Too many pension fund portfolios get cluttered up with unwanted exposures. Optimal rebalancing offers a way for asset owners to get back to strategic asset allocation weights in a highly cost-effective way. Andrew Capon and Sébastien Page explain how it works

One of the best known verses of the much loved American children's poet Shel Silverstein concerns the fate of Sarah Cynthia Sylvia Stout. It is a morality tale. Her crime is that she never takes the garbage out and is therefore condemned to live in ever increasing squalor until it finally overwhelms her. For asset owners content to let their portfolios drift with the ebb and flow of markets it also offers a warning.

The process by which asset owners decide their strategic asset allocation policy is perhaps the most time consuming and intellectually challenging of all the many judgments that they have to make. Assets and liabilities are carefully weighed. Actuarial assumptions are agonised over. Even small changes may take many months of painstaking work.

Unfortunately, as soon as the theoretically perfect asset allocation mix is implemented, the real world rudely intervenes. Weights drift as the prices of the underlying securities change at different speeds. These overweight and underweight positions in certain assets are akin to garbage cluttering up the portfolio. They are unwanted exposures as they are at odds with the pristine, carefully thought through asset allocation policy.

These rapidly accumulating unwanted exposures are often simply ignored. Many investors have taken the view that these variances wash out in the long run. The folly of this stance is illustrated in the graph. A fund with a 60/40 stock/bond allocation split starting in September 1996 would have seen its commitment to equities rise to 72% at the peak of the TMT bubble in March 2000.

That over-allocation to equities would have only corrected itself by early 2004, by which time a €10bn fund would have lost €1.3bn as a result of this unwanted equity exposure. This big hit was entirely avoidable. All that the pension fund needed to do was to clean its house and get the asset allocation mix back to the original strategic policy.

Part of the reluctance of many asset owners to rebalance may reflect the paucity of current approaches. The most common method is calendar-based, rebalancing the portfolio at set intervals such as quarterly or half-yearly. This is not optimal. It may compel the fund to rebalance the portfolio and incur trading costs when the weights have drifted very little.

Another approach is to set tolerance bands. This might prompt a rebalancing if, for example, the equity allocation rises more than 5% above the policy weight. Though superficially more sophisticated than simply looking at the calendar it is also sub-optimal. What matters is not the drift away from the policy weight of one asset class, rather how all of the asset classes in the overall portfolio have moved relative to each other.

Optimal rebalancing is a huge advance on current practice. It offers the best trade-off between the cost of rebalancing and the impact of tracking error. Unlike the simple, mechanistic approaches most frequently used, it addresses the fact that current decisions impact on future decisions and costs by using a multi-period optimisation. This process generates rebalancing rules and a ‘roadmap', which specify the optimal decisions in the case of any deviation from the target asset mix.

 

he decision on whether to trade back to target weights, trade some of the way or not trade at all, over multiple time-periods for large number of assets is a far from trivial undertaking. This problem was posed by Mark Kritzman, founding partner of State Street Associates, to his students taking the graduate course on Financial Engineering at the MIT. They came up with a dynamic programming solution .

Though a good theoretical solution, it is not possible given the constraint of current computing power to implement it for more than a handful of assets. For example, a portfolio of only 10 assets requires calculations that sum to 29 digits. A typical computer workstation would be calculating the optimal solution for more than 12,000 times the age of the universe.

In reality, most institutional portfolios contain many hundreds of assets. When the paper on dynamic programming was published in 2006, Harry Markowitz suggested adapting a heuristic he had designed to account for changing returns. This heuristic is basically a sampling device, which dramatically cuts down the number of calculations required to reach an optimal solution . However, even this approach requires the power of grid computing.

In extensive back-testing the heuristic was shown to improve performance relative to the dynamic programming solution as more assets are added. It is the best method by far for optimally rebalancing portfolios of more than a few assets. The cost savings that can be achieved are impressive. For example, simulations suggest that a €5bn fund with 100 assets rebalancing on a calendar basis once every six months would save €4.5m annually using optimal rebalancing.

Optimal rebalancing can be customised to investors' tracking error target, cash inflows, benefit payments, and maximum allowed deviations. It is also possible for an asset owner to entirely outsource the operational burden of maintaining their strategic asset mix to a provider acting as a fiduciary. The provider would monitor positions, equitise cash and trade futures, transition assets when necessary, keep track of costs and tracking error, and provide the investor with regular reporting.

Optimal rebalancing is a spring cleaning service for portfolios. It allows asset owners to stay close to their policy asset allocation weights by using a rebalancing methodology that is quantitatively rigorous, rather than the naïve approaches currently used.

Sarah Cynthia Sylvia Stout eventually succumbs to: "Pizza crusts and withered greens, Soggy beans and tangerines, Crusts of black burned buttered toast, Gristly bits of beefy roasts."

Your portfolio does not need to suffer a similar fate.

Andrew Capon is editor-in-chief at State Street Global Markets Research in London. Sébastien Page is head of the portfolio and risk management research team at State Street Associates in Cambridge, Massachusetts

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