Investment Analysis and
Portfolio Management
Eighth Edition
by
Frank K. Reilly & Keith C. Brown
Chapter 7:
Appendix
Chapter 7 - Appendix
Questions to be answered:

What components of modern portfolio
theory (MPT) are being questioned?
– MPT is a one period model. Does it still hold
when the time horizon is extended?
– MPT assumes normality. Are financial markets
really normal?
» Evidence from Mandlebrot on the normality of markets
» Evidence regarding Power Functions
2
3
Total Real Return Indices
January 1802 – June 30, 2005
$632,680
$1,000,000.
STOCKS
$100,000.
$10,000.
BONDS
$1,000.
$1115
$292
$100.
BILLS
$10.
GOLD
$1.
$0.1
DOLLAR
$1.38
$0.06
$0.01
1801 1811 1821 1831 1841 1851 1861 1871 1881 1891 1901 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001
4
Annual Stock Market Returns
Updated through
June 30, 2005
LongTerm
Major
SubPeriods
1802-2005
6.8%
I 1802-1870
7.0%
6.6%
6.7%
6.8%
10.0%
-0.4%
13.6%
8.9%
II 1871-1925
III 1926-2005
1946-2005
1946-1965
Post-War
Periods
Real
Returns
1966-1981
1981-1999
1984-2005
5
Annual Bond Market Returns
Updated through
June 30, 2005
LongTerm
Major
SubPeriods
1802-2005
3.5%
I 1802-1870
4.8%
3.7%
2.3%
1.5%
-1.2%
-4.2%
8.4%
7.2%
II 1871-1925
III 1926-2005
1946-2005
1946-1965
Post-War
Periods
Real
Returns
1966-1981
1981-1999
1984-2005
6
Long and Short-term
Risk of
Stocks and Bonds
7
Holding Period Risk for Annual Real Returns
Historical Data and Random Walk (Dashed Line)
1802 – 2004
20%
20%
Actual Stocks
18%
18%
Actual Bonds
16%
16%
Actual Bills
14%
14%
12%
12%
Risk 10%
10%
8%
8%
6%
6%
4%
4%
2%
2%
0%
0%
1
2
5
10
20
30
Holding Period
8
Is there a “Corporate El Dorado”?
Quotation from Foster and Kaplan’s Creative Destruction: p. 9

“McKinsey’s long-term studies of corporate birth, survival,
and death in America clearly show that the corporate
equivalent of El Dorado, the golden company that
continually performs better than the markets, has never
existed (emphasis theirs). It is a myth.”

Top Performing Stock From 1925-2004
– Philip Morris, Return 17.36% vs. 10.04% Market.

Top Performing Stock From 1950
– Philip Morris, Return 17.87% vs. 11.47% Market.

Top Performing Stock from original S&P 500 in 1957
– Philip Morris; Return 19.72% vs. 10.86% for S&P 500.

$1,000 put in S&P 500 when it was founded would turn into
$138,549 by the end of 2004.

$1,000 put in Philip Morris at the same time would grow
to over $5.5 million.
9
Dividend Yield and Relative Performance
$1,000,000
$100,000
Dividend
Yield
Highest
High
Return
14.22%
13.28%
Risk
19.09%
16.49%
Middle
Low
Lowest
10.60%
9.84%
9.53%
16.35%
18.57%
23.52%
S&P 500
11.17%
16.84%
High Div
Yield
$517,188
$351,581
S&P 500 $144,996
$113,894
$ 82,341
$ 72,068
Low Div
Yield
$10,000
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
1965
1963
1961
1959
1957
$1,000
10
Which Stock is Better
Growth
Measures
Revenue per
share
Dividends per
share
Earnings per
share
Sector
Growth*
IBM
12.19%
Standard Oil
of New Jersey
8.04%
9.19%
7.11%
10.94%
7.47%
14.65%
-14.22%
* Change in Market share of technology & energy sectors, 1957 - 2003
11
Which Stock is Better?
Valuation
Measures
Average P/E
IBM
Standard Oil
26.76
12.97
Average
Dividend
Yield
2.18%
5.19%
12
Which Stock is Better?
Return
Measures
IBM
Standard Oil
Price
Appreciation
11.41%
8.77%
Dividend
Return
2.18%
5.19%
Total Return
13.83%
14.42%
13
Which Stock is Better?

