Friday, June 15, 2012

Adaptive Asset Allocation for a Regime Agnostic 'Balanced Fund'

Risk Parity: Past its Prime
This is a follow-on to our research on Adaptive Asset Allocation

Our last article described an Adaptive Risk Parity (ARP) framework for a stock/bond balanced allocation, and discussed the advantages and risks relative to traditional 60/40 approach. While ARP makes intuitive, logical and empirical sense as an allocation framework, there are long-term risks to this approach related to asset class regimes.

Stocks, bonds and other asset classes generally move through long periods of high total return followed by long-periods of low total return. While there is more contention about where we are in the long-term stock cycle, there can be little debate about whether we are closer to the end or the beginning of the long-term interest rate cycle.

The chart below from Mebane Faber's great new(ish) series on Risk Parity demonstrates the long-term efficacy of a static version of the approach for a portfolio of stocks and bonds using long-term relative stock and bond volatility for allocations, and targeting the same long-term volatility as the 60/40 portfolio (10.44%). Notice that to achieve the same level of risk as a 60/40 portfolio, the risk parity portfolio must be levered by 160%.

Chart 1. Long-term risk parity with S&P 500 and 10-Year Treasuries, 1972 - 2012

Source: Mabane Faber, 2012

While the performance of the static risk parity approach is better over the full period, Faber points out that the relative out-performance is sensitive to the start and end dates of the observation period. If we go back in time to mid 2000 and observe the relative performance over the first 28 years, we may have drawn a different conclusion.

Chart 2. Long-term risk parity with S&P 500 and 10-Year Treasuries, 1972 - 2000
Source: Mabane Faber, 2012

So what happened during the last decade to create such a massive disparity in returns? The next chart offers a clue: it plots the progression of interest rates since 2000.

Chart 3. 10-Year Treasury yield, 2000 - 2012
 Source: FRED database

Clearly this has been an exceptional period for interest rates, as they have dropped by over 70% over the past 12 years, delivering almost 7.6% in total returns per year, compared with 0.80% per year for stocks.

The question is, with interest rates at or very near historic lows, and the relative return differential between risk parity and more traditional approaches at an all-time high, should we expect this approach to continue to dominate other approaches going forward? Or should we acknowledge that the best days for risk parity are probably behind us - and adapt?

Adaptive Asset Allocation (AAA)

In this article we will apply the integrated AAA approach described in our whitepaper to a more traditional stock and bond portfolio to create a resilient 'balanced fund' that is immune to the interest rate bias that represents the Achilles Heel of risk parity.

AAA uses estimates of returns, volatility and correlation for assets in a portfolio based on recently observed measures of these parameters, rather than long-term averages. These estimates are then integrated using a robust mean-variance optimization algorithm analogous to the equations described under the banner of Modern Portfolio Theory.

Estimates for returns and correlations are drawn from time series for each asset over a 6-month look-back horizon, while volatility is measured over a shorter 60 day horizon. Further, portfolio level volatility at each rebalance period is managed to a 10% target. Depending on the measured volatility of the assets, and the correlation between them, at each rebalance period, cash or leverage may be required to reach the volatility target. No yield on cash or cost of leverage is included for this illustration.

Chart 4. Adaptive Asset Allocation balanced portfolio, rebalanced monthly, 1995 - May 31, 2012
Max 200% exposure
Source: Data from Yahoo Finance

For those with no tolerance for leverage or margin, here is a version of the AAA approach with a maximum 100% portfolio exposure.

Chart 5. Adaptive Asset Allocation balanced portfolio, rebalanced monthly, 1995 - May 31, 2012
Max 100% exposure
Source: Data from Yahoo Finance

You can see that the Adaptive Asset Allocation framework described in our whitepaper applies quite well to a typical balanced portfolio of stocks and bonds. To illustrate the adaptive nature of the program, the diagram below illustrates how the portfolio adapts its allocations over time based on changing momentum, volatility and correlation dynamics.

You can see that the starting allocation for June would have been 53.72% in stocks and 46.28% in bonds.

Chart 6. Adaptive Asset Allocation balanced portfolio, historical allocations, Aug 31, 2011 - May 31, 1012. Max 100% exposure.
Source: Data from Yahoo Finance

Notice how during late 2011's extreme market behaviour, the AAA balanced portfolio dramatically reduced exposure to both stocks and bonds, lowering equity allocation to 11% and Treasury allocations to 39% at the end of September, with the balance in a 50% cash allocation. This was necessary to maintain the target 10% portfolio volatility during a period where the observed volatility was much too high. 

