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MODERN PORTFOLIO THEORY AND THE EFFICIENT MARKETS HYPOTHESIS: HOW WELL DID THEY SERVE CANADA'S BABY-BOOM GENERATION?

Abstract

Modern Portfolio Theory (MPT) and the Efficient Markets Hypothesis (EMH) have had considerable influence over portfolio management strategies for the last forty years. This is also the time that the bulk of the baby boom generation entered and started to retire from the work force. Taking the example of an average Canadian family from 1977 to 2016, this paper examines how well the tenets of MPT and EMH served this generation of investors. A model investing strategy was constructed based on the principles of MPT and EMH. The results of this strategy were evaluated for the portfolio's ability to adequately provide for the subject couple's financial needs in retirement. Results of the model portfolio were compared to other popular investment alternatives. Using generally-accepted rules-of-thumb in financial planning, the model portfolio was found to have provided an adequate retirement income for the subject couple. Some of the other strategies moderately exceeded the returns of the model portfolio, while others underperformed this benchmark. Analysis of these discrepancies reinforced the significance of diversifying among and within asset classes, and of rebalancing portfolios through dynamic asset allocation.
27 August 2019, 12th Economics & Finance Conference, Dubrovnik ISBN 978-80-87927-80-9, IISES
DOI: 10.20472/EFC.2019.012.006
JIM FISCHER
Mount Royal University, Canada
MODERN PORTFOLIO THEORY AND THE EFFICIENT MARKETS
HYPOTHESIS: HOW WELL DID THEY SERVE CANADA’S
BABY-BOOM GENERATION?
Abstract:
Modern Portfolio Theory (MPT) and the Efficient Markets Hypothesis (EMH) have had considerable
influence over portfolio management strategies for the last forty years. This is also the time that the
bulk of the baby boom generation entered and started to retire from the work force. Taking the
example of an average Canadian family from 1977 to 2016, this paper examines how well the tenets
of MPT and EMH served this generation of investors. A model investing strategy was constructed
based on the principles of MPT and EMH. The results of this strategy were evaluated for the
portfolio’s ability to adequately provide for the subject couple’s financial needs in retirement. Results
of the model portfolio were compared to other popular investment alternatives. Using
generally-accepted rules-of-thumb in financial planning, the model portfolio was found to have
provided an adequate retirement income for the subject couple. Some of the other strategies
moderately exceeded the returns of the model portfolio, while others underperformed this
benchmark. Analysis of these discrepancies reinforced the significance of diversifying among and
within asset classes, and of rebalancing portfolios through dynamic asset allocation.
Keywords:
Modern Portfolio Theory (MPT), Efficient Markets Hypothesis (EMH), baby-boom generation,
indexing, portfolio management
JEL Classification: G11
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1. Introduction
Harry Markowitz’s 1952 paper on Modern Portfolio Theory (MPT) introduced guidelines
for investment choice and portfolio management that departed from previously accepted
practices. His advocacy of diversification among and within asset classes took some time
to catch on, but by the 1970s MPT and its balancing act between risk and return had
become the template for portfolio selection and management (Rubinstein, 2002).
Complementing Markowitz’s MPT, the Efficient Markets Hypothesis (EMH) paved the
way for the concept of indexing, or achieving diversity through a broadly based market
index, allowing any investor to hold an array of stocks without having to pick individual
securities.
The 1970s also ushered the baby-boom generation into the work force. Hence, their
investment strategies would be heavily influenced by investment advisors who were
guided by Markowitz’s MPT. It continued to hold court as the predominant view of how to
manage investment choices for the next 40-plus years, and EMH and its indexing
strategy provided a ready means for any investor to achieve instant diversity.
With the global financial crisis and ensuing recession that started in 2007, the continued
relevancy of these theories was questioned. By then, the first members of the boomer
generation were starting to retire. While faith in MPT and EMH might have been shaken
by the economic events of the early 21st Century, they were the theoretical basis upon
which the portfolios of an entire generation of investors were managed. With the
vanguard of the boomer cohort entering their retirement years now, it was the opportune
time to examine the efficacy of MPT.
This paper asks the question, was the average baby-boomer well-served by following an
investment strategy guided by the principles of MPT and EMH? A model portfolio was
constructed that encompassed the tenets of these theories. This was compared to other
popular investment alternatives. Conclusions as to the efficacy of the model portfolio or
other alternatives were based on their ability to provide for the retirement needs for the
average Canadian who reached age 65 in 2016. It hypothesizes that the model portfolio
constructed here would provide for an adequate income for the average Canadian family
retiring in 2017.
2. Methodology
Canadian economist and demographer David Foote defines the Canadian baby-boom
generation as those born from 1947 to 1966 (Foot & Stoffman, 1998). The generation is
significant because of the large number of members in the cohort. Throughout those
years, there were over 400,000 new Canadians born annually (Foot & Stoffman, 1998, p.
24). To compound the significance of the cohort’s size, there was also significant
immigration to Canada at the same time, notably of people who were in their prime child-
bearing years.
