as discussed on page 103 of our text, the expected return of a portfolio is taking into account all possible outcomes, and calculating the average expected outcome. Let's use the example from page 103:

year | return |
---|---|

1995 | 37.43% |

1996 | 23.07% |

1997 | 33.36% |

1998 | 28.58% |

1999 | 21.04% |

The average return would simply be the average of the five given returns above, or 28.7%. Now, hypothetically, let's assume that each year is twice as good of an indicator of future earnings as the previous year. That is, 1999 is twice as good of an indicator of 2000 than 1998. And 1997 is four times as good of an indicator of 2000 than 1995 and so forth. We are weighting the more recent years moreso than the later years. Here's the result:

(16 / 31) * 21.04 + (8 / 31) * 28.58 + (4 / 31) * 33.36 + (2 / 31) * 23.07 + (1 / 31) * 37.43 = 25.2%

Notice that all the numerators add to 31. It's important that the sum of all probabilities adds to 1.