10
The most representative people supporting the arguments pro-time diversification are Jeremy J.
Siegel and Burton Malkiel which published two books2 in which they show the U.S. stock
markets return from the 18th century compared with the returns of Bonds, Bills, Gold and
Inflation, demonstrating the superiority of the investment in equities for the long run. But
different critics are made to this approach: the first is that past performance is not guarantee of
future results and the second is that it is true that U.S. stock markets outperformed over the long
run short term government bonds, but in other markets the same thing didn’t happened. Dimson,
Marsch and Staunton3 show the return of stocks and bonds on the 20th century for 12 different
countries and the results are different from market to market.
At the other side, we find some academics which refuse the validity of time diversification with
different arguments. The most important critics to time diversification come from Samuelson4
and then from Kritzman5, which use expected utility models to demonstrate that holding period
doesn’t affect asset allocation, Zvi Bodie 6, which demonstrates using Option Pricing Theory that
the cost for the insurance of a portfolio increases at the increase of the holding period and Fisher
and Statman7, which use Behavioral Finance concepts to explain why the time diversification is a
fallacy.
My work wants to illustrate all these arguments in favor and against Time Diversification with
the critics that have been taken by academics and not in these years, and then to make an
historical simulation using the Bootstrap methodology introduced by Efron8 to try to simulate the
behavior of an investor with a long holding period.
More specifically, in Chapter 2 I’ll speak about the arguments in favor of Time Diversification,
starting from a theoretical approach, which explains why in the long run above average returns
tend to offset below average return, and than showing the verdict of history, with the historical
stock and bond markets return for different countries, with the critics that have been made to this
approach.
In Chapter 3 I’ll turn the attention to the arguments against Time Diversification exposing the
point of view of Paul Samuelson, Zvi Bodie and Fisher and Statman also with the critics made to
these economists at their approaches.
2
Jeremy J. Siegel, Stocks for the long run, (1994, 2002) McGraw-Hill
Burton Malkiel, A random walk down Wall Street, (2003) W. W. Norton & Company
3
Dimson, Marsch and Staunton, The triumphs of Optimism: 101 years of Global Investment return (2003)
4
Paul Samuelson, The long-term case for equities and how it can be oversold, The Journal of Portfolio
Management, vol. 21 no.1 (Fall 1994), pp 15-24
5
Mark Kritzman, What practitioners need to know…about Time Diversification, Financial Analysts Journal
(January-February 1994), p. 14-18
6
Zvi Bodie, On the risk of stocks for the long run, Financial Analysts Journal (May-June 1995), pp. 18-22
7
Kenneth L. Fisher and Meir Statman, A Behavioral Framework for Time Diversification, Financial Analysts
Journal (May-June 1999)
8
Bradley Efron and Robert J. Tibshirani , An introduction to the Bootstrap, Chapman & Hall
11
In Chapter 4 then, after a brief exposure of the methodology and of the data used, I’ll show the
results of my analysis, trying to conclude if Time Diversification is a fact of a fallacy.
Before starting with the exposure, I want to say some words about the importance of this
question, turning the attention to pension funds, which for definition are long-time investors.
1.2) The importance of Time Diversification in the Portfolio Management Process
Why it’s important to determine if time diversification is a fact or a fallacy? Suppose you plan to
purchase a new home in the next three months, at which time yo u will be required to pay €
300,000 in cash. Assuming you have the necessary funds, would you be more inclined to invest
these funds in a riskless asset such Ordinary Treasury Bonds (BOT, the Italian equivalent of
Treasury Bills) or in a risky asset such an ETF on MIB30? Now consider a second question.
Suppose you plan to purchase a new home ten years from now, and that you currently have €
300,000 to apply toward the purchase of this home. How would you invest these funds, given the
choice between a riskless investment and a risky investment?
The only difference between these two scenarios is the length of your investment horizon. In the
first case, you have a three-month investment horizon; in the second case your investment
horizon equals to ten years. If you are a typical investor, you would probably select the riskless
investment for the three-month horizon and the ETF (or another risky asset) for the longest time
horizon.
You might rationalize your cho ice as follows. Even though you expect stocks to generate a
higher return over the long term, by investing in BOT you are certain to have the requisite funds
to satisfy your payment three months from now; you should be called a very risk averse investor.
If you were to invest in stocks, there is a significant chance you could lose part of your savings,
with little opportunity to recoup this loss, and be unable to meet the down payment requirement.
But over a ten-year investment horizon, favorable short-term stock return are likely to offset poor
short term stock returns; it is thus more likely that stocks will realize a return close to their
expected return.
