connected with transportation: wharves, canals, turnpikes, and bridges.
But the important stocks of the early nineteenth century were financial
institutions: banks and, later, insurance companies. Banks and insurance
companies held loans and equity in many of the manufacturing firms
that, at that time, did not have the financial standing to issue equity. The
fluctuations in the stock prices of financial firms in the nineteenth cen-
tury reflected the health of the general economy and the profitability of
the firms to whom they lent. The first large nonfinancial venture was the
Delaware and Hudson Canal, issued in 1825, which also became an orig-
inal member of the Dow Jones Industrial Average 60 years later. In 1830,
the first railroad, the Mohawk and Hudson, was listed, and for the next
50 years railroads dominated trading on the major exchanges.
APPENDIX 2: ARITHMETIC AND GEOMETRIC RETURNS
The average arithmetic return rAis the average of each yearly return. If r 1
tornare the nyearly returns, rA(r 1 r 2 ... rn)/n. The average geo-
metric, or compound, return rGis the nth root of the product of one-year
total returns minus 1. Mathematically this is expressed as rG[(1r 1 )(1
r 2 )... (1 rn)]1/n1. An asset that achieves a geometric return of rG
will accumulate to (1 rG)ntimes the initial investment over nyears. The
geometric return is approximately equal to the arithmetic return minus
one-half the variance ^2 of yearly returns, or rGrA–^1 ⁄ 2 ^2.
Investors can be expected to realize geometric returns only over
long periods of time. The average geometric return is always less than
the average arithmetic return except when all yearly returns are exactly
equal. This difference is related to the volatility of yearly returns.
A simple example demonstrates the difference. If a portfolio falls by
50 percent in the first year and then doubles (up 100 percent) in the sec-
ond year, “buy-and-hold” investors are back to where they started, with
a total return of zero. The compound or geometric return rG, defined
above as (1 0.5)(11)1, accurately indicates the zero total return of
this investment over the two years.
The average annual arithmetic return rAis25 percent (50 per-
cent100 percent)/2. Over two years, this average return can be turned
into a compound or total return only by successfully “timing” the mar-
ket, specifically increasing the funds invested in the second year, hoping
for a recovery in stock prices. Had the market dropped again in the sec-
ond year, this strategy would have been unsuccessful and resulted in
lower total returns than achieved by the buy-and-hold investor.
22 PART 1 The Verdict of History