Also notice that, for the most part, the allocations do not stray too far from the Investment Policy Statement (IPS) guidelines for a typical balanced investor. Where deviations do occur, they are usually biased toward too much cash, and rarely last more than a month or two except during extreme situations like 2008.

Fortunately, many IPSs have enough flexibility in their guidelines to to allow for deviations from stated benchmarks over periods up to 3 months, and longer deviations are allowed with appropriate client consultation.

As a result, while portfolio flexibility is an important and central element of the AAA framework, the examples above demonstrate that it is constrained enough to make it a compelling and comprehensive alternative for traditional balanced clients.


The November article 'Rebalancing Resurrected' introduced the concept of weighting portfolio allocations based on relative volatility rather than as a set portion of capital. It was shown that relative volatility sizing delivered a substantial improvement to risk-adjusted returns without sacrificing absolute returns.

The prior article on Adaptive Risk Parity was a natural extension to a volatility sizing approach because it applies the same math to allocate between the assets based on volatility, but then overlays a risk budget at the portfolio level. The ARP approach further improved risk adjusted performance with consistent absolute performance.

Further, by allowing the portfolio to take on a limited amount of leverage at times of low asset level volatility and/or very low asset correlations in order to achieve the target risk budget, the ARP portfolio delivered a 27% improvement in absolute returns with the same level of portfolio volatility as the traditional balanced portfolio.

Finally, in acknowledgment of the primary flaw in the usual risk parity approach - the structural overweight to fixed income - we applied an Adaptive Asset Allocation framework that applied better estimates of return, volatility and correlation to create rolling optimal portfolios. This framework delivered performance consistent with the ARP approach, but because it is guided by asset class momentum as well as relative volatility and correlations, it is robust to structural shifts in interest rate regimes.

Investors are looking for robust, adaptive investment solutions to manage indelible liabilities like funding objectives or retirements. Traditional SAA and endowment model 60/40 portfolios are vulnerable to long-term shifts in return, volatility and correlation regimes across asset classes. This risk is especially acute with interest rates at historic lows.

The Adaptive Asset Allocation framework offers a working solution for investors that provides strong returns with managed risk, a combination that substantially and positively skews the probability of success for investors, regardless of market outcomes.

Wednesday, June 6, 2012

Adaptive Risk Parity for a Better 'Balanced Fund'

Rebalancing Revisited

Back in November of 2011 we published our first article introducing the concept of volatility sizing for asset allocation within a stock and bond portfolio as an alternative to traditional static capital weightings, such as 60/40. The volatility sizing technique produced an 18% improvement in risk-adjusted performance, including a 30% reduction in peak-to-trough drawdown.

More recently, we integrated volatility related ideas from the original article along with concepts related to momentum, correlation, and the architecture of Modern Portfolio Theory, to introduce a novel Adaptive Asset Allocation framework (expanded whitepaper here) for a broad basket of global asset classes.

In this article we revert our focus back to stocks and bonds. Specifically, we will demonstrate how to create a more optimal 'balanced fund' using ETFs tracking the S&P 500 and long-term Treasuries by applying a strategy we call Active Risk Parity (ARP). This approach borrows heavily from the literature related to standard risk parity, but overlays active volatility management both at the individual asset class level, and the portfolio level, to achieve a 27% improvement in absolute returns, and a 29% improvement in risk-adjusted performance, relative to a traditional balanced portfolio.

Recall that the difference between the previously described volatility weighted approach and a typical balanced approach, is that rather than allocating equal portions of capital to assets in a portfolio, the volatility weighted portfolio allocates equal portions of risk, as measured by recently observed volatility.

To illustrate this concept consider the following chart, which captures the relative contribution of portfolio volatility from stocks versus bonds in a typical 60/40 balanced portfolio.

Chart 1. Marginal risk contribution: 60/40 portfolio of U.S. stocks vs. Treasuries, 1995 - 2012
Source: Data from Yahoo Finance

The blue area reflects the proportion of portfolio volatility attributable to the 60% stock allocation, while the red area indicates the proportion contributed by the 40% Treasury allocation. Note that while the capital is allocated 60/40 to stocks and bonds respectively, the risk is actually allocated about 80/20. This reality is lost on most investors, including most investment managers, despite the hard lessons learned during recent bear market periods.

The volatility weighting framework allocates capital to assets at each rebalance period such that each asset class contributes an equal amount of risk to the portfolio rather than a set proportion of capital. In our November article we compared the performance of a traditional 50/50 capital allocated approach to the performance of a volatility weighted approach using data for stocks and Treasuries going back to 1995. The following charts update the performance of these two mandates through the close of trading on May 31, 2012.

