Volatility Harvesting and the Importance Of Rebalancing

We have now written about the importance of observing historical volatility when making rebalancing decisions (see here, here and here) and the importance of keeping portfolio volatility low (see here).  This post will discuss the benefits inherent in volatility itself through the concept of “harvesting” the volatility of individual positions within a portfolio.


We can simplify the idea of volatility harvesting through a thought-experiment developed in the 1940s by Claude Shannon, renowned genius and investor, averaging 28% annually in his lifetime! (Source: W. Poundstone, (2005) Fortune’s Formula). His experiment, known as Shannon’s Demon, showed how it was possible to profit even from markets that were characteristic of a random walk, as long as they were volatile.

The experiment is simple: Imagine a stock that is highly jittery and either doubled or halved in value every day. You then invest half of your portfolio in the stock, while the rest remains in cash. At noon each day you rebalance the portfolio back to a 50-50 even split. So, if you started with $1,000 and the stock got cut in half, the following day your portfolio would be $750 ($250 in the stock $500 in cash). After rebalancing, the portfolio would have $375 in stock and $375 in cash. As the chart below shows that after rebalancing only 72 times our $1,000 initial investment is now worth just under $100,000! That is not a bad chunk of change given that we didn’t have to do any stock forecasting to make this profit! In fact, had you bought and held this stock you would make zero profit.

 Source: Butler|Philbrick|Gordillo and Associates*

    

How can this be? Well, the key is to understand that as long as there’s volatility in at least one of your holdings you will benefit from the most basic of concepts in portfolio theory: Rebalancing.

In the fictitious case above we are looking at a stock that is volatile but has no return. What if we were to do the same experiment and this time use two stocks that have low correlation to each other but both lose money in the long-run? This is exactly what was examined in a recent study done by Dempster, Evstigneev and Schenk-Hoppe in “The Joy of Volatility”. Their experiment assumed that Stock A would either gain +40% or lose -30% at each period and Stock B would either lose -20% or gain +15% at each period (randomly). The results were impressive:

Source: Dempster, Evstigneev and Schenk-Hoppe

The author puts it best by saying that “poverty is the inevitable fate of the passive investor.” However, the active investor achieves certain success through rebalancing.

When applying this to the real world the problem we face is in finding stocks that are actually uncorrelated to one another to that degree. In today’s macro news driven environment we find that most risky assets have become too highly correlated.

So let’s apply this concept to the real world, but instead of stocks let’s use two asset classes we know to generally have low-to-negative correlation to one another: stocks and bonds. Let’s work with the Japanese stock market (Nikkei 225), which has lost -48% since 1995, and combine them with Japanese government bonds. We will rebalance this portfolio quarterly using the dynamic volatility weighting method[i] (click here for a detailed article on this simple concept).

Source: Butler|Philbrick|Gordillo and Associates*, data from Bloomberg

This chart shows how the use of an uncorrelated asset class along with simple rebalancing can make a big impact on anyone’s investment success. The portfolio went from losing -48% and having a peak-to-trough maximum loss of -79% in the Nikkei, to making a profit of +138% and keeping the worst peak-to-though loss at a manageable -13.97%.  Though the result of this two asset class portfolio is impressive, we would in no way espouse this model as an optimal framework not least of which because the stock / bond diversification ignores the myriad of opportunities available from other markets and asset classes (Click here for more detail on how we deal with this).  

The most important point behind these examples is that one doesn’t necessarily have to be right about which stocks, sectors or other asset classes will do well in the future, as long as they all experience bouts of uncertainty (i.e. volatility), they are significantly uncorrelated to each other and you employ an active portfolio approach designed to harvest that uncertainty. The math will take care of the rest.

If you are an avid risk junky and have always thought bonds were for losers, this exercise may be a good way of helping you talk yourself into introducing some cash and bonds into your otherwise risky portfolio. But make sure to always follow the number one rule … don’t forget to rebalance!

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[i] This is important in order to keep the experiment in line with the Dempster study which requires us to keep the bet sizes the same in each rebalancing period. In the example of the two stock portfolio the odds are known in advance and the bet size is always constant. In the real world, bet sizes change with volatility. It is only by controlling the bet sizes through dynamic volatility sizing that we can come as close as possible to the results in the two stock study. Having said this, even if one decides to employ traditional equal dollar rebalancing quarterly we go from losing money in the Nikkei to making a profit of +41% and keeping the drawdown to only -33% (Click here for these results).

