Rebalancing Resurrected - Butler|Philbrick & Associates

5/11/2018 Rebalancing Resurrected - Butler|Philbrick & Associates - slidepdf.com

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UPDATED JANUARY 201

Butler|Philbrick and Associates*

*Butler|Philbrick and Associates is part of Macquarie Private Wealth Inc.

REBALANCING

RESURRECTED



1

Rebalancing resurrected

We have poked a lot of fun at Strategic Asset Allocation (SAA) and Modern Portfolio Theory (MPT) over the years, so this

white paper is somewhat of an olive branch to the traditional investment community. It should be noted that in fact we do

not, of course, take issue with Markowitz' elegant mathematical relationship between risk, return and inter-asset

correlation, but rather with the standard implementation of the concept: Strategic Asset Allocation.

Strategic Asset Allocation is the process of evaluating an investor's tolerance (both emotional and financial) for risk, and

then creating an allocation to stocks, bonds and cash which theoretically maximizes an investor's expected return given

his or her specific risk tolerance. For example, upon visiting an Investment Advisor, an early Baby Boomer investor, age

65, with average risk tolerance might be instructed that an appropriate asset allocation would include 50% bonds and

50% stocks.

This paper will revisit the concept of SAA first by illustrating how the traditional SAA approach violates the most basicprecepts of common sense by discussing the concept of 'informed bias'. We then move on to discuss several evolutions

of the concept, and demonstrate how an evolved form of SAA can work quite effectively in a portfolio framework. Finally,

we revisit the concept of informed bias with a practical implementation.

Traditional strategic asset allocation makes sense about 40% of the time

Our frustration with traditional SAA is rooted in the following:

1. There are superior long-term allocation strategies for investors with much more predictable return distributions.

2. Traditional SAA explicitly ignores conditional intermediate-term return probabilities.

For example, an investor who describes himself as 'Aggressive' would, under traditional SAA, be advised to invest 100%of his capital in stocks regardless of extreme levels of stock market valuations, such as at the stock market peak in 2000.

This despite the fact that in early 2000 stocks were the most expensive they had every been, and therefore returns to

stocks from that peak were likely to be low and volatile, and certainly less prospective than government bond returns.

Let's put it another way: If you were stopped by a couple in Bangkok and asked to recommend appropriate attire for

their trip to Toronto, what would you recommend? Do you have all the information you need to make a reasonable

recommendation? Could you make a recommendation without knowing what month they would be visiting? Would your

recommendation change if they were coming in July versus January?

If they were visiting in April, May, June or September, you would perhaps be more circumspect and suggest they pack

lighter clothes, but a few warm items just in case. However, if they were visiting in July or August you would advise them

to pack shorts, and if they were traveling in December, January or February you would advise them to pack a parka and

boots. This is called an ‘informed bias’, as we are able to favorably bias our advice based on better information.

In the same way, if markets are mildly cheap or mildly expensive, future returns are likely to approximate the long-termaverage. However, if markets are extremely cheap (bottom 20% of all valuation periods) or extremely expensive (top 20%

of all valuation periods), then the evidence clearly shows that allocations in portfolios should be raised or lowered

accordingly. Expensive markets should receive a smaller allocation, and inexpensive markets should receive a larger

allocation as a result of our new and meaningful information.

It isn’t very helpful to advise a traveler to lug a parka and snow boots to Toronto in July. Neither is it very helpful to advise

clients to have a full allocation to stocks at periods of peak valuations.



2

The magic of simple rebalancing

If we assume for a moment that stocks and bonds are in ‘neutral’ valuation territory (they are not, but let’s ignore this fact

for a second), then it is worthwhile to explore the power implicit in the mathematical elegance of Markowitz' original

framework, if properly applied.

Importantly however, Strategic Asset Allocation requires one further step beyond the initial asset allocation decision:

periodic rebalancing. This is the process whereby each asset is bought or sold on a fixed schedule to bring the

stock/bond allocation ratio back into alignment. The assets frequently move out of alignment when one asset class

outperforms the other in any period.

While adherents to a Strategic Asset Allocation approach are explicitly expected to perform rebalancing on a pre-

established schedule, for example annually or bi-annually (defined in your Investment Policy Statement), in my experiencemany Advisors do not revisit the rebalancing decision on a regular basis, and so many clients miss out on the value of

this simple exercise over time.

Remember our Boomer investor with average risk tolerance and a recommended 50/50 stock/bond portfolio? If this

investor had adopted a 50/50 stock/bond Strategic Asset Allocation strategy with quarterly rebalancing in mid-1993 (our

earliest data), and stuck with the strategy through to the present, his returns would look something like the chart on the

next page.