Markowitz’s portfolio theory in 1952 challenged the previous predominant investment
strategy championed by Keynes and others (Boyle, Garlappi, Uppal, & Wang, 2012). For
Keynes, acquired competence of certain asset classes and their specific securities
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allowed the investor to discover undervalued securities of local enterprises.
Diversification was not considered important, but troublesome, as all investors had limited
expertise to draw from, thus limiting their investments to those securities they understood
and found value in (Boyle, Garlappi, Uppal, & Wang, 2012). In contrast, Markowitz
recognized the relationship between risk, return, and covariance (Markowitz, 1952). His
MPT stressed the need for diversification among asset classes. This allowed the investor
to hold a broad array of investments, distributed across assets such as stocks, bonds and
real estate. Traditionally these asset classes had low positive or even negative
covariance, meaning they would not all perform well at the same time, although the long-
term returns of each class individually were positive. The volatility risk, as measured by
standard deviation, was smoothed for the entire portfolio if asset allocation included
investments that lacked positive covariance. This diversification theme was taken a step
further, to suggest securities within each class should also be considered for their
covariance within the class. For example, the equity portfolio should not consist only of
automobile manufacturers, steel companies, and coal companies, all of which follow the
same economic cycle.
The EMH suggests that securities prices quickly adjust as investors react to information
that has been disseminated to them (Fama, 1970). A strong believer in the EMH would
deduce that because all information is available to all investors equally, no one has any
advantage in choosing securities over anyone else. Therefore, trusting professional
portfolio managers to outperform the market benchmark is folly. One is better served by
investing in a broad basket of securities representative of all segments of the market,
such as a market index (Buffett, 1991).
This study modelled the retirement planning of an average Canadian family in the 40-
year span from 1977 to 2016, using principles associated with MPT and EMH. The
beginning of this time frame marks the point at which individuals in the middle range of
the baby boomer generation entered the work force and started careers.
Income data for Canadians was readily available from Statistics Canada (Statistics
Canada, 2017). This study included data for non-elderly couples and couples with
children, using one or the other depending on the position of the economic life cycle the
subject couple were in at any given point in the timeframe studied.
In 1977 the average Canadian male married at the age of 25.2, the average female at
22.9 (Statistics Canada, October 1979). The newlywed couple in 1977 were born in 1951
and 1953 respectively, in the first half of the baby-boom generation. Our study begins in
1977, and follows an economic family unit of a couple with two children, as defined by
Statistics Canada. The average age of a mother at first birth in 1977 was 24.5 years of
age (Statistics Canada, 2015). Recognizing this average for our economic family, in 1977
we start to use the average after-tax income for a couple with children. This is maintained
until 2003, when the data for couples without children is used. It assumes the couple
have two children relatively close together, and, 26 years after the birth of the first, all
children have left the economic family unit. The children were two years apart in age, and
left at an average age of 25.
27 August 2019, 12th Economics & Finance Conference, Dubrovnik ISBN 978-80-87927-80-9, IISES
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Data for average after-tax income is provided by Statistics Canada in 2015 constant
dollars. For each year it is converted to real dollars using the inflation calculator of the
Bank of Canada (Government of Canada, 2018).
All income sources were considered, including: employment income of wages, salaries
and commissions, self-employment income, investment income, retirement income, and
government transfers.
As the last Canadian Census was in 2016, there is data on average family incomes only
up to 2015. For 2016, the year in which the male of our study turned 65, incomes were
deemed to be the same as those of 2015.
When Registered Retirement Savings Plans (RRSPs) were introduced in Canada in
1957, contribution limits were based on a percentage of the current year’s income.
Maximum amounts were increased infrequently. There was no carry-forward provision for
unused contributions. For the time-frame of this study, starting in 1977 until 1985, the
limit was 20% of earned income up to a maximum of $5,500 for an individual with no
pension plan (Franken, 1990). This amount increased from 1986 to 1990, to 20% up to a
maximum of $7,500. From 1990 on, contribution limits have been based on 18% of the
previous year’s earnings, to a maximum which increased regularly. These amounts are
available from Canada Revenue Agency (Canada Revenue Agency, 2016). For all years
in this study, the amounts saved for investment from after-tax income for the two adults in
the family falls within the contribution limits allowed for RRSPs. The family members are
assumed to be rational investors, taking advantage of any tax-favored accounts at their
disposal. Therefore, the investments made can be deemed to be growing tax free
throughout the time period.
The adults in the family were deemed to be employed in jobs which did not provide for
any pension. Their income in retirement was dependent on their own savings and
investments.
The family unit is deemed to have invested 20% of their after-tax monthly income each
month, at the end of the month, into their investments throughout the time period.
