The Mathematics of Financial Modelingand Investment Management

16-Port Selection Mean Var Page 496 Wednesday, February 4, 2004 1:09 PM

496 The Mathematics of Financial Modeling and Investment Management

EXHIBIT 16.7 Annualized Returns Using Historical Performance Depend on the

Time Period

Period Lehman Aggregate S&P 500 MSCI EAFE MSCI EM Free

Five year

1990–1995 9.2% 15.9% 10.5% 16.3%

1996–2000 6.3 18.3 8.2 0.1

Ten year

1990–2000 7.7 17.1 9.3 8.2

Note: Based on monthly returns of Ibbotson Associates.

Source: Exhibit 3.3 in Frank J. Fabozzi, Francis Gupta, and Harry M. Markow -

itz, “Applying Mean-Variance,” Chapter 3 in Frank J. Fabozzi and Harry M.

Markowitz (eds.), The Theory and Practice of Investment Management (Hobo -

ken, NJ: John Wiley & Sons, 2002), p. 46.

econometricians have pushed to study dynamic return models, for

instance Markov switching Hamilton models, that might capture fluctu-

ations such as those that appear in the exhibit.^21 Note that, even using

more complex models, fluctuations of the estimates will still exist. They

are an ineliminable consequence of the global uncertainty in financial

markets. The point is that the fluctuation of the estimates should not be

too large to invalidate the model that is assumed.

Based on historical performance, a portfolio manager looking for

estimates of the expected returns for these four asset classes to use as

inputs for obtaining the set of efficient portfolios at the end of 1995 might

have used the estimates from the five-year period, 1990–1995. Then

according to the portfolio manager’s expectations, over the next five

years, only the U.S. equity market (as represented by the S&P 500) out-

performed, while U.S. bonds, Europe and Japan and Emerging Markets

all underperformed. In particular, the performance of Emerging Markets

was dramatically different from its expected performance (actual perfor-

mance of 0.1% versus an expected performance of 16.3%). This finding

is disturbing, because if portfolio managers cannot have faith in the

inputs that are used to solve for the efficient portfolios, then it is not pos-

sible for them to have much faith in the outputs (i.e., the makeup and

expected performance of the efficient and optimal portfolios).

Portfolio managers who were performing the exercise at the begin-

ning of 2001 faced a similar dilemma. Should they use the historical

returns for the 1996–2000 period? That would generally imply that the

(^21) For a discussion of these techniques, see Chapter 18.