If you had invested $1,000 in each of
IBM & Standard Oil in 1950, by 2003
your shares would be worth:
– Standard Oil $1,260,000
– IBM $961,000

Your terminal wealth was $300,000 or
31% more in Standard Oil (even
though the average annual was only
0.59% higher in Standard Oil)
14
Are Financial Markets Normal?

Following data is from The (Mis)Behavior of
Markets: A Fractal View of Risk, Ruin &
Reward by Benoit Mandelbrot

In the summer of 1998, the improbable
happened
– On August 4th, the Dow Jones fell 3.5%
– Three weeks later, it fell again by 4.4%
– On August 31, it fell by 6.8%
15
Are Financial Markets Normal?

If markets follow a normal distribution, the
probability of the fall on August 31, 1998 was
one in 20 million.
– If you traded daily for 100,000 years, you would not
expect to see it once

The probability of three such declines in one
month – about one in 500 billion

Was this just a freak accident, an “Act of God”
so rare that it would never happen again?
16
Are Financial Markets Normal?

In 1997, the Dow fell 7.7% in one day
(Probability – one in 50 billion)

In July, 2002, the index had three sharp
falls in seven trading days (Probability –
one in 4 trillion)

On October 19, 1987 the index fell 29.2%,
the worst day in history (Probability – one
in 1050)

Mandelbrot believes that we need to scrap
the entire concept of MPT, as its basic
premise of normally distributed returns is
false
17
Ubiquity: Why Catastrophes Happen by
Mark Buchanan
Sarajevo, 11:00 AM, June 28, 1914

A car carrying the Austro-Hungarian
Archduke Franz Ferdinand & his
wife Sophie takes a wrong turn

It stops directly in front of Gavrilo
Princip, a 19 year old Bosnian Serb
student and member of the Serbian
terrorist organization Black Hand.

Princip pulls a gun from his pocket
and kills the Archduke and his wife
18
War

Within hours the political fabric of Europe
began to unravel
– Austria used the assassination as an excuse to plan
an invasion of Serbia
– Russia guaranteed protection to the Serbs
– Germany offered to intercede on behalf of Austria
if Russia become involved
– Within 30 days, this chain reaction of threats and
promises had mobilized vast armies and tied
Austria, Russia, Germany, France, Britain and
Turkey into a deadly knot
19
War

When the first world war ended five years
later, 10 million lay dead

Twenty years of uncomfortable peace were
followed by WWII and another 30 million
dead

Was this all due to one chauffeur’s
mistake?

Although many explanations have been
given for WWI, it must be remembered
that the century preceding 1914 had been
like a “long peaceful afternoon in
European history and that to the historians
of the time, wars seemed to erupt like
terrifying and inexplicable storms in a
20
Earthquakes

Kobe, Japan is one of the gems of modern
Japan

It lies along the southern edge of Honshu,
the largest of the Japanese islands

Its port is the 6th largest in the world and
handles nearly a third of all Japan’s
imports and exports

The city has excellent schools and calls
itself an “urban resort”

At 5:45 am on January 17, 1995 a few rocks
began to crumble on the ocean floor, 20
kilometres southwest of Kobe

In 15 seconds the earth ripped apart along
21
Earthquakes

The resulting earthquake had the power
of a hundred nuclear bombs

It ruined every road and rail link into
Kobe

100,000 buildings were damaged or
destroyed

Only 9 out of 186 berths in the port of
Kobe remained operable

5,000 people died, 30,000 were injured
and 300,000 were left homeless

Although Japan is known for
22
Forest Fires

Not far to the west of Wyoming’s vast
Bighorn Basin, the wild and unrestrained
landscape of Yellowstone National Park
climbs into the Rockies

Yellowstone is America’s most beautiful
national park, set aside for protection back
in 1872 and the holiday destination of
more than 1 million visitors a year

Lightning sparks several hundred forest
fires a year in the park. Most burn less
than a few acres before dying out.