The equity portion of the portfolio is deemed to have been invested in the S&P/TSX
Composite Index. This index serves as the main broad-based index of the Canadian
equity market (S&P Dow Jones Indices LLC, 2018). It was launched in January 1977,
and therefore serves the entire time frame of the study. Investments were deemed to
have been made into an index mutual fund replicating the S&P/TSX Composite Index. As
there was no such instrument at the time, a simulated index fund was created using the
following parameters. The closing price of the index was used on the last trading day of
the month as reported by the Toronto Stock Exchange (TSX) (Toronto Stock Exchange,
2018). This is consistent with the practice of having mutual funds ascertain their Net
Asset Value Per Share (NAVPS) after market, on a daily basis, rather than continuously
during the day. A Management Expense Ratio (MER) of 1% annually was subtracted
from the fund. This is consistent with the average MER taken from an equity index fund in
2018. In keeping with mutual fund practice, the MER was subtracted quarterly, at a rate
of 0.25% of the fund. Distributions were paid each month, consistent with the dividend
27 August 2019, 12th Economics & Finance Conference, Dubrovnik ISBN 978-80-87927-80-9, IISES
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ratio of the index each month as reported by the TSX (Siblis Research, 2018). The family
invested at the end of each month. Distributions of dividends were reinvested to buy
more units of the fund rather than receiving them as cash at the time of each monthly
deposit. Because the amount invested annually by the family was within the amount
allowed for RRSP purposes, all contributions were made in an RRSP account. The
couple were exempt from paying any taxes on their monthly savings or the annual mutual
fund distributions deemed to have been received.
For the fixed-income portion, the family is deemed to have invested in a bond index fund
fashioned after the total returns of the FTSE TMX Canadian Universe Bond Index,
formerly the DEX and ScotiaMcLeod Bond Index. This index is the broadest and most
widely used measure of performance of marketable government and corporate bonds
outstanding in the Canadian market (FTSE Russell, 2018). Like the equity portion, the
fixed-income portion was invested at the end of the month at the closing price for the
bond index. The price of the index was reported on a total return basis, therefore income
received during the year was deemed to have been reinvested in the fund. A MER of
0.50% annually was subtracted from the fund, consistent with the average MER taken
from a fixed-income index fund in 2018. Price data from FTSE Russell was available for
all years of the study except from 1977 to 1979. Returns for these three years were
available, however, from the Financial Planning Standards Council (FPSC) of Canada
(Financial Planning Standards Council, 2018). For these years, the annual returns were
used to calculate a beginning price for the year, and that price was graduated or reduced
monthly at an even rate to meet the next year’s index level.
The amount marked for investment in either equity or fixed-income was based on a
generally accepted rule-of-thumb in financial planning. This involves taking one’s age and
using that as a percentage to be invested in fixed-income, with the rest going to equity.
Another way of saying this is to subtract your age from 100, and place this percentage in
equity. For a 26-year old, this meant putting 74% in equity and 26% in fixed-income.
Each year, as the investor aged, less was apportioned to equity and more to fixed-
income.
The investor in the study was deemed to have practiced dynamic asset allocation. This
involved reshuffling the portfolio annually if the portfolio becomes unbalanced as a result
of one asset class having had an extraordinary year of returns. For example, at age 30,
the investor should have been invested 30% in fixed income and 70% equity. If the
previous year saw extraordinary gains for the stock market index, and the equity
percentage of the portfolio was instead 75%, money was taken off of the equity portion
and reassigned to the fixed-income portion to rebalance. This was done in December
based on the portfolio weightings as new money was committed to the portfolio.
The model portfolio was based on dollar-cost-averaging into the S&P/TSX Composite
Index and the FTSE TMX Universe Bond Index, reinvesting distributions, and practicing
dynamic asset allocation or re-balancing annually. Initial asset allocation followed the
rule-of-thumb, with 26% of the portfolio invested in equity when the male was 26 years of
age. This was referred to as:
27 August 2019, 12th Economics & Finance Conference, Dubrovnik ISBN 978-80-87927-80-9, IISES
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1. The Model Portfolio
Its forty-year returns were compared to a number of other investment strategies:
2. Investing in the model portfolio, but without rebalancing;
3. Investing in both the S&P/TSX Composite Index and the FTSE TMX Universe Bond
Index, but with a 50% allocation to each, rebalancing annually;
4. Investing in both the S&P/TSX Composite Index and the FTSE TMX Universe
Bond Index, but with a 50% allocation to each, without rebalancing annually;
5. Investing in both the S&P/TSX Composite Index and the FTSE TMX Universe Bond
Index, reinvesting dividends, and practicing dynamic asset allocation or re-balancing,
but assigning asset allocation in the reverse order of what it is applied in the first
example. In other words, at age 25 the couple would invest 25% of their money in
equites rather than fixed-income, increasing each year until at age 65 they would
have 65% in equity and 35% in fixed-income.
6. Investing in just the S&P/TSX Composite Index on a dollar-cost-averaging basis,
reinvesting distributions as they are received;
7. Investing in just the FTSE TMX Universe Bond Index on a dollar-cost-averaging
basis;
8. Investing in Guaranteed Investment Certificates (GICs) each month through a
laddered portfolio technique.