Low Volatility as a Fiduciary Duty

Mike Moody, John Lewis and the Dorsey Wright team run a superb shop, and our views overlap about 80% of the time (systematic vs. clinical, anti-forecast, RS, etc.), but I feel compelled to address a recent post on their SystematicRelativeStrength blog (SRS).


The SRS blog took issue with a quote by investment legend and individual investor advocate David Swenson, who has led Yale's endowment fund successfully since 1985. We endorsed his statement yesterday in a post, but here it is again:

“A fiduciary would offer low-volatility funds and encourage investors to stay the course,” he said. “But the for-profit mutual fund industry benefits by offering high-volatility funds.”

SRS was troubled by the assertion that investors are more likely to stick with a low volatility strategy, and used Dalbar's study of investment behaviour to prove their point. Specifically, they noted that historically investors have been no more inclined to hold onto lower volatility bond funds than higher volatility stock funds. From SRS:

"I have a few issues with this. First, the data argues that low-volatility funds are not the answer. If low volatility were the answer, customers would hold their low-volatility bond funds longer than they hold their high-volatility stock funds—but they don’t."

I find this argument disingenuous and logically flawed. For evidence, I have drawn a chart using data from the 2011 Dalbar study (see full study here):

Source: Dalbar (2011)

Note that investors are indeed no more likely to hold onto bond funds than equity funds, with the average holding period for both around 3.2 years or so. However, what the SRS article did not mention (strangely, since they have several asset allocation funds), was that the investors tended to hold asset allocation funds for a full 33% more time than either stock or bond funds on their own. Huh.

The category of Asset Allocation funds is overwhelmingly dominated by balanced funds of stocks and bonds. Investors who allocated capital to asset allocation funds explicitly outsource the asset allocation decision to the fund manager, who they expect will bias the fund toward or away from stocks or bonds as opportunity knocks.

Dorsey Wright manages a Balanced Fund (Arrow DWA Balanced Fund) with annual turnover of 59%, which implies an average holding period of 1.69 years (1/0.59). The highest ranked fund in the U.S. Balanced Fund category, the Intrepid Capital Fund, had an annual turnover of 88%, implying that the fund turns over almost its entire portfolio about once per year (every 1.14 years to be exact).

Does this high turnover mean that these fund managers are trading their portfolio on intuition or emotion? Does it demonstrate a lack of expertise or conviction in their approach? I don't think so. Rather, the managers of these successful funds are moving capital around to take advantage of opportunities they identify, in DWA's case through their proven relative strength system.

Turnover is not a measure of investors' preferences; rather investors prefer the best returns for the lowest risk. Neither stocks nor bonds on their own can deliver this objective because they are much better together than either is on its own. Investors know intuitively that there are times to emphasize bonds and times to emphasize stocks. The less successful ones try to time these changes on their own, and make binary decisions to switch between them, while the successful ones leave the decision to experts who adapt portfolios incrementally over time.

Literature from the institutional space is beginning to identify the power of dynamic asset allocation (DAA). This approach advocates more frequent rebalancing based on changing expected return, volatility and correlation dynamics. This type of strategy often has higher turnover, but can be engineered for quite low volatility. Their objective is to capture a large proportion of upside returns from a diverse set of asset classes, but continuously optimized diversification protects portfolios from major losses. As a result, investors are more likely to stick with these strategies because they experience a steady return trajectory like bonds, but capture substantial equity returns as well.


Low volatility DAA strategies are also highly optimal for retirement outcomes because of the sensitivity of retirement plans to large sustained losses, especially in early years.

In summary, Swenson asserts that investment advisors with their clients' best interests at heart would guide clients toward low volatility strategies, mostly because these strategies are much easier to stick with through thick and thin. We have also shown, counterintuitively, that low volatility strategies may provide stronger absolute returns as a result of their smoother ride. This makes them especially compelling for investors nearing or in retirement, and who wish to maximize retirement spending while sleeping well at night.

We practice what we preach. Find our whitepaper here.

Consulting Behemoth Russell Investments Advocates Volatility Sizing

We published a whitepaper in November that demonstrated the importance of sizing asset class exposures based on volatility that received a lot of attention. It turns out that global investment consultant Russell Investments also advocated for this approach in a recent study targeted at institutional asset allocators.