Given this, it is important to emphasize the value of time diversification: Table 1.1 shows the
expected return over different holding periods for an investment of € 100 in respectively BOT
12
and Stocks. It is supposed that the Government Bonds grant a return of 7%, while stocks shows
an expected return of 12%9.
Expected Return
Holding Period
BOT Stocks
Outperformance
1 year 7.00% 12.00% 5.00%
3 years 22.50% 40.49% 17.99%
5 years 40.26% 76.23% 25.65%
10 years 96.72% 210.58% 113.87%
20 years 286.97% 864.63% 577.76%
30 years 661.23% 2895.99% 2234.77%
Table 1.1
This data shows that over very long time periods (20-30 years), if time diversification is verified,
an asset allocation in stocks would outperform the asset allocation in short-term government
bonds of an impressive 2234%.
It could seem that time diversification is a free lunch to improve everyone’s wealth but it isn’t
so: while the investment in short-term Government Bonds can be considered low risky, the
investment in stocks is a risky issue and the outperformance of 2234% is not guaranteed. In the
following chapters I will describe all these arguments in favor of time diversification, but I’ll
expose different critics made to these arguments which have to be considered in the security
selection.
Different researches demonstrate that the return of a portfolio derive principally from the asset
allocation, rather than active management10; for this reason it’s important to determine whether
the asset allocation for a long time investor should be shifted in equities or not.
1.3) An example of importance of Time Diversification: the case of Pension Funds
One of the institutional investors more involved by the debate around time diversification are
pension funds. This derive from the long temporal horizon that these type of investors have and
the same can be said for the private investors which invest their savings to have at the moment of
9
These values are the average return exhibit by U.S. markets from around 1900 till today. U.S. markets have been
chosen because there is sufficient reliable data for the analysis, while for other markets data is incomplete or not
affidable.
10
Gary P. Brinson, Brian D. Singer and Gilbert L. Beebower, Determinants of Portfolio Performance II: An update,
Financial Analysts Journal (may-June 1991), pp. 40-48
13
their retirement a sufficient wealth to be able to sustain their quality of living. This can be
measured by the substitution ratio which is the ratio between the pension paid and the last salary:
if this ratio is near one it means that the retired people can maintain its standard of living; if the
ratio is low it means that he has got to reduce his expense or increase his revenues, like with a
pension fund financed during its working life.
The dramatic aging of the developed world’s population is making pay-as-you-go pension
provision less feasible than in the past. As a result, some countries, like Italy, are willing to
establish a system of funded pension plans rather than a State-based pensions plan.
Due to their long time horizon, a decrease in the annual return rate dramatically increases the
cost or, depending on the law system, decreases significantly the wealth of the investor. A
research of Mark W. Griffin11 demonstrates that a 1 percent decrease in the annual return of the
pension fund implies a 20 percent increase in a plan’s costs for a contribution-defined fund.
If the time diversification exists, the asset allocation for pension funds would have a higher
weight in risky assets like equities, while if time diversification doesn’t exist the asset allocation
would be unaffected by the long time horizon.
The research of Mark W. Griffin shows a graph (Figure 1.1) with the average asset allocation of
pension funds in different countries. The hypothesis tested in his study was that the allocation to
equities will be highest where the historical (in the period from 1985 to 1999) outperformance of
domestic equities over domestic bonds has been highest. The Figure 1.2 shows this hypothetical
relationship: it can be said that there is no apparent relationship between the historical domestic
stock market outperform (the graph below) over domestic bonds and the percentage of total
assets invested in equities.
What does it mean? That time diversification doesn’t exist? Or that the managers don’t exploit
all the benefit of time diversification?
The answer at these questions cannot be definitive: one factor that influences hardly the asset
allocation in various countries is the legislation, besides cultural differences. Table 1.2 shows the
asset allocation restriction imposed by law in the major counties analyzed.
An interesting comparison can be made for Netherlands and United Kingdom, where the national
law don’t impose any particular restriction about asset allocation. However, in these two
countries the difference in the asset allocation is remarkably: in the Netherlands pension funds
invest as much as about 60% in bonds, while in the UK this percentage drops at 10%.