In the GIC alternative, interest was deemed to be paid annually. Interest received was
added to the amount being saved and invested. Five-year terms were always purchased,
with an interest rate commensurate with the five-year chartered bank administered
interest rates for the month as reported by the Bank of Canada (Bank of Canada, 1965).
When the five-year GIC matured, its principal and final interest payment was reinvested
in a new five-year GIC along with any regular monthly savings.
3. Results
In December of 2016, at the age of 65 and 63, the average Canadian couple who had
invested for 40 years would have invested a total of $425,389.68.
After dollar-cost-averaging into the S&P/TSX Composite Index and the FTSE TMX
Universe Bond Index, rebalancing to meet asset allocation targets each year, the couple
had a total of $1,607,058.92 in their RRSP accounts (Portfolio 1). Of their total amount,
$629,580.99 (65%) was in the S&P/TSX Composite Index fund and $976,079.60 (35%)
was in the FTSE TMX Bond Index fund. A new deposit of $489.02 had just been made.
Without annual rebalancing of the portfolio through dynamic asset allocation, Portfolio 2
yielded $1,481,156.62.
If the couple had allocated 50% to both the equity and bond indexes every month, and
rebalanced the portfolio annually (Portfolio 3), they would have had $1,677,369.26.
If they had allocated 50% to both the equity and bond indexes every month, but not
rebalanced annually (Portfolio 4), they would have had $1,569,493.55.
27 August 2019, 12th Economics & Finance Conference, Dubrovnik ISBN 978-80-87927-80-9, IISES
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If they had practiced the inverse asset allocation of the model portfolio, investing 65% in
fixed-income at the beginning (Portfolio 5), they would have had $1,741,533.37.
If the couple had only invested in the S&P/TSX index over the 40 years, with distributions
reinvested (Portfolio 6), they would have had RRSP accounts equaling $1,257,859.24.
Investing in only the FTSE TMX Universe Bond Index (Portfolio 7), the couple would have
had a total of $1,971,470.23. This was the highest returning portfolio choice in the study,
surpassing equity-only portfolios, or any portfolio where equities and bonds were
combined.
The GIC portfolio (Portfolio 8) returned $1,001,745.02 at the end of the 40-year period.
These results are summarized in Table 1.
Table 1. Model portfolio returns 1977-2016 for an average Canadian family, with 20% of
after-tax income invested monthly
Portfolio 1: S&P TSX Composite Index and FTSE TMX Bond Universe Index,
beginning with 65/35 equity/fixed-income in year one, with annual rebalancing
$1,607,058.92
Portfolio 2: S&P TSX Composite Index and FTSE TMX Bond Universe Index,
beginning with 65/35 equity/fixed-income in year one, without annual
rebalancing
$1,481,156.62
Portfolio 3: S&P/TSX Composite Index and the FTSE TMX Universe Bond
Index, but with a 50% allocation to each, with annual rebalancing
$1,677,369.26
Portfolio 4: S&P/TSX Composite Index and the FTSE TMX Universe Bond
Index, but with a 50% allocation to each, without rebalancing annually
$1,569,493.55
Portfolio 5: S&P/TSX Composite Index and the FTSE TMX Universe Bond
Index, reinvesting dividends, with annual rebalancing, but assigning asset
allocation beginning with 35/65 equity/fixed-income in year one, with annual
rebalancing
$1,741,533.37
Portfolio 6: S&P/TSX Composite Index only, on a dollar-cost-averaging basis,
reinvesting distributions monthly as received
$1,257,859.24
Portfolio 7: FTSE TMX Universe Bond Index only, on a dollar-cost-averaging
basis, total return
$1,971,470.23
Portfolio 8: GICS only, invested monthly in five-year terms, interest reinvested
annually as received
$1,001,745.02
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Figure 1 displays the returns of the various portfolios, and the total money invested, over
the 40-year period.
Figure 1. Portfolio Returns 1977-2016
4. Observations
To determine if the model portfolio served our average Canadian couple suitably, we had
to consider their requirements at retirement. Popular financial planning practice suggests
having retirement savings to provide 70% of pre-retirement income. In 2016 the couple
made $83,900. The desired annual income in retirement, following the rule-of-thumb,
would be 70% of this amount or $58,730, in real dollars, throughout the life of the couple.
Four possible retirement scenarios were illustrated. A post-retirement annual return of 5%
was considered for the resulting portfolio at age 65. Consideration was given to how long
the couple’s retirement funds would last if they took an annual income equal to 100% of
their annual income received in their last year in the work force, and how long it would
0,00
500 000,00
1 000 000,00
1 500 000,00
2 000 000,00
2 500 000,00
1.77
6.78
11.79
4.81
9.82
2.84
7.85
1.87
6.88
11.89
4.91
9.92
2.94
7.95
1.97
6.98
11.99
4.01
9.02
2.04
7.05
1.07
6.08
11.09
4.11
9.12
2.14
7.15
Portfolio Returns 1977-2016
Total Invested
Portfolio 2
Portfolio 3
Portfolio 4
Portfolio 5
Portfolio 6
Portfolio 7
Portfolio 8
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last if they took 70% of this amount. A post-retirement annual return of 0% was also
considered for the resulting portfolio at age 65. Again, consideration was given to the
couple taking 100% of their pre-retirement annual income, or 70% of the same amount.
