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that also averages a 10 percent return, except it

Figure 2

moves in the opposite direction. An investment

Distribution of Annual Returns of the U.S. Market

in either portfolio would earn a 10 percent return

with volatility. But an equal investment in each

12

portfolio would earn the same 10 percent with

no volatility at all because of their perfect nega-

tive correlation.

10

It is common practice to construct portfolios

using many different asset classes that are not

8

highly correlated to achieve less risk for any

given return. This diversification protects the

investor from a dramatic fall in any single mar-

6

ket. However, it also reduces the return to the

portfolio from a single market's spectacular

4

performance.

Given the financial structure of Social

Security and the history of markets, one could

2

reasonably estimate the future tradeoff between

a pay-as-you-go and a market-based retirement

system. The former will require tax increases

0

and/or benefit cuts resulting in lower returns

than projected under current law, which are

already substantially below market rates for

Return

today's younger workers.21 The latter would

This is the annual return of a 90 percent large capitalization and 10 percent small capitalization equity portfolio. Data are

allow retirement benefits in excess of those

from Ibbotson and Associates, Stocks, Bonds, Bills and Inflation, 1997 Yearbook.

from Social Security even if the stock market

were to return only its worst long-run historical

performance.

Figure 3

Risk Reduced by Holding Two Uncorrelated Assets

Objection #4: Although the

16

stock market rises over the

long term, it could collapse at

14

the end of one's working career,

leaving little or nothing

12

for retirement.

Many critics of privatization admit that long-

10

term private investment trends are positive, but

warn that a short-term market drop could wipe

out a retiree's gains just when he needs it most.

8

Asset A

History shows that short-term market drops can

Asset B

be significant. Tables 5­7 list the worst ten

6

Portfolio

declines in percentage terms by day, month, and

quarter from 1926 to 1996. Data are taken from

S&P 500 1996 Directory.

4

As dramatic as they were, declines of this

Time

nature were infrequent. Figures 4 and 5 show

the frequency of monthly and quarterly returns,

respectively. The ten worst months, those with

declines of 14 percent or more, represented only

The vertical axis is annual return and the hor-

1.2 percent of all months; and the ten worst

izontal axis is time. The bold line depicts a port-

folio that averages a 10 percent return, but

quarters, declines of at least 18 percent,

which is volatile. The dashed line is a portfolio

accounted for only 3.6 percent of the total.

8