Prior to 1988, the largest fire ever recorded,
in 1886, had burned just 25,000 acres

In June, 1988, a lightning bolt sparked a
23
Forest Fires

The fire was named Shoshone and the Forest
Service began to monitor its progress

On July 10, rain fell in Yellowstone and the
fires seemed well under control

It did not turn out that way

By mid-July, several other fires had sprung
up and began burning large swaths of land
–
–
–
–

Clover spread to 4,700 acres
Fan covered 2,900 acres
Mink Creek fire covered 13,000 acres
Shoshone covered 30,000 acres in just a few days
By August 200,000 acres of Yellowstone had
been consumed by fire
24
Forest Fires

Over the next two months, more than 10,000
fire fighters using 117 aircraft and more than
100 fire engines struggled to contain the
blaze

When it was finally over, more than
1,500,000 acres of Yellowstone had been
burned and $120 million in funds spent
fighting the fire
25
Financial Markets

On September 23, 1987 the headline in the
Wall Street Journal read, “Stock Prices Soar
in Heavy Trading: Industrials Rise Record
75.23 Points”

It had been an incredible summer and almost
every week records were broken and new
highs obtained

There was a minor correction in late summer
but the surge of September 23 was what
most traders expected – it was the natural
end of a minor correction and it set the stage
for further gains
– “In a market like this” one trader said, “any news is good news.
It’s pretty much taken for granted now that the market is going to
26
Financial Markets

When the market opened for trading on
October 6, 1987 most analysts fully expected
stock prices to keep climbing

When prices began to tumble, at first there
was little concern

It was obvious to most analysts that this was
merely another insignificant correction, a
temporary setback caused by investor
uncertainly about interest rates or the value
of the dollar

But for some reason this tiny correction took
and by the end of the day the bulls were
bloodied. As one said,
27
Financial Markets

The market continued to slide over the next
week and then October 14, 15 and 16th saw
three considerable losses in a row. But
according to a Wall Street Journal article on
the 16th,
– “It was the third major decline in as many days. But several
technical analysts said that the big volume accompanying
Friday’s session might mean better things ahead”

Reality was somewhat different

When trading opened on Black Monday,
October 19, 1987, it was immediately swept
away in a mad panic. Prices began to
plummet
28
Financial Markets

The rush to sell was so overwhelming that
by late afternoon over $500 billion of wealth
had been erased

It was the largest one-day free fall in market
history
– Newsweek said, “It felt like the end of the world, after two
generations of assurances that it couldn’t possibly happen”
– The crash was almost twice as severe as the infamous stock
market crash of 1929
– “It was God tapping us on the shoulder”, one billionaire
investor said, “a warning to us to get our act together”.

But virtually nobody had predicted it!
29
Wars, Earthquakes, Forest Fires &
Financial Panics

Each of these disasters erupted from its own
particular setting. How are they related?

In each case, it appears that the organization
of the system – the web of international
relations, the fabric of the forest or the earth’s
crust or the network of linked expectations
and trading perspectives of investors – made
it possible for a small shock to trigger a
response out of all proportion to itself.

It is as if these systems were poised on some
knife-edge of instability, merely waiting to be
set-off
30
Wars, Earthquakes, Forest Fires &
Financial Panics

The key to a unified understanding lies in
the subtle and powerful concept of the
critical state, an idea that appears to be
central to the scientific understanding of
many processes in which the notion of
history plays a fundamental role

For centuries, physicists have sought to
capture the fundamental laws of the
universe in timeless and unchanging
equations, often with great success

But the paradox is this: if the laws of physics
are so simple, why is the world itself so
complex?
31
Wars, Earthquakes, Forest Fires &
Financial Panics

In the 1970s and 1980s, scientists discovered
at least part of the answer – chaos

The molecules inside a balloon move
according to the law of chaos. Give just one
molecule a nudge and soon every molecule
inside the balloon will be affected.