Investment account balances for each scenario were calculated to age 100. In each of
these four cases, the returns to the retired couple and the longevity of their funds are
represented in Table 2.
Table 2: Annual retirement incomes for Canadian couple starting at age 66, and age at
which savings are depleted
Annual retirement income, indexed to 2% inflation, starting at age 66
With 5% annual investment return
With 0% annual investment return
Portfolio
value at age
65
$83,900
(100% of last
year income in
work force,
indexed to
inflation)
$58,730
(70% of last
year income in
work force,
indexed to
inflation)
$83,900
(100% of last
year income in
work force,
indexed to
inflation)
$58,730
(70% of last
year income in
work force,
indexed to
inflation)
Portfolio 1: S&P TSX Composite Index and FTSE TMX Bond Universe Index, reinvesting
distributions, initially at 65/35 equity/fixed-income in year one, with annual rebalancing
$1,607,058.92
Depleted at age
93
Balance
$1,843,491.35
at age 100
Depleted at age
81
Depleted at age
86
Portfolio 2: S&P TSX Composite Index and FTSE TMX Bond Universe Index, beginning with
65/35 equity/fixed-income in year one, without annual rebalancing
$1,481,156.62
Depleted at age
90
Balance $
1,149,012.33
at age 100
Depleted at age
80
Depleted at age
85
Portfolio 3: S&P/TSX Composite Index and the FTSE TMX Universe Bond Index, but with a
50% allocation to each, with annual rebalancing
$1,677,369.26
Depleted at age
95
Balance
$2,231,324.27
at age 100
Depleted at age
81
Depleted at age
87
Portfolio 4: S&P/TSX Composite Index and the FTSE TMX Universe Bond Index, but with a
50% allocation to each, no annual rebalancing
$1,569,493.55
Depleted at age
92
Balance
$1,636,280.19
at age 100
Depleted at age
80
Depleted at age
86
Portfolio 5: S&P/TSX Composite Index and the FTSE TMX Universe Bond Index, reinvesting
distributions, but initial asset allocation at 35/65 equity/fixed-income in year one, with annual
rebalancing
$1,741,533.37
Depleted at age
97
Balance
$2,585,254.48
at age 100
Depleted at age
82
Depleted at age
88
Portfolio 6: S&P/TSX Composite Index only, reinvesting distributions monthly as received
$1,257,859.24
Depleted at age
85
Depleted at age
99
Depleted at age
78
Depleted at age
82
Portfolio 7: FTSE TMX Universe Bond Index only, total return
$1,971,470.23
Balance
$844,559.59
at age 100
Balance
$3,853,589.74
at age 100
Depleted at age
84
Depleted at age
90
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Portfolio 8: GICS only, invested monthly in five-year terms, interest reinvested annually as
received
$1,001,745.02
Depleted at age
79
Depleted at age
89
Depleted at age
75
Depleted at age
79
If the model portfolio provided a 2% increase in income each year to accommodate
inflation, by age 90 the couple would be receiving $137,646.84 annually and, at that time,
could leave their estate $462,148.47. If they continued to receive inflation-indexed
amounts, they would exhaust their savings at age 93.
If the couple took only the prescribed amount of 70% of their annual pre-retirement
income, or $58,730 annually, indexed to inflation of 2%, they would leave their estate
$1,956,125.50 at age 90, or $1,843,491.35 at age 100.
In either of these scenarios, the couple that followed the model portfolio strategy had
enough savings to provide for a comfortable retirement.
There is one caution for the couple if they take 100% of their annual pre-retirement
income. This alternative brings with it the possibility of outliving their savings if they live
beyond 93 years of age, even if their investments continued to grow at a rate of 5%
annually. If the account had a return of 0% annually, it would be depleted by age 81.
The retirement incomes and their longevity from the other model portfolios are shown in
Table 2. Most of these also provided for a reasonable retirement on their own. This is
particularly the case if the couple took an income equal to 70% of annual pre-retirement
income, and the portfolio continues to grow at a rate of 5% annually. The exception was
the GIC portfolio. To meet the minimum annual income of $58,730, the GIC portfolio
would need to be topped up by Canada Pension Plan (CPP) and Old Age Security (OAS)
payments. The couple would normally be entitled to these benefits. If they elected to start
receiving them at age 65, they could expect to receive up to approximately $20,000
annually in CPP benefits, and an additional $14,000 in OAS benefits in 2016 dollars,
indexed to inflation (Government of Canada, 2016). The addition of government pensions
also makes the GIC alternative a feasible retirement savings strategy. Government
pensions also extend longevity of a number of the other portfolios if they reduce their
income taken from their investment savings relative to the amount they receive in CPP
and OAS benefits.