11
Mark W. Griffin, A global perspective on Pension Fund Asset Allocation , Financial Analysts Journal (March-
April 1998), pp. 60-68
14
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Figure 1
.2
16
Country Restriction
Belgium > 15% Government Bonds
< 65% Equities
Canada < 20% International assets
France < 65% Equities
< 10% Property
Germany < 5% International
< 30% Equities
< 25% Property
Italy No formal restriction
Japan < 30% Equities
< 20% Property
< 30% International assets
> 50% Principal guarantees
Netherlands No restriction
UK No restriction
USA No formal restriction
South Africa < 10 % International assets
< 75 % Equities
Switzerland < 20% Foreign denominated
< 50% Total equities
< 25% International equities
Table 1.2
On the contrary, the investments in risky assets like equities in the UK are higher (more than
75%) than in the Netherlands (26%). So, what can determine this remarkable difference
between the two asset allocations? The motivation can be found in how pension plans are
accounted for in the two countries. In the UK, assets are held at the actuarially assessed value;
to calculate the assessed value of equities, the plan’s actuary projects dividends using a long-
term dividend growth assumption and then discounts dividends using a long-term interest rate
assumption. The actuary discounts bond cash flows using the same long-term interest rate to
determine the assessed value of the bond portfolio. In contrast, in the Netherlands, most plans
hold bonds and real estate at book value and equities at market value.
The actuarial assumption involved in calculating UK assessed values are intended to be long
term and are not sensitive to market moves; on the contrary, in the Netherlands volatility in
the funded level of the plan comes almost entirely from the equity allocation, while the other
assets have an extremely stable value; furthermore, if a Dutch plan fall below a 100 percent
funded level (that is when the liabilities for the erogation of pensions are more than the assets
holds by the fund), the plan must be restored at 100 percent immediately.
The combination of these actuarial and accounting standards gives UK plan sponsor a greater
ability than the Dutch plan sponsor to take risk through holding equities in the portfolio. As
17
further evidence that UK actuarial and accounting standards allow a larger allocation to
equity, one can look to other countries where the same standards are used: Ireland, South
Africa, Australia and Canada. The pension funds of these countries represents five of the top
six countries in the world in terms of total equity allocation (the other is the U.S. which uses a
more complicated process to evaluate assets). A net disparity exists also between the average
asset allocations in equities of these top six countries compared with the average of the other
nine countries: 58.5 percent against 22.2 percent.
Which conclusion can be drawn from these data? Why countries have profoundly different
pension fund asset allocations?
The research of Mark W. Griffin cannot determine conclusively which is the optimal asset
allocation for an investor with a long time horizon, like a pension fund, but thanks to him we
can be able to make a number of important observations. The most important are two:
evidence shows that it is not a rule to move a large part of the investments in risky assets
sustaining who believe in time diversification; the second important conclusion is that
actuarial and accounting standards developed in the UK and successively adopted in
Australia, Canada, Ireland and South Africa, mitigate the effect of equity market volatility on
contribution levels and thereby encourage an higher allocation to equities.
19
Chapter 2
THE ARGUMENTS IN FAVOR OF TIME DIVERSIFICATION
After the introduction made in the first chapter, now I want to expose the arguments that
practitioners and some economists take in favor of Time Diversification.
After a brief history of the perspectives on stocks as the best investment for the long run, with
an exposure of the sentiment about equities throughout the 20th century, I want to expose the
reasons for which stocks are considered “for the long run”. These reasons can be divided in
two groups: theoretical reasons and practical reasons. The first group starts from a
mathematical and statistical framework, while the second group watches closely to
fundamentals and history.
2.1) A brief history of perspectives on stocks as investments for the long run
Throughout the 19th century, stock markets were considered the province of speculators and
insiders but certainly not conservative investors. Only in the early 20th century some
researchers came to realize that stocks, as a class, might be suitable investments, under certain
economic environment. The most important researcher which contributed to this view is
Irving Fisher (1867-1947). He demonstrated that stocks are superior to bonds during
inflationary times, but that common shares likely would underperform bonds during periods
of declining prices12. This view of stocks return became the conventional wisdom of the early
twentieth century. In a seasonally cool Monday evening on October 14th, 1929, Irving Fisher,
at that time professor at Yale University, spoke at a monthly meeting of the Purchasing
Agents Association (PAA). Fisher’s speech was designed mainly to defend investments trusts,
the forerunners of mutual funds. The sentiment of investors at that time wasn’t high: Roger
Babson, businessman and market seer, predicted a “terrific crash in stock prices”. During his
speech, Fisher uttered a sentence that became one of the most quoted phrases in market
history:
“Stock prices have reached what looks like a permanently high plateau”13
Five days after Fisher’s speech, stock crasher: October 19th, 1929: the Dow Jones Industrial
Average lost 12.82%; starting the drop in stock prices which has characterized the 1929-1930
12
Irving Fisher, How to invest when prices are rising (Scranton, PA: G. Lynn Sumner & Co.), 1912.
13
“Fisher sees stocks permanently high”, The New York Times, October 16, 1929, p. 2
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