To Research (Abstract)
Bank of Israel researchers used a new methodology for identifying asset price bubbles to examine if an equity price bubble exists or existed—in Israel, using Book-to-Market ratio data.
Within the framework of the research, indicators were constructed that allow real time monitoring of the development of stock market price bubbles, at the aggregate level as well as at the individual industry level. No evidence for a bubble was found; neither at the aggregate level nor from an industry perspective.
Many asset prices in Israel and abroad—particularly equity prices—recently reached record levels, against the background of the low interest rate environment that has been typical in recent years of most advanced economies, including Israel. Meital Graham and Itamar Caspi, researchers at the Bank of Israel’s Research Department, examined whether there is—or was—a stock price bubble in Israel.
The theoretical framework of the research is based on standard asset pricing models. Based on these models, investors have rational expectations and the price of an asset is equal to its fundamental value—that is, the present value of its future dividend stream. In certain cases, an asset price may reflect a value higher than its intrinsic value, as a result of a bubble component. A bubble exists when investors are willing to purchase an asset at a price greater than its fundamental value solely because they expect that they will succeed in selling it at a higher price in the future.
The researchers used a new econometric methodology to identify and date bubbles. The methodology was developed by Peter Phillips, et al., in a series of articles published in recent years. The method is based on the insight that when the price of any asset includes a bubble component, then the price itself, as well as the ratio between the price and the dividend, will increase by an accelerating rate. That is, a bubble component is reflected in explosive behavior of the asset price and of the price-dividend ratio. Accordingly, Phillips et al. developed an econometric test for the explosiveness of a series. When its results indicate explosive behavior in the price of a specific asset, they are interpreted as evidence of a price bubble.
As dividend data in Israel are not readily available and are discontinuous, they cannot be used in this examination. The research shows that instead of dividend data, the inverse of the Book-to-Market ratio (the ratio between market value and the book value of equity) can be used, as it is also expected to behave in an explosive manner
when there is a bubble in the price of the asset. Book-to-Market data refer to both the aggregate level and the individual industry level (seven industries in the study), and in neither was evidence of a bubble found.
The figure below is taken from the paper, and illustrates how the bubble monitoring method operates in the stock market. A bubble period begins when the bubble detection indicator (the blue line) rises and crosses the threshold level (the red line), and ends when the indicator returns to below the red line—provided the indicator remains above the threshold level for more than five months. The threshold level is calculated according to Phillips’s methodology, and the bubble detection indicator is derived from the (log) equity multiple. It can be seen that throughout the measurement period, the indicator does not cross the threshold level for a period exceeding five months. The data accumulated since November 2014 do not present a different picture. An expanded discussion of the calculation method appears in Section 4 of the paper.
The bubble detection indicator at the aggregate level and the threshold level for identifying bubble periods (monthly data, July 1996–November 2014)
Note: This figure does not present the bubble dating indicator (the blue line) and the threshold level for identifying bubble periods (the red line) with regard to the aggregate equity multiplier. When the indicator crosses the threshold for more a period exceeding five months, it signals the existence of a bubble. The figure above does not indicate a bubble.
 In the research, shares were divided among seven industries—insurance, banks, holding and investment, oil and gas exploration, trade and services, real estate, and manufacturing and construction.
 The component is termed a “rational bubble” in the literature. The expression reflects the fact that an asset price incorporating this bubble component does not necessarily contradict the rational expectations assumption.
 The data in the research are taken from the period between July 1996 and November 2014.
 Setting a minimum period of time is intended to prevent a situation in which periods are classified as a bubble when they reflect sharp one-off rises in stock prices. The minimum span of time for a period to be classified as a bubble is set as function of the size of the sample.