Abstracts

Never put all your eggs in one basket. Investors are well aware of this advice and prefer to compose a blend of different stocks to invest in. This is a prudent strategy because heavy losses in one asset can be countered by gains of others. However, this diversification effect is fading away when there is an increased co-movement between the stocks. It is well documented that periods of increased co-movement are tied to periods of high market stress. As a result, the diversification benefit is evaporating when it is needed the most. Therefore, having a notion about the strength of the co-movement between stock prices gives market participants the opportunity to take the necessary cautionary actions. In this paper, we construct two general frameworks to determine the implied degree of co-movement between stock prices.
Index options are traded and their prices can be observed in the market. The index option curve gives information about the real market situation. However, it is also possible to construct a second, synthetic, index option curve. This curve represents the index option curve which would be observed if the components of the stock market index were to move perfectly together. It can be proven that this synthetic index option curve is always an upper bound for the observed index option curve. The degree of herd behavior is measured by quantifying the gap between the two curves. Indeed, if this gap is small, the market is pricing index options as if they will be moving almost perfectly together.
We explore two possible methodologies to quantify the gap between the two option curves. A first approach is to capture each index option curve in a single number using swap rates. The corresponding Herd Behavior Index is then defined as the ratio between these two numbers. A second approach is similar to the first approach, but now distorted expectations are used instead of swap rates.