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Case 1: 50/50 stock/bond portfolio with quarterly rebalancing

Source: Butler|Philbrick and Associates

The table at the bottom may require some explanation. For our purposes, you want to focus on the following data:

• CAGR (second from the top on the left): This is the annualized return to the portfolio over the entire duration of the test.

This strategy delivered a CAGR of 7.29% per annum.

• Sharpe (third from the top on the left): This is perhaps the most common measure of the 'efficiency' of a portfolio, and in

this case it measures the annualized return to the strategy divided by the standard deviation, which is the most common

measure of portfolio risk. The higher this ratio the better. This strategy had a Sharpe ratio of 0.73.

• Max Daily Drawdown (six from the top on the left): This is the worst drop in the portfolio from peak-to-trough measured

from the highest closing high to the highest closing low. It is a measure of how much loss an investor had to bear when

investing in this strategy. This strategy had a Max Daily Drawdown of -26.01%.

• % Winning Months (top right): This is the percentage of months in which the strategy delivered positive absolute returns.

This strategy delivered positive returns in 66% of months.

http://1.bp.blogspot.com/-21ivX04F0Kc/TqC5XlJ9cwI/AAAAAAAAAgI/phNjEGjzBtQ/s1600/50+50+static+rebalanced



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Let's contrast the performance of this 50/50 SAA portfolio with the return to a 100% stock portfolio over the same time

frame:

Case 2. S&P 500 ‘Buy and Hold’


Note that stocks alone over this period delivered 5.89% annualized returns, with a Sharpe ratio of 0.30, a Max DailyDrawdown of 56% (!!), and delivered positive returns in 61% of months.

Incredibly, a simple SAA portfolio with 50/50 stocks/bonds delivered 50% more total growth (262% vs. 176%), with over

twice the efficiency (Sharpe ratio of 0.73 vs. 0.30), half the investor pain (Max Daily Drawdown -26% vs. -56%), and more

winning months (66% vs. 61%).

Even simple SAA with regular rebalancing does much better than stocks alone over the long-term.

http://3.bp.blogspot.com/-njQaqvWYdh8/TqC9gbzyFmI/AAAAAAAAAgQ/L57sK1NhsRU/s1600/buy+and+hold+s&p500



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True risk optimization

While a simple, traditional SAA portfolio with periodic rebalancing delivered much stronger, and more efficient returns

over the period tested than did stocks on their own, the simple SAA framework as described can still be substantially

improved upon.

Let's revisit the true objective of the SAA process: to ensure that an investor achieves the maximum return available at

a fixed level of risk that is a function of the investor's risk tolerance. Unfortunately, we know from experience and a

mountain of research that in real life, market risk is constantly changing. When markets are rising in a nice orderly

uptrend, market risk (volatility) is generally very low. When markets are falling, or even going sideways, uncertainty and

risk (volatility) is generally elevated.

If the objective of SAA is to maintain a fixed level of portfolio risk that is commensurate with each investor's risk tolerance,then shouldn't we reduce our allocation to each asset class dynamically when it begins to demonstrate amplified levels of

risk (volatility), and increase our allocation when volatility declines? In this way we can preserve a much more consistent

level of risk within the portfolio. Such expansion and contraction in portfolio allocations might be considered at each

rebalance period.

If we simply alter the traditional SAA strategy to reduce relative allocations to stocks or bonds when they exhibit relatively

risky behaviour (geek note: based on 20 day trailing volatility), and increase allocations when they exhibit low relative risk,

then we can achieve a much more efficient portfolio, again just with stocks and bonds:



6

Case 3: SAA with Dynamic Volatility Weighted Rebalancing, 50/50 stocks/bonds


Note that the objective of this portfolio is to keep the risk constant by reducing allocations to assets when they are

exhibiting risky behaviour (high trailing volatility), and increasing allocations to assets when they are exhibiting low risk

behaviour (low trailing volatility). In traditional SAA, the focus is on maintaining a fixed allocation. In contrast, and in

keeping with the broader objective of SAA, this risk-weighted approach is focused on maintaining a fixed level of risk .

This approach delivers much more efficient performance than the traditional SAA approach. While the annualized returns

to this strategy improve by just 0.6% per year, the real benefit is clear from the risk metrics.

The Sharpe ratio for this approach is 0.98, which represents 35% greater efficiency than traditional SAA, and over 300%

more efficiency than a pure stock portfolio. Of even greater interest for most investors, the Maximum Daily Drawdown

drops to 14% from 26% for traditional SAA and 56% for stocks, an improvement of 85% and 370% respectively .