Sharpe ratios were calculated for each of the portfolios which held equities, bonds, or
both, using the following:
Sharpe Ratio = {[E(Rp-Rrf)] / ơ(Rp-Rrf)} x √N
Where:
Rp = the monthly return of the portfolio
Rrf = the risk-free rate of return, in this case the monthly return of the 3-month
Canadian Treasury Bill (Statistics Canada, 2019) (Government of Canada, 2019)
Rp-Rrf = the return differential between the portfolio and the risk-free rate
E(Rp-Rrf) = the average of the monthly differential returns
ơ(Rp-Rrf) = the standard deviation of the differential returns
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N = 12, the number of months in the year, to annualize the Sharpe ratio results
gleaned from monthly data
Sharpe ratios are displayed in Table 3.
Table 3. Sharpe Ratios for Portfolios
Portfolio 1: S&P TSX Composite Index and FTSE TMX Bond Universe Index,
beginning with 65/35 equity/fixed-income in year one, with annual rebalancing
29.64
Portfolio 2: S&P TSX Composite Index and FTSE TMX Bond Universe Index,
beginning with 65/35 equity/fixed-income in year one, without annual
rebalancing
22.77
Portfolio 3: S&P/TSX Composite Index and the FTSE TMX Universe Bond
Index, but with a 50% allocation to each, with annual rebalancing
32.22
Portfolio 4: S&P/TSX Composite Index and the FTSE TMX Universe Bond
Index, but with a 50% allocation to each, without rebalancing annually
31.27
Portfolio 5: S&P/TSX Composite Index and the FTSE TMX Universe Bond
Index, reinvesting dividends, with annual rebalancing, but assigning asset
allocation beginning with 35/65 equity/fixed-income in year one, with annual
rebalancing
33.94
Portfolio 6: S&P/TSX Composite Index only, on a dollar-cost-averaging basis,
reinvesting distributions monthly as received
14.86
Portfolio 7: FTSE TMX Universe Bond Index only, on a dollar-cost-averaging
basis, total return
38.46
The Sharpe ratio is used with ex-post returns to measure the excess return earned given
the excess risk (standard deviation) undertaken to earn it. Where portfolios have
equivalent returns, the one with the higher standard deviation will have a lower Sharpe
ratio. Higher Sharpe ratios therefore demonstrate a higher performance given the relative
amount of risk taken in the portfolio. Portfolios 1, 3, 4, and 5 all employ a similar
investment strategy, combining equity and fixed-income indexing. They are distinguished
from each other by differences in their rebalancing and initial distribution of those assets.
Their ratios of 29.64, 32,22, 31.27 33.94 respectively are close for a 40-year time frame.
These four portfolios are composed solely of the same one equity and one bond index
throughout their 40-year period and no efforts were made in any of the portfolios to
change their strategy during the time period. Thus, it is not surprising that their relative
performance would be similar. The underperforming Portfolio 6, composed of the equity
index only, givens a much lower ratio of 14.86. The superior-performing Portfolio 7,
composed of the bond index only, gives a much higher ratio of 38.46. During the 40-year
period, the Canadian bond market outperformed the Canadian equity market as
measured by their relative indexes. Historically, this is an anomaly (Ibbotson & Chen,
2009). In particular, the 21st Century has been a difficult time for equities, and this period
constitutes the last 16 years of the 40-year study. The higher Sharpe ratio for Portfolio 7
reflects its acceptance of higher risk through less diversification, being composed of only
bonds. It is not a reflection of manager out-performance, as the bond portfolio was
passively managed. Moreover, it is a reflection of the portfolio’s time period chance
conclusion with back-to-back corrections in the stock market. If anything, the Sharpe
ratios of the various portfolios demonstrate the expediency of diversifying among asset
27 August 2019, 12th Economics & Finance Conference, Dubrovnik ISBN 978-80-87927-80-9, IISES
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classes as well as within. A lesson that can be learned for any investor, no matter which
portfolio they might have pursued, is the advantage given by regularly investing 20% of
after-tax income on a dollar-cost averaging basis.
It is notable that the FTSE TMX Universe Bond Index portfolio outperformed all others,
including the equity-only or the model portfolio. In the 40-year period studied, the
Canadian stock market as evidenced by the S&P/TSX Composite underwent two 50%
corrections, beginning in 2000 and 2007 respectively. The “lost decade” followed the
historical bull market for stocks in the 1990s. While the 40-year period does suggest
bonds outperform stocks, longer-term analysis still says otherwise. While the couple in
this study from 1977 to 2016 would have done better had they invested only in the bond
index, the anomalies of the stock market in the new millennium could not have been
known to them. In any time period measured, either bonds or stocks will likely outperform
the other by some degree. While stocks might historically have been the favorite in the
long term to outperform, the 40-year period studied here provides proof that
diversification among asset classes is necessary, and returns in any one-time period can
be surprising.