Their study includes some neat charts that further validate the mechanics of this approach. For example, the success of this approach is based on gambling theory which describes optimal bet sizing. If we assume expected return is either constant or unknowable, but positive, then it is optimal to always bet the same amount. However, markets force most investors to increase and decrease their bet sizes, sometimes dramatically, based on changing volatility. An investor's exposure to risk is much larger when the market's volatility is 30% than when it is 15%, but most investors fail to adjust portfolios for this higher risk.

The charts below illustrate how this plays out in markets. The charts at the top prove that returns in one month have little relationship to returns in the next month (left), but the volatility in the current month does a good job of forecasting the volatility in the subsequent month (right). So adjusting one's exposure based on the most recent month's volatility makes sense.

Source: Russell Investments

Some might argue that higher volatility should equate to higher expected returns, but the chart below invalidates that assumption. There is no relationship between volatility and expected return.

Source: Russell Investments

If higher volatility does not improve expected returns, then we should concern ourselves with optimal bet sizing. By doing so, we substantially improve investment results, especially after accounting for risk.

Source: Butler|Philbrick|Gordillo & Associates, 2012. Results are pro-forma and for illustrative purposes only.

See also:

• Rebalancing resurrected: Japan
• Rebalancing resurrected: Canada
• Rebalancing resurrected

Rebalancing Canada

Prologue: 

This is a 'Canadian-ized' version of an article we published on Monday, December 19, 2011, which featured a study of US equity and fixed-income markets. As we are located in Canada, we were motivated to see how well the same techniques work in our home market using the S&P/TSX Composite.

As expected, it turns out that they work quite well.

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The investment community is in the midst of an identity crisis, though admittedly many in the industry don't know it yet. At the heart of the matter is the following misconception:

Investors perceive that investment professionals add value via security selection and market timing. What's worse, most investment professionals believe that they add value via security selection and market timing. This perception is dangerously misguided.

Repeat after me: Investment professionals add value via asset allocation, not security selection. Again: Investment professionals add value via asset allocation, not security selection.

The following chart is from Pawley (2004) who sourced Brinson, Hood and Beebower (1986) and Simon (1998). The chart contrasts perceived sources of investment value from a large survey of investors with the empirical sources of investment value from the Brinson study. The average investor thinks that their Advisor adds value by picking stocks and bonds; my sense is that the average Advisor thinks that too. The reality however is that a good Advisor adds value by having a system to emphasize stocks versus bonds or cash, and vice versa. That is, a good Advisor adds value through intelligent asset allocation.Click for a larger image

The Brinson study is controversial, mostly because it is improperly cited as validation for pseudo (read false) asset class diversification, such as small-cap versus large-cap, or value versus growth. It is also used to justify Strategic Asset Allocation (SAA) whereby very long-term averages (returns, volatility and correlation) are used to model an 'optimal' allocation to stocks, bonds and cash for each individual based on their risk tolerance. While this justification for SAA makes intuitive sense, we will demonstrate how traditional SAA is a suboptimal diversification approach by every metric except perhaps 'simplicity'. But then, why do you pay your Advisor those big fees?

The Magic of Simple Rebalancing

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 experience many 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.

Let's conceive of a real life example, say a retired couple with just enough money to sustain a reasonable lifestyle assuming that they are able to receive average returns in retirement. These Canadian domestic investors may have been advised to adopt a 50/50 stock/bond Strategic Asset Allocation with quarterly rebalancing. If they had started with this approach in Canada in 1993 (our earliest data), and stuck with the strategy through to the present, their returns would look something like this:

Case 1: 50/50 stock/bond portfolio with quarterly rebalancing
Source: Butler|Philbrick & Associates, Click for a larger image

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 9.89% 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 1.11.
• 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 -25.05%.
• % Winning Months (top right): This is the percentage of months in which the strategy delivered positive absolute returns. This strategy delivered positive returns in 69% of months.

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/TSX Composite 'Buy and Hold'
Source: Butler|Philbrick & Associates, Click for a larger image

Canadian investors have enjoyed two decades of very strong returns, benefitting from the strong U.S. economic expansion of the 1990s and then again from China's decade- long infrastructure boom during the 'aughts' which drove prices for Canada's commodities to record levels.

