0 10 20 30 40 50 60 70 Asset, billions of dollars

FIGURE 14.1 Relationship of advisory fees to fund assets.

initially fa = 0.45 and fa = 0.01. These are pure guesses, sometimes based on prior experience or prior empirical work or obtained by just fitting a linear regression model even though it may not be appropriate. At this stage do not worry about how these values are obtained.

Since we know the values of fa and fa, we can write (14.2.2) as:



Since Y, X, ft, and ft are known, we can easily find the error sum of squares in (14.3.2).4 Remember that in OLS our objective is to find those values of the unknown parameters that will make the error sum of squares as small as possible. This will happen if the estimated Y values from the model are as close as possible to the actual Y values. With the given values, we obtain E u? = 0.3044. But how do we know that this is the least possible error sum of squares that we can obtain? What happens if you choose another value for ft and ft, say, 0.50 and -0.01, respectively? Repeating the procedure just laid down, we find that we now obtain Eu? = 0.0073. Obviously, this error sum of squares is much smaller than the one obtained before, namely, 0.3044. But how do we know that we have reached the lowest possible error sum of squares, for by choosing yet another set of values for the ft's, we will obtain yet another error sum of squares?

As you can see, such a trial-and-error, or iterative, process can be easily implemented. And if one has infinite time and infinite patience, the trial-and-error process may ultimately produce values of ft1 and ft2 that may guarantee the lowest possible error sum of squares. But you might ask, how did we go from ft = 0.45; ft? = 0.01) to ft = 0.50; ft? = -0.1)? Clearly, we need some kind of algorithm that will tell us how we go from one set of values of the unknowns to another set before we stop. Fortunately such algorithms are available, and we discuss them in the next section.

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