While the normal rule-of-thumb suggests investing in 65/35 equity/fixed-income early and
adjusting annually, the portfolio which did the opposite of 35/65 equity/fixed-income
performed marginally better. This can be accounted for by the lackluster performance of
stocks since 2000.
In all cases where there was rebalancing annually, the results were higher than when
rebalancing was not done. There are not significant differences between 50/50 portfolios
held throughout, or 65/35 portfolios to start or 35/65 portfolios to start. Whichever
breakdown in asset allocation is used, the key to enhancing returns seemed to be
rebalancing.
For the subject couple, stock markets recovered from their lows by the time the male
reached age 65. For an investor at the very vanguard of the boomer generation, who
might have reached age 65 and retired a few years earlier than the subject couple, in the
depths of the Great Recession, their equity portion would have been significantly less.
However, by practicing dynamic asset allocation at that time and rebalancing, they would
eventually recoup those losses and make gains, if they took retirement income from the
bond side only. This would necessitate a firm belief in the fact that for stock markets in
Western industrialized nations, the long-term trend is up, despite disappointing returns in
the short or medium term.
In summary:
1. The MPT portfolio served the average couple in the study by providing an adequate
retirement income.
2. Variations in asset allocation on occasion outperformed the model portfolio, as did the
portfolio investing only in the bond index. These differences can largely be accredited to
the lackluster performance of stocks in the 21st Century. This demonstrates the
uncertainty as to which markets will outperform in the short and medium term,
emphasizing the case for diversity.
27 August 2019, 12th Economics & Finance Conference, Dubrovnik ISBN 978-80-87927-80-9, IISES
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3. There was no great difference in returns between portfolios that started with either a
65/35 or 35/65 asset mix, or that maintained a 50/50 asset mix.
4. Dynamic asset allocation, or rebalancing, enhanced returns in all cases.
5. Conclusions
Data reflected average earnings for a Canadian couple for the 40-year time period, with
no consideration for the variables of occupation, career changes, changing family status,
or geographic location within Canada. While this study has attempted to remain
observant of a much-generalized average Canadian family, it is understood that one
individual is likely to undergo many personal and professional changes in the course of
40 years of adulthood.
This paper hypothesized that an investment strategy following principles of MPT and
EMH and followed by an average Canadian couple retiring in 2017 would have provided
them with an adequate income in retirement. The focus here was on a baby-boom family
which would recently have reached retirement age. While adherence to the model
portfolio in their time frame provided them with an adequate income in retirement, and
was therefore successful, this is not necessarily the case for the rest of the baby-boom
generation. The methodology can be duplicated on earlier retirees to determine if the
portfolio strategy has served all boomers to date, and how it is serving those who have
some years yet to retire. More general conclusions might be reached about the efficacy
of MPT and EMH strategies with such further analysis which is beyond the scope of this
paper.
Investors and investment professionals have been applying MPT and EMH principles of
investing strategy for roughly 40 years. While the strategies of diversification within and
among asset classes seemed to be sound advice, forecasting based on expected market
returns was fraught with difficulty. Investors and their advisors alike have had to take
something of a leap of faith that the theories were sound. With the passing of time, this
study is able to look back on this one case study and verify that, in this instance, the
investing strategy did indeed meet the goals of the subject investor by providing an
adequate retirement income. Markets will always be characterized by uncertainty,
particularly in the short term. However, any investor needs to have some parameters to
operate within in order to try and succeed in the long term. While the instruments that
were used in this study were synthesized due to the absence of suitable index funds in
the beginning years of the time frame discussed, such instruments are now plentiful.
Investing in index funds on a disciplined, dollar-cost-averaging basis with regular re-
balancing is now easily done. The results found here should provide investors and their
advisors looking at the long-term horizon to continue to view such an investment strategy
favorably.
Markowitz and his followers advocated asset allocation across a number of asset
classes. This study saw the subject couple diversify across stocks and bonds, and
diversify widely within those two classes by investing in the relative indexes. No
consideration was given for real estate. Further study could examine the outcome for the
same couple who also invested another 20% (or other percentage) in home ownership,
using average home prices and mortgage rates over the same period. The couple could
27 August 2019, 12th Economics & Finance Conference, Dubrovnik ISBN 978-80-87927-80-9, IISES
73https://iises.net/proceedings/12th-economics-finance-conference-dubrovnik/front-page
then consider down-sizing from the home they had bought to provide for their family-
rearing years to something smaller, investing any gains accrued.
This study can be easily replicated in other industrialized economies where there are
mature stock and bond markets.
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... In contrast, MPT determines the best possible portfolio by distributing it according to the selected risk level. In fact, it suggests that it is more logical to use investment instruments in different sectors rather than use the ones in the same sector when distributing portfolios (Fischer 2019). The core point of MPT is that high return comes with high risk. 1 Capturing the many basic points of MPT, Eugene Fama (1965) and Paul A. Samuelson (1965) developed the efficient market hypothesis (EMH) in the 1960s. ...