Over the past 18 years Canadian stocks delivered a remarkable 9.41% per year including reinvested dividends. To compare, Canadian stocks delivered 1.83 percentage points per year more than US stocks, and 12% per year more than Japanese stocks. Of course, investors still had to endure two near 50% drops, and a 6-year period of zero returns (from 1998 through 2003), which would have wreaked havoc on retirement plans. Further, despite the strong overall performance, stocks only delivered positive returns in 74% of 12-month periods — not a very consistent experience.

While a traditional SAA approach definitely improved results over a pure Canadian equity portfolio, we can improve the performance even more by reconsidering how we think about risk.

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 still has some very serious drawbacks.

Let's revisit the true objective of the SAA process: to ensure that an investor achieves the maximum return available at a specified 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) are generally elevated. (See our article Jekyll or Hyde Markets for more on the market's multiple personalities.)

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 we start to experience 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 so that at each rebalance date we reduce relative allocations to stocks or bonds when they exhibit relatively risky behaviour (geek note: based on 60 day trailing volatility), and increase allocations when they exhibit low relative risk, we can achieve a much more efficient portfolio, again just with stocks and bonds:

Case 3: SAA with Dynamic Volatility Weighted Rebalancing, 50/50 stocks/bonds
Source: Butler|Philbrick & Associates, Click for a larger image

Note that the objective of this portfolio is to keep the risk stable 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 risk allocation.

It will come as no surprise by now that the volatility weighted rebalancing framework performs much better than the traditional 50/50 approach. Indeed, the relative volatility approach delivered 10.28% annualized returns, maximum drawdown of just 15.3%, and 90% positive rolling 12-month periods. In fact, this simple approach produced a Sharpe ratio over 1.5!

Not bad for a simple and intuitive twist on an old idea. The following chart draws on US data to illustrate how this approach also exposes an investor to a much more consistent portfolio experience as the grey line in the chart below (relative volatility weighted portfolio) tracks well below the black line (SAA 50/50) for most of the past 18 years, indicating much lower and more consistent volatility for the investor. The blue line is beyond the scope of this article, but suffice to say that by explicitly holding risk constant by systematically adding cash, portfolio risk and return characteristics can be improved even more dramatically.

Source: Butler|Philbrick & Associates, Click for a larger image

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 two record-setting equity bull markets during the 1990s and 2000s, interspersed with two intense bear markets in 2001-2003, and 2008.

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 Strategic 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 36% and Maximum Daily Drawdown was reduced by 65%.

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. 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.

Rebalancing Japan

Prologue:
This is a 'Japan-amized' version of an article we published on Monday, December 19, 2011, which featured a study of US equity and fixed-income markets. The Japanese experience since 1993 was dramatically different than the U.S. experience. While U.S. stocks climbed 267% over the past 18 years, Japanese stocks dropped 48% over the same period, which annualizes to losses of 3.43% 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. Japan's multi-decade crash and stagnation is unique among modern market economies (so far), so we wanted to see how well our volatility adjusted rebalancing framework worked in this difficult environment.

The results are even better than we had any right to expect, which gives us some hope for investors over what we forecast to be a very difficult decade for equities going forward.

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The investment community is in the midst of an identity crisis, though admittedly many in the industry don't know it yet. At the heart of the matter is the following misconception:

Investors perceive that investment professionals add value via security selection and market timing. What's worse, most investment professionals believe that they add value via security selection and market timing. This perception is dangerously misguided.

Repeat after me: Investment professionals add value via asset allocation, not security selection. Again: Investment professionals add value via asset allocation, not security selection.


The following chart is from Pawley (2004) who sourced Brinson, Hood and Beebower (1986) and Simon (1998). The chart contrasts perceived sources of investment value from a large survey of investors with the empirical sources of investment value from the Brinson study. The average investor thinks that their Advisor adds value by picking stocks and bonds; my sense is that the average Advisor thinks that too. The reality however is that a good Advisor adds value by having a system to emphasize stocks versus bonds or cash, and vice versa. That is, a good Advisor adds value through intelligent asset allocation.

Click for a larger image


The Brinson study is controversial, mostly because it is improperly cited as validation for pseudo (read false) asset class diversification, such as small-cap versus large-cap, or value versus growth. It is also used to justify Strategic Asset Allocation (SAA) whereby very long-term averages (returns, volatility and correlation) are used to model an 'optimal' allocation to stocks, bonds and cash for each individual based on their risk tolerance. While this justification for SAA makes intuitive sense, we will demonstrate how traditional SAA is a suboptimal diversification approach by every metric except perhaps 'simplicity'. But then, why do you pay your Advisor those big fees?


