Harry Markowitz's mean-variance model for portfolio choice posits a
linear relationship between the return of a portfolio and the
returns of its component securities. This linear relationship does
not hold in an ex post setting when monthly or quarterly returns
are used.
Historical returns depend on historical closing prices and
distributions. We describe how to compute adjusted closing prices
from price/distribution data with an emphasis on spreadsheet
implementation. Then the growth of a security from one date to
another (1 + the total return) is just the ratio of the
corresponding adjusted closing prices.
Everybody knows that
1/3 = 0.33333.....
This is a simple example of a geometric series. In motorcycle
racing a rider can qualify to race only if he can complete a lap
within a fixed percentage (e.g. 10%) of the time required by the
fastest rider. So how often (in laps) does the fastest rider lap a
borderline qualifier during the race? This is a natural application
of geometric series. For our 10% example the answer is every 11 laps.