... The core point of MPT is that high return comes with high risk. 1 Capturing the many basic points of MPT, Eugene Fama (1965) and Paul A. Samuelson (1965) developed the efficient market hypothesis (EMH) in the 1960s. Completing Markowitz's (1952) MPT, EMH provided diversity through the concept of indexing or a broad-based market index by holding an array of stocks without having to select individual securities (Fischer 2019). ...
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THIS YEAR MARKS the fiftieth anniversary of the publication of Harry Markowitz's landmark paper, "Portfolio Selection," which appeared in the March 1952 issue of the Journal of Finance. With the hindsight of many years, we can see that this was the moment of the birth of modern financial economics. Although the baby had a healthy delivery, it had to grow into its teenage years before a hint of its full promise became apparent. What has always impressed me most about Markowitz's 1952 paper is that it seemed to come out of nowhere. Compared to the work of his 1990 co-Nobel Prize winners (Sharpe primarily for his paper on the capital asset pricing model and Miller for his paper on capital structure), Markowitz's paper seems to have more of this flavor. In 1676, Sir Isaac Newton wrote his friend Robert Hooke, "If I have seen further it is by standing on the shoulders of giants" (Newton (1959)) and that is true of Markowitz as well, but, like Newton, he certainly saw a long distance given the height of those shoulders. Markowitz was hardly the first to consider the desirability of diversification. Daniel Bernoulli in his famous 1738 article about the St. Petersburg
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We develop a model of portfolio choice capable of nesting the views of Keynes, advocating concentration in a few familiar assets, and Markowitz, advocating diversification across all available assets. In the model, the return distributions of risky assets are ambiguous, and investors are averse to this ambiguity. The model allows for different degrees of familiarity for various assets and captures the tradeoff between concentration and diversification. The models shows that if investors are not familiar about a particular asset, then they hold a diversified portfolio, as advocated by Markowitz. On the other hand, if investors are familiar about a particular asset, they tilt their portfolio toward that asset, while continuing to diversify by holding the other assets in the market. And, if investors are familiar about a particular asset and sufficiently ambiguous about all other assets, then they hold only the familiar asset, as Keynes would have advocated. Finally, if investors are sufficiently ambiguous about all risky assets, then they will not participate at all in the equity market. The model shows that even when the number of assets available for investment is very large, investors continue to hold familiar assets, and an increase in correlation between familiar assets and the rest of the market leads to an increase in the allocation to familiar assets, as we observe empirically during periods of financial crises. We also show how beta and the risk premium of stocks can depend on both systematic and unsystematic volatility. Our model predicts also that, when the aggregate level of ambiguity in the economy is large, investors increase concentration in the assets with which they are more familiar (flight to familiarity), even if these happen to be assets with a higher risk or lower expected return.
Selected Historical Interest Rates
  • Bank
  • Canada
References Bank of Canada. (1965). Selected Historical Interest Rates. Retrieved January 16, 2018, from Bank of Canada: https://www.bankofcanada.ca/rates/interest-rates/selected-historical-interest-rates/
Letter to shareholders
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Buffett, W. (1991). Letter to shareholders. Retrieved May 15, 2011, from http: //www.berkshirehathaway.com/letters/ 1991.html
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Canada Revenue Agency. (2016, Dec 15). MP, DB, RRSP, DPSP, and TFSA limits and the YMPE. Retrieved Nov 27, 2017, from Government of Canada: https://www.canada.ca/en/revenueagency/services/tax/registered-plans-administrators/pspa/mp-rrsp-dpsp-tfsa-limits-ympe.html#
RRSPs: Tax-assisted retirement savings. Perspectives on Labour and Income, 2. Canada: Statistics Canada
  • H Franken
Franken, H. (1990). RRSPs: Tax-assisted retirement savings. Perspectives on Labour and Income, 2. Canada: Statistics Canada. Retrieved November 27, 2017, from http://www.statcan.gc.ca/pub/75-001-x/1990004/121-eng.pdf
Quarterly report of Canada Pension Plan and Old Age Security monthly amounts and related figures
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FTSE Russell. (2018, April 3). FTSE Russell. Retrieved April 3, 2018, from FTSE TMX Canada Indices: http://www.ftse.com/products/FTSETMX/Home/Methodologies Government of Canada. (2016, Oct 13). Quarterly report of Canada Pension Plan and Old Age Security monthly amounts and related figures -October to December 2016. Retrieved May 17, 2018, from Government of Canada: https://www.canada.ca/en/employment-socialdevelopment/programs/pensions/pension/statistics/2016-quarterly-october-december.html#topic3
Are Bonds Going to Outperform Stocks Over the Long Run? Not Likely. Chicago: Ibbotson Associates
  • R Ibbotson
  • P Chen
Ibbotson, R., & Chen, P. (2009). Are Bonds Going to Outperform Stocks Over the Long Run? Not Likely. Chicago: Ibbotson Associates. Retrieved May 17, 2018, from https://corporate.morningstar.com/ib/documents/MediaMentions/AreBondsGoingToOutPerformStoc ks.pdf