clusters are periods in which markets are highly volatile for longer periods of time or exhibit low volatility for long periods of time.8 In the words of B. Mandelbrot, “Large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes.”9
In the long run, however, volatility tends to revert to a mean value.
Other than volatility, another statistical term that plays an important role in the construction of portfolios is correlation. It is just as important as return and risk. Even though the risk/return trade-off has become a household term, correlation somehow has been left out. The popular business press does not refer to risk/return/correlation trade-offs.
Correlation describes the comovement of two different assets and can range from
Volatility of Stocks Going through a Merger
Once a merger is announced, the volatility of a stock declines markedly. Figure 3.1 shows the stock prices of Autonomy Corporation before and after the announcement of its cash merger. It can be seen that price fluctuations following the announcement of the merger are much smaller than before. Figure 3.1 shows daily price changes of Autonomy Corporation, a U.K. – based infrastructure software firm, that was acquired by Hewlett-Packard Co in 2011. This merger was discussed in more detail in Chapter 2. It is clear from the picture that daily price variations are much smaller following the announcement of the merger on August 11, 2011, than prior to that date.
Figure 3.1 Daily Price Changes (in pence) of Autonomy Corporation before and after the Merger Announcement
Daily total returns differ from daily stock price returns in that they incorporate dividends. For dividend paying stocks, price return will be negative on the ex-date of a dividend, even though the investor receives a separate cash flow from the dividend payment. Therefore, total returns are the appropriate measure that will be used for the remainder of this book.
To demonstrate that this is not just an effect in isolated cases, pre- and post-announcement volatilities of 258 mergers were analyzed. The data set consists of 258 cash mergers for the period of March 31, 2010, until March 31, 2014, retrieved from the Bloomberg database. Total returns for these stocks were retrieved also from Bloomberg. The calculation for premerger volatilities and returns starts 60 trading days before the announcement, and post-merger returns and volatilities are calculated from the day following the announcement for 60 days or until completion, whichever came first. The histogram in Figure 3.2 shows the resulting cross-sectional distribution of returns. The height of the bars in these histograms shows the number of stocks whose returns fell within a given range. The distribution of dark bars is that of pre-announcement returns, that of light bars of the returns post-announcement.
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