Читать книгу Advanced Portfolio Management - Giuseppe A. Paleologo - Страница 10

Consider the regression line for SYF again. The complete formula for a linear regression includes an intercept and an error term, or residual. We write this explicitly. For a given stock,

(3.1)

Visually, this relationship is shown in Figure 3.2. We already introduced the term . This market component of the stock return is also called the systematic return of a stock. The first term on the left is the intercept ; it is a constant. When the market return is zero, the daily stock return is in expectation equal to alpha. No one observes expected returns, however. Even in the absence of market returns, the realized return of the stock would be . The last term is the “noise” around the stock return; it is also called idiosyncratic return of the stock. The terms specific and residual are also common, and we use all of them interchangeably. We would like to believe that this nuisance term is specific to the company: every commonality among the stocks comes the beta and the market return. The simple model of Equation (3.1), with a single systematic source of return for all the stocks, is called a single-factor model.

Figure 3.2 Flowchart illustrating the relationships between market, idio and asset returns, mediated by betas and offset by alphas. Market return times beta is added to alpha and idiosyncratic return to yield the total return.

The term is only dependent on the company and nothing else. If that is the case, then the nuisance of many stocks diversifies away, a phenomenon that we will revisit many times in the following chapters. Alpha is the expected value of idiosyncratic return, and is the noise masking it. So, if we take the expectation of a stock return, what do we get? Alpha and Beta are constant, epsilon has expectation equal to zero, and the market return has a non-zero return.

There is general agreement that accurately forecasting market returns is very difficult, and it is, at the very least, not in the mandate of a fundamental analyst. A macroeconomic investor may have an edge in forecasting the market; a fundamental one typically does not have a differentiated view. We can sketch the roles of various investment professionals as follows:

 To estimate as accurately as possible is the job of the fundamental investor.

 To estimate , identify the correct benchmarks , and the returns is the job of the quantitative risk manager.

 To estimate the expected value of (especially if the expectation changes over time) is the job of the macroeconomic investor.

But ultimately it is the job of the portfolio manager – who combines knowledge about mispricing with portfolio construction – to make use of relationship (3.1) to her own advantage.