But chaos cannot explain the upheavals that
we often witness
– For example, chaos would suggest that a butterfly
flapping its wings in Brazil might, weeks later,
lead to a thunderstorm in Europe
– But if the butterfly were inside a balloon, then it
could never affect the air outside of the balloon.
The air inside the balloon would be in a state of
equilibrium
32
Wars, Earthquakes, Forest Fires &
Financial Panics

For the air inside the balloon, the past and the
future are essentially the same; the idea of
history has no meaning

In contrast, the air in the earth’s atmosphere is
very much out of equilibrium. It is constantly
stirred and agitated and energized by the sun.
The result is the rich and ever unfolding
history of the weather and climate.

When out of equilibrium, there is such a thing
as history

Upheavals occur when systems are out of
equilibrium

The key idea is the notion of the critical state, a
special kind of organization characterized by a
33
Wars, Earthquakes, Forest Fires &
Financial Panics

This is the first landmark discovery in the
emerging science of non-equilibrium physics,
which is also referred to as complexity theory

When things are out of equilibrium, they
tend to be complex
– Complexity usually involves a string of historical
accidents
» The structure of a snowflake or a food web

However, since there are no fundamental
equations for things in which history
matters, how can we understand them?
34
Understanding through Games

“All great deeds and all great thoughts have
ridiculous beginnings” wrote Albert Camus,
a French philosopher

1987 – Per Bak, Chao Tang & Kurt
Weisenfeld begin to play a sandpile game in
their lab at the Brookhaven National
Laboratory. They are trying to understand
dis-equilbrium. In the process, they discover
the critical state

In the sandpile game, a grain of sand is
dropped onto a pile. As each grain of sand is
dropped, the pile becomes steeper and it is
more likely that the next grain of sand will
cause the side of the pile to slide

Sand would then slide downhill to a flatter
35
The Sandpile Game

To speed up their work, Bak et al developed
a computer game to drop imaginary grains of
sand for them.

A java version of the sandpile game is found
here:
http://www.cmth.bnl.gov/~maslov/Sandpi
le.htm

The first simple question they hoped to
answer was, “What is the typical size of an
avalanche?”
– After observing millions of avalanches in thousands of sandpiles,
the answer: there was no “typical” avalanche. Some involved a
single grain of sand; some involved the entire side of the sandpile.
– But an amazing result became obvious. As the size of the
36
The Sandpile Game

The reason is due to the “fingers of
instability” that run through the
sandpile.

When a new grain of sand is
dropped, its effects are totally
unknown.
– It might affect only one or two grains
nearest to it.
– However, if it falls on a very unstable
area, it may cause a chain reaction that
causes much of the sandpile to slide.
37
And Earthquakes . . .

After analyzing both US and
international seismic data,
researchers found a similar pattern

As the magnitude of the earthquake
doubled, it became four times as rare

Thus everyday there are a large
number of very small earthquakes.
Occassionally, a very large
earthquake will occur.

But when an earthquake begins, it is
impossible to predict how large it
will become – it depends on the
fingers of instability in its immediate
38
And Forest Fires

Later, researchers discovered a very
similar pattern with respect to forest
fires.

There are a very large number of
small fires but few large fires.

The actual ratio is as area doubles,
fires become 2.48 times as rare
39
And Forest Fires

Another insight also came from
studying forest fires.
– The longer the period of stability, the
greater the instability that built up in the
system
– Greenspan has often spoken about this
with respect to financial markets. The
longer the period of stability, the greater
the instability that exists in the financial
sector.
40
And Financial Markets

In 1998, Gene Stanley of Boston U led
a group studying the price history of
the S&P 500. They studied prices
recorded every 15 seconds over 13
years – a total of 4.5 million data
points

Stanley et al found that price changes
became 16 times as unlikely every
time the size of the change doubled

This implies that there is no such
thing as a “typical” fluctuation and
so there is no reason to think that
41