The Magic of Simple Rebalancing


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 experience many 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.

Let's conceive of a real life example, say a retired couple with just enough money to sustain a reasonable lifestyle assuming that they are able to receive average returns in retirement. These Japanese domestic investors may have been advised to adopt a 50/50 stock/bond Strategic Asset Allocation with quarterly rebalancing. If they had started with this approach in Japan in 1993 (our earliest data), and stuck with the strategy through to the present, their returns would look something like this:

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

Source: Butler|Philbrick & Associates, Click for a larger image


With such a long-term downtrend, even traditional SAA with quarterly rebalancing couldn't salvage a Japanese investor's portfolio from near-zero returns, as illustrated in the following equity-only example.

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 1.84% 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 0.16.
• 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 -33.6%.
• % Winning Months (top right): This is the percentage of months in which the strategy delivered positive absolute returns. This strategy delivered positive returns in 55% of months.

Of course, the 50/50 portfolio did much better than stocks on their own. Let's contrast the performance of the traditional 50/50 SAA portfolio with the return to a 100% stock portfolio over the same time frame:

Case 2. Nikkei 'Buy and Hold'

Source: Butler|Philbrick & Associates, Click for a larger image


Over the past 18 years Japanese stocks delivered a truly dismal -3.43% per year including reinvested dividends for a total aggregate loss to investors of 48% top date. To compare, US stocks delivered 11 percentage points per year more than Japanese stocks.


While a traditional SAA approach definitely improved results over a pure Japanese equity portfolio, it probably didn't serve as much comfort to Japanese investors.

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 still has some very serious drawbacks.

Let's revisit the true objective of the SAA process: to ensure that an investor achieves the maximum return available at a specified 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) are generally elevated. (See our article Jekyll or Hyde Markets for more on the market's multiple personalities.)

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 we start to experience 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 so that at each rebalance date we reduce relative allocations to stocks or bonds when they exhibit relatively risky behaviour (geek note: based on 60 day trailing volatility), and increase allocations when they exhibit low relative risk, we can achieve a much more efficient portfolio, again just with stocks and bonds:

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

Source: Butler|Philbrick & Associates, Click for a larger image


Note that the objective of this portfolio is to keep the risk stable 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 risk allocation.

While a traditional 50/50 allocation with rebalancing struggled to deliver returns (but delivered an abundance of hope and despair), relative volatility weighting between stocks and bonds provided investors with tolerable, if not robust, results of 4.71% annualized over the period, with a very respectable Sharpe ratio of 0.78. Further, the portfolio never experienced a loss greater than 14% from peak to trough, less than half the drawdown experienced by a traditional balanced portfolio.

Not bad for a simple and intuitive twist on an old idea. The following chart uses US data to illustrate how a volatility based approach also exposes investors to a much more consistent portfolio experience as the grey line in the chart below (relative volatility weighted portfolio) tracks well below the black line (SAA 50/50) for most of the past 18 years, indicating much lower and more consistent volatility for the investor. The blue line is beyond the scope of this article, but suffice to say that by explicitly holding risk constant by systematically adding cash, portfolio risk and return characteristics can be improved even more dramatically, even in Japan!

Source: Butler|Philbrick & Associates, Click for a larger image


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 long-term secular bear market with several bull-market episodes.

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, it is much better than typical 'Aggressive' all-equity allocations.



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 Strategic 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 substantially improved absolute returns, but also dramatically improved portfolio efficiency: in the Japanese study above, the Sharpe ratio improved by 700% and Maximum Daily Drawdown was reduced by 240% over traditional SAA.

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. 


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.

Rebalancing Resurrected

The investment community is in the midst of an identity crisis, though admittedly many in the industry don’t know it yet. At the heart of the matter is the following misconception:

Investors perceive that investment professionals add value via security selection and market timing. What’s worse, most investment professionals believe that they add value via security selection and market timing. This perception is dangerously misguided.

Repeat after me: Investment professionals add value via asset allocation, not security selection. Again: Investment professionals add value via asset allocation, not security selection.
The following chart is from Pawley (2004) who sourced Brinson, Hood and Beebower (1986) and Simon (1998). The chart contrasts perceived sources of investment value from a large survey of investors with the empirical sources of investment value from the Brinson study. The average investor thinks that their Advisor adds value by picking stocks and bonds; my sense is that the average Advisor thinks that too. The reality however is that a good Advisor adds value by having a system to emphasize stocks versus bonds or cash, and vice versa.