Chart 2. Equal weight portfolio of stocks and bonds, rebalanced quarterly, Jan 1995 - May 2012
Source: Data from Yahoo Finance

Chart 3. Equal volatility weighted portfolio of stocks and bonds, rebalanced quarterly, Jan 1995 - May 2012
Source: Data from Yahoo Finance

The relative volatility weighted portfolio delivers better risk adjusted, and absolute, performance than the traditional 50/50 portfolio. Further, in two other prior articles we demonstrated that this approach to asset allocation is equally robust for Canadian and Japanese balanced portfolios as well.

Given that asset allocation is improved by focusing on proportional risk rather than proportional capital, we are ready to explore a more robust application of this concept.

Active Risk Parity

The volatility weighting approach described above ensures that the volatility contributions of stocks and bonds are equal in a fully invested portfolio. While this approach promises a much more stable return distribution than the traditional 50/50 capital allocation framework, it is still vulnerable to short- and intermediate-term changes in asset correlations which impacts total risk at the portfolio level.

Recall that portfolio volatility is impacted by the volatilities of the individual assets AND the correlation between those assets. For example, if we assume two assets have the same volatility, then the following chart quantifies the change in portfolio level volatility as a function of the change in correlation between the assets based on Markowitz' famous equation.

In contrast, in a Risk Parity framework once the assets have been risk-weighted within the portfolio, the portfolio itself is then levered or de-levered to achieve a desired target for portfolio volatility. The math for volatility targeting is simply:  

target volatility
observed volatility

For example, a Risk Parity investor targeting a 10% risk budget for a portfolio with observed volatility of 8% would allocate 10% / 8% = 125% to the portfolio, which would require 25% leverage. 

Typically, Risk Parity suffers from the same issues as Strategic Asset Allocation related to the fact that the guiding assumptions for the volatility and correlation inputs to the portfolio optimization are derived from long-term average values. We have published several research pieces (here) discussing the dangers of using long-term average values for portfolio inputs, so we will avoid that error here. Rather, we will use 60 day rolling measures of volatility and correlation for allocation decisions at each rebalance period. 

For the purpose of this article we have coined a new term, Active Risk Parity (ARP), which captures the risk parity concept but applies better portfolio optimization estimates based on near-term observed values.  The following ARP performance chart uses a 60 day trailing observation period to allocate  at each rebalance period, and to also target a 10% portfolio volatility, rebalanced quarterly. In an effort to keep leverage to manageable levels, maximum portfolio exposure has been limited to 200%, which is practical for typical margin accounts. Note that we have assumed no yield on cash nor costs associated with the use of leverage for this illustration.

Chart 4. Active Risk Parity balanced portfolio, rebalanced quarterly, 1995 - May 31, 2012
Max 200% exposure
Source: Data from Yahoo Finance

For investors with no tolerance for margin or leverage, the following chart updates the ARP portfolio   assuming a maximum of 100% exposure.

Chart 5. Active Risk Parity balanced portfolio, rebalanced quarterly, 1995 - May 31, 2012
Max 100% exposure
Source: Data from Yahoo Finance

Risk Parity, and ARP in particular have significant advantages over a typical asset allocation framework. Obviously, risk adjusted performance is improved substantially in terms of both average portfolio volatility and drawdowns. In addition, absolute performance is consistent with no leverage, and about 27% higher with leverage, at a similar average level of volatility.

Some Challenges

However, Risk Parity skeptics have long complained that the success of the approach can largely be attributed to the much higher relative allocation to fixed income over a testing period where interest rates have steadily declined. Bonds are structurally much less volatile than stocks, and so command a much higher allocation in a Risk Parity framework on average relative to a typical balanced approach. Obviously during a period of steadily declining rates a risk parity portfolio will have an advantage.

But what happens to a risk parity approach when, inevitably, rates start to rise again. Should bonds continue to maintain such a perpetually overweighted position in portfolios when long-term Treasuries promise yields of less than 3% for the next 30 years?

We feel this is a valid point. Obviously, return estimates need to be factored into the portfolio optimization somehow. However, we don't accept that this argument suggests that investors should move away from risk parity back toward the traditional Strategic Asset Allocation approach.

The next article will apply our Adaptive Asset Allocation framework to improve on the ARP approach by introducing a return estimate. This will short-circuit the fixed income conundrum so that balanced investors have a chance to capture a larger proportion of returns to stocks as rates normalize.