Not bad for a simple and intuitive twist on an old idea.

http://3.bp.blogspot.com/-WVME3wMDtGY/TqDlzOz8RmI/AAAAAAAAAgg/QPEezu33x7k/s1600/vol_size_q_reb



7

Informed bias

In our discussion about the pitfalls of traditional approaches to SAA, we introduced the concept of informed bias when

we discussed whether an investor should be fully invested in any asset class, in proportion to his risk tolerance, when

there is a strong likelihood that returns to that asset class will be low or negative over the individual’s investment horizon.

We used the example of expensive markets at the peak of the technology bubble as an example of where introducing

informed bias to the allocation decision could add substantial value.

In that case, we might have considered biasing portfolios away from equities because they were fundamentally

expensive, and therefore future returns were likely to be low. Thus the portfolio would be skewed toward bonds until

equity valuations returned to more normal levels, at which point we might neutralize our asset allocation.

However, valuation is not the only tool at our disposal to produce an informed bias.

In prior articles, we have spilled a great deal of ink on the power of price momentum to forecast future price

performance. Conceptually, price momentum resembles the idea of physical momentum, which is a derivative of

Newton's First Law: an object in motion will stay in motion unless acted upon by an external force.

Similarly, we know from voluminous financial literature that the prices of stocks, commodities, bonds, industry sectors,

markets, houses, commercial real-estate, art, wine, and virtually every other asset one could own, display trending

behaviour whereby strong prior price performance predicts strong subsequent price performance. In other words, we

know that past winners are much more likely to be future winners, and past losers are more likely to be future losers, at

least over a forecast horizon of a few weeks to several months.

Suppose we apply a momentum filter to produce a simple informed bias to our relative volatility adjusted SAA given the

same portfolio of stocks and bonds. Specifically, we will allocate 25% more ‘risk’ to the asset class that has

demonstrated the stronger and more consistent price momentum relative to the other asset class, while the weaker

asset class is penalized with 25% less share. For example, when stocks have performed strongly and persistently over

the past 1 to 3 months, we will allocate 25% more to stocks, and vice versa.



8

Case 4: Relative Volatility Rebalanced SAA with Momentum Bias, 50/50 stocks/bonds


You can see that by introducing a simple informed bias to skew allocations toward the asset class with more prospective

returns (based on historical price momentum only), we increase returns by 47% (421% vs. 287% total return), increase

our Sharpe ratio by almost 10% (1.07 vs. 0.98), and increase our % Winning Month ratio (66% vs. 65%). As a bonus, we

have further reduced our Maximum Daily Drawdown by 25% (-10.5% from -14.2%) .



9

Opportunities for action

We have demonstrated that over several market cycles a diversified portfolio substantially outperforms an all-equity

portfolio, both in absolute terms and on a risk adjusted basis. The period studied, from 1993 through 2011 is especially

interesting because it includes a record setting equity bull market during the 1990s with a volatile sideways market

through the 2000s.

While the success of the diversified and rebalanced stock and bond portfolio relative to stocks on their own is not a

revelation, many investors might be surprised at just how well this portfolio has done over the past 18 years on both an

absolute and risk adjusted basis. Further, while we would in no way espouse this model as an optimal framework, not

least of which because the stock / bond diversification framework ignores the myriad opportunities available from other

markets and asset classes, this simple portfolio outperformed the average retail investor by 8% per year over the same

period (See Dalbar, 2011).

We also demonstrated the conceptual and empirical validity of implementing portfolio allocations based on a true risk

target that is commensurate with each individual’s risk tolerance, rather than on static asset allocation percentages. In a

traditional SAA approach, a stock/bond allocation is chosen at the inception of the investment process, and the portfolio

is altered at each rebalance date to move it back toward its long-term target allocation. In a risk-optimized framework

however, the allocation to both equities and bonds depends on the relative risk associated with each asset class based

on their relative volatilities at each rebalance date. In this way, portfolio allocations to stocks and bonds will ebb and flow

according to their respective risk, holding aggregate portfolio risk near the initial target over time.

Empirically, this simple technique measurably improved absolute returns, but dramatically improved portfolio efficiency:

Sharpe ratio improved by 35% and Maximum Daily Drawdown was reduced by 80%.

Dovetailing off our introductory discussion on some of the weaknesses with traditional Strategic Asset Allocation, we

introduced the concept of informed bias, and demonstrated how a simple and well-documented momentum-based

informed bias could substantially enhance both absolute, and risk adjusted performance.

In closing, we would assert that Advisors and investors should consider an approach to Strategic Asset Allocation that

incorporates explicit ‘buffers’ which expand and contract allocations to assets when they are volatile so as to keep

aggregate portfolio volatility constant. This approach has merit conceptually, mathematically, and empirically as seen in

the associated tests.

