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 + total return) is just the ratio of the
corresponding adjusted closing prices.
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.
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.
