DYNAMIC FEEDBACK EFFECTS AND HERDING BEHAVIOR

Game theory in its simplest form does not consider dynamics, as it revolves around a static equilibrium concept: It posits a situation such that no player has an incentive to deviate. But how is that equilibrium reached dynamically? And what about the disorderly interaction of many stakeholders, maybe stockholders in financial markets? Addressing such issues is beyond the scope of this book, but we illustrate their relevance with two real-life examples; they show that the effects of such interactions may be quite nasty and that uncertainty may not always be adequately represented by an exogenous probability distribution.

Example 14.11 (Long-Term Capital Management) Many financial equilibrium models, like CAPM, assume that no player is big enough to influence markets. However, in specific conditions, players may turn out to be so big that their actions on thin or illiquid markets are significant, with perverse effects. Long-Term Capital Management (LTCM) was a successful hedge fund, which has become famous for its demise.²¹ The fund took hugely leveraged positions, betting on spreads between securities, such as bonds. A simplified explanation of the strategy is the following:

• The required yield on bonds depends on many factors, including the credit standing of the issuer. If you do not trust the ability of the issuer to repay its debt, you require a higher interest rate to buy its bond, whose price is reduced. If the balance sheet of the issuer is rock solid, you settle for a lower yield, implying a higher price. The difference in required yields is the spread.
• If a bond issuer is in trouble, but you believe that its difficulties are overstated by the market and that it will recover, you could buy its bonds (which are cheaper than they should) and take a short position in high-quality bonds (selling them short), because sooner or later, according to your view, the two bond prices will converge.²²

In 1998, the strategy backfired because of a default on Russian bonds; markets got nervous and everyone rushed to sell risky bonds to buy safe ones. This “flight to quality” widened the spreads, resulting in huge losses for LTCM. In such a case, if your positions are leveraged, your creditors get nervous as well, and start asking you to repay your debt; in financial parlance, you get a margin call. This implies that you should liquidate some of the securities in your portfolio to raise some cash. Unfortunately, this exacerbates your trouble, since prices are further depressed by your sales. In normal times, a small trade on a very liquid market should not move prices too much. But if troubled markets get illiquid and you try unloading a huge position in an asset, you get a nasty vicious circle: The more you sell, the more money you lose, the more margin calls you get, the more you should sell. In the end, a committee of bankers had to rescue and bail out the fund in order to avoid a dangerous market crash.

Example 14.12 (The Black Monday crash of 1987) Portfolio insurance is a portfolio management strategy that aims at keeping the value of a portfolio of assets from falling below a given target. The idea is to create a synthetic put option by proper dynamic trading. To cut a long story short, the idea is that when asset value falls, one should sell a fraction of the assets in well-determined proportions. On Monday, 19 October, 1987, stock markets around the world crashed. In what has been aptly named the Black Monday, the Dow Jones Industrial Average index dropped by 22.61%. An explanation of this crash was put forward, which blames portfolio insurance. The idea is rather simple; the market goes south and you start selling to implement dynamic portfolio insurance. Unfortunately, you are not alone, as many other players do the same; hence, there is a further drop in prices that in turn triggers further sales. The result is a liquidity and feedback disaster, exacerbated by the use of automated, computer-based trading systems.²³

The above stories, and all of the similar ones, are controversial; there is no general agreement that portfolio insurance has caused the Black Monday crash. Whatever your opinion is, feedback effects and the partial endogenous character of uncertainty cannot be disregarded.