the informed trader loses part of the informational advantage to another trader with a negative impact on his profits. On the other hand, the informed trader knows exactly how much the prices are affected by the trade of the other less informed strategic trader and he can use it to his advantage.
The informational advantage of the informed trader over the market maker is given by the difference between his information and the expected value of the asset or v – µ. Similarly the informational advantage of the informed trader over the other strategic trader who got the signal is given by v – s and that of the other strategic trader over the market maker is s – µ. Solving the game theoretic problem implied by the sequence of events, it must be that the prices set by the market maker are increasing in the total total order volume.
The trade of the informed traders is increasing in their informational advantage(s). The informed strategic trader would be willing to transfer information for free if in the case without transfer of information his trading profits are not too high or if the variance of the underlying asset value is large enough. Moreover, as the number of traders to whom he can transfer the information increases, his trading profits increase.
The interesting result is also that the informed trader does not always choose to transfer information. He only transfers the information if his informational advantage over the market maker is not too high. In other words, he transfers information only if the information does not have too much value to begin with or the liquidation value of the asset is very unpredictable. If the information is indeed very lucrative, which in this model implies the realised v is very far away from its expected value of µ then the informed trader keeps it to himself!
This article shows that there is indeed an economic motive for the financial gurus to make public predictions about stock price movements. But the adherents of such gurus must keep in mind that public predictions are only made when the future price movements is going to be relatively small. Any information which predicts massive swings in the prices is always kept private.♦