Chapter 3The Role of Merger Arbitrage in a Diversified Portfolio
Portfolio theory reduces investments to two dimensions: risk and return. Both variables are forward looking and hence difficult to assess without perfect foresight. Therefore, analysis relies on historical relationships that are extrapolated to the future. It is assumed, or rather hoped, that the historical relationships will also hold in the future. This may or may not be the case.
Risk is a variable that is particularly difficult to define. The most common substitute for risk is price volatility. An asset's historical price fluctuations are observed, and it is assumed that these historical fluctuations incorporate all the risks that stockholders faced in the past. This historical volatility is then used in forward-looking analysis, and it is assumed that any risks that this stock faces have already occurred in the past and hence are incorporated in the historical volatility. The length of time over which historical volatility is calculated is the most important determinant of whether there is any validity to this approach. It clearly makes no sense to produce 10-year forecasts based on historical volatilities observed over only one or two years.
More fundamentally, it is a strong assumption that all risks inherent in a stock have already manifested themselves in the past. The economy evolves constantly and markets are in flux; assuming that future fluctuations will somehow resemble those of the past is not obvious. ...
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