Further, Advisors should incorporate well documented sources of informed bias, such as value, sentiment, breadth,

seasonality, and momentum, to further skew portfolios away from, and toward, asset classes with below average, or

above average prospects respectively. This type of framework should be robust to asset classes, market regimes, and

exogenous shocks, and provide a much more stable return experience for investors.



10

Appendix: The Japanese experience

The Japanese experience since 1993 was dramatically different than the U.S. experience. While U.S. stocks climbed

176% over the past 18 years, Japanese stocks dropped 49% over the same period, which annualizes to losses of

3.47% per year. Of course, Japanese investors endured a seemingly endless series of intermediate term extremes of

hope and despair as markets oscillated wildly above and below their long-term negative trend.

Case 5: Japanese stocks, Buy and Hold


With such a long-term downtrend, even traditional SAA with quarterly rebalancing couldn’t salvage Japanese investor’s

portfolio from near-zero returns, as illustrated in the following Case example. Of course, the 50/50 portfolio did much

better than stocks on their own.



11

Case 6: Japanese 50/50 stock/bond portfolio with quarterly rebalancing


Traditional SAA with rebalancing delivered 1.5% annualized per year in Japan over the past 18 years. What’s worse,

Japanese investors experienced two entire bull/bear cycles over this period where they saw their wealth begin to grow

again only to watch it collapse over and over. This must have been psychologically excruciating.

While a traditional 50/50 allocation with rebalancing struggled to deliver returns (but delivered an abundance of hope and

despair), relative volatility weighting provided investors with tolerable, if not robust, results of 4.4% annualized over the

period, with a reasonable Sharpe ratio of 0.72. Further, the portfolio never experienced a loss greater than 15.44% from

peak to trough.



12

Case 7: Relative Volatility Weighted Rebalancing, 50/50 Japanese stocks / bonds


Not surprisingly, the same ‘informed bias’ momentum strategy applied in the U.S. example above also worked well in

Japan, improving returns by 23% (154% versus 125%), and the Sharpe ratio by almost 10% versus the already impactful

relative volatility SAA approach.



13

Case 8: Relative Vol Rebalanced SAA with Momentum Bias, 50/50 Japanese stocks/bonds


The evidence strongly suggests based on examples from both secular bull and bear markets that volatility adjusted

portfolio rebalancing delivers better and more efficient returns, regardless of the long-term bullish or bearish regime.



14

Butler|Philbrick and Associates*

Adam Butler , CFA, CAIA

Senior Vice President

Portfolio Manager, Investment Advisor

T: 416 572 5477

E: [email protected]

Lee Richards

Associate Investment Advisor

T: 416 572 5479


David Varadi

Investment Services Associate

T: 416 572 5475


Michael Philbrick, CIM, AIF

Senior Vice President

Portfolio Manager, Investment Advisor

T: 416 572 5478


Roxana Mosneagu

Investment Services Associate

T: 416 572 5476


Carmen MacCallum

Investment Services Assistant

T: 416 572 5474


Macquarie Private Wealth Inc.

181 Bay Street, Suite 3200

Brookfield Place

Toronto ON M5J 2T3

TF: 1 866 775 7704

F: 416 864 9888

*Butler|Philbrick and Associates is part of Macquarie Private Wealth Inc.

This material is provided for general information and is not to be construed as an offer or solicitation for the sale or purchase of securities mentioned herein. Past performance maynot be repeated. Every effort has been made to compile this material from reliable sources however no warranty can be made as to its accuracy or completeness. Before acting onany of the above, please seek individual financial advice based on your personal circumstances. However, neither the author nor Macquarie Private Wealth Inc. (MPW) makes anyrepresentation or warranty, expressed or implied, in respect thereof, or takes any responsibility for any errors or omissions which may be contained herein or accepts any liabilitywhatsoever for any loss arising from any use or reliance on this report or its contents.

No entity within the Macquarie Group of Companies is registered as a bank or an authorized foreign bank in Canada under the Bank Act, S.C. 1991, c.46 and no entity within theMacquarie Group of Companies is regulated in Canada as a financial institution, bank holding company or an insurance holding company. Macquarie Bank Limited ABN 46 008 583542 (MBL) is a company incorporated in Australia and authorized under the Banking Act 1959 (Australia) to conduct banking business in Australia. MBL is not authorized to conductbusiness in Canada. No entity within the Macquarie Group of Companies other than MBL is an authorized deposit-taking institution for the purposes of the Banking Act 1959(Australia), and their obligations do not represent deposits or other liabilities of MBL. MBL does not guarantee or otherwise provide assurance in respect of the obligations of anyother Macquarie Group company. Macquarie Private Wealth Inc. is a member of the Canadian Investor Protection Fund and IIROC.

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