BA 133 PORTFOLIO THEORY, CONTINUED, LECTURE ELEVEN
1, 4, 9a, 13, 14, 18-20.
Diversification and Portfolio Risk:
Much written on this since the pioneer papers in the early 1970s…back then the papers
concluded that most of the diversifiable risk could be eliminated by a portfolio contain-
ing 12-18 stocks, depending on whose paper you read (numerous examples, e.g. Archer
and Evans’s article in the Journal of Finance
, years ago).
The Figure in your text, 8.2 on p. 209 looks impressive showing that most of the risk
that can be eliminated via diversification is achieved within twenty or so stocks, and
very little additional risk reduction is accomplished at 1,000 stocks.
The chart is an ex-
cerpt from an article by Meir Statman, a finance professor at Santa Clara.
What you might also notice is the tendency for sigma to remain near 19%; a big stand-
ard deviation—more recently the volatility has declined to the 15 % level.
The primary caveat is
all of those studies, including Statman’s selected stocks ran
BUT: no active manager selects stocks randomly
. They select stocks within
industries, and there may only be ten or fifteen industries in those portfolios.
managers use five or six industries, concentrating their positions in the six or so stocks
they like within each of those five or six industries.
Because of the non-randomness, empirical evidence reveals that it takes many more
stocks, perhaps hundreds, to eliminate the unique risk, because of the industry concen-
trations, and non-random selection.
In fact, these portfolios will still probably have risk
that could otherwise be eliminated by more efficient diversification.
Most successful active portfolio managers aren’t always interested in eliminating
If you have to pay brokerage commissions and collect a
management fee, you cannot beat the index/benchmark using a well diversified
Your portfolio is either the market or something very close to it.
total portfolio risk can be separated into categories, risk that can be eliminated
by diversification and risk that remains in the portfolio, regardless of diversification at-
Diversifiable risk comes with many names, all of which are used interchangeably, in-
unique, firm-specific, non-systematic, and unsystematic risk to name a few.