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.