Click chart for a bigger version.
The Brinson study is controversial, mostly because it is improperly cited as validation for pseudo (read false) asset class diversification, such as small-cap versus large-cap, or value versus growth. It is also used to justify Strategic Asset Allocation (SAA) whereby very long-term averages (returns, volatility and correlation) are used to model an ‘optimal’ allocation to stocks, bonds and cash for each individual based on their risk tolerance. While this justification for SAA makes intuitive sense, we will demonstrate how traditional SAA is a suboptimal diversification approach by every metric except perhaps 'simplicity'. But then, why do you pay your Advisor those big fees?
The Magic of Simple Rebalancing

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 experience many 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.
 
Let’s conceive of a real life example, say a retired couple with just enough money to sustain a reasonably lifestyle assuming that they are able to receive average returns in retirement. This investor may be advised to adopt a 50/50 stock/bond Strategic Asset Allocation with quarterly rebalancing. If they had started with this approach in mid-1994 (our earliest data), and stuck with the strategy through to the present, their returns would look something like this:
Case 1: 50/50 stock/bond portfolio with quarterly rebalancing

Click chart for a bigger version. Source: Butler|Philbrick & 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 8.54% 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 0.84.
• 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 -24.33%.
• % 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.

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’

Click chart for a bigger version. Source: Butler|Philbrick & Associates.

Note that stocks alone over this period delivered 7.58% annualized returns, with a Sharpe ratio of 0.37, a Max Daily Drawdown of 55% (!!), and delivered positive returns in 61% of months.
This means a simple SAA portfolio with 50/50 stocks/bonds delivered 24% more total growth (330% vs. 267%), with twice the efficiency (Sharpe ratio of 0.73 vs. 0.37), half the investor anxiety (Max Daily Drawdown -24% vs. -55%), and more winning months (66% vs. 61%).
These are actually pretty good stats, but SAA only scratches the surface of what is possible with more thoughtful asset allocation techniques.
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 still has some very serious drawbacks.
Let's revisit the true objective of the SAA process: to ensure that an investor achieves the maximum return available at a specified 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) are generally elevated. (See our article Jekyll or Hyde Markets for more on the market's multiple personalities.)
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 we start to experience 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 so that at each rebalance date we reduce relative allocations to stocks or bonds when they exhibit relatively risky behaviour (geek note: based on 60 day trailing volatility), and increase allocations when they exhibit low relative risk, we can achieve a much more efficient portfolio, again just with stocks and bonds:
Case 3: SAA with Dynamic Volatility Weighted Rebalancing, 50/50 stocks/bonds

Click chart for a bigger version. Source: Butler|Philbrick & Associates.

Note that the objective of this portfolio is to keep the risk stable 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 risk allocation.
This approach delivers much more efficient performance than the traditional SAA approach. While the annualized returns to this strategy improve by just 0.15% per year, the real benefit is clear from the risk metrics.
The Sharpe ratio for this approach is 0.99, which represents 18% greater efficiency than traditional SAA, and 300% more efficiency than a pure stock portfolio. Of even greater interest for most investors, the Maximum Daily Drawdown drops to 17% from 24% for traditional SAA and 55% for stocks, an improvement of 40% and 300% respectively.
Not bad for a simple and intuitive twist on an old idea. The following chart shows how this approach also exposes an investor to a much more consistent portfolio experience as the grey line in the chart below (relative volatility weighted portfolio) tracks well below the black line (SAA 50/50) for most of the past 18 years, indicating much lower and more consistent volatility for the investor. The blue line is beyond the scope of this article, but suffice to say that by explicitly holding risk constant by systematically adding cash, portfolio risk and return characteristics can be improved even more dramatically.

Click chart for a bigger version. Source: Butler|Philbrick & Associates. 

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 1994 through 2011 is especially interesting because it includes a record setting equity bull market during the 1990s and 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 Strategic 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 18% and Maximum Daily Drawdown was reduced by 40%.

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. 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.
Adam Butler and Mike Philbrick are Portfolio Managers with Butler|Philbrick & Associates at Macquarie Private Wealth in Toronto, Canada.