Taking LDI To the Next Level

Welcome back stochastic life-cycle management.

October 20, 2010

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59943_boomerangIn the beginning, there was stock selection. And value was added. But lo, there were risks in the land and clients did gnash their teeth. The Nobellists prophesied asset allocation and diversification across risky and risk-free assets. And more value was added. But lo, there were more risks in the land, and clients did gnash their teeth anew. The academics besought themselves of portfolio construction. Even more value could be added — before clients sought dentures.

Or to put this in a modern-day narrative, “For more than fifty years, the industry has in fact focused mostly on security selection as a single source of added value. This focus has somewhat distracted the industry from another key source of added value, namely, portfolio construction and asset allocation decisions.”

Now it’s about portfolio solutions, write Noël Amenc, Lionel Martellini, Felix Goltz and Vincent Milhau, researchers at the EDHEC Risk Institute, in their paper “New Frontiers in Benchmarking and Liability-Driven Investing. Portfolio solutions mean a greater emphasis on risk management, which in turn bifurcates portfolio construction.

“These solutions involve, on the one hand, the design of a customised liability-hedging portfolio (LHP), the sole purpose of which is to hedge away as effectively as possible the impact of unexpected changes in risk factors affecting liability values (most notably interest rate and inflation risks), and, on the other hand, the design of a performance-seeking portfolio (PSP), whose raison d’être is to provide investors an optimal risk/return trade-off.”

Let’s start with the PSP. Cap-weighted benchmarks don’t work. They aren’t efficient at capturing the optimal risk/reward trade-off. That’s because of a variety of heroic assumptions built into William Sharpe’s Capital Asset Pricing Model, among them: unlimited short-selling, uniform investment horizons and no tax friction. In the real world, these reduce the Sharpe ratio.

Beyond that, investors aren’t buying the theoretical market portfolio, the authors assert. They’re looking for a positively skewed, low kurtotic returns – no fat tails, no surprises, just steady returns, And they are willing to accept a lower expected return – albeit with a higher Sharpe ratio.

“Investors, of course, would prefer high weights in stocks that contribute positively to the portfolio’s Sharpe ratio and low weights in stocks that contribute less to increasing the Sharpe ratio,” Armenc and colleagues write. So that’s the PSP optimization problem.

Then comes part two: the liabilities they are trying to match. “Risk diversification is only one possible form of risk management. … In particular, it is clear that the risk factors impacting pension liability values should be hedged rather than diversified away.”

Unfortunately, the putative liability-hedging portfolio – real return bonds or inflation swaps —  isn’t a very efficient or optimal hedge, they argue.

“Such solutions generate very modest performance given that real returns on inflation-protected securities, negatively impacted by the presence of a significant inflation risk premium, are usually very low. In this context, it has been argued that some other asset classes, such as stocks, real estate, or commodities, could provide useful inflation protection, especially when long-term horizons are considered, at a cost lower than that of investing in TIPS.”

Thus, it seems, the two portfolios, the PSP and the LHP, are not terribly different in composition, even if they are managed to different objectives.

But these two objectives cannot be met in isolation. Instead, they have to combine: “allocation decisions involved in the design of the performance-seeking or the liability-hedging portfolio (design of better building blocks, or BBBs), and asset allocation decisions involved in the optimal split between the PSP and the LHP (design of advanced asset allocation decisions, or AAAs).”

The result, which the authors use in the context of target-date funds, is that:  “a sound investment solution involves a dynamic asset allocation strategy that takes into account (i) the stochastic features of the investor’s lifetime income progression (where is the money coming from), (ii) the stochastic features of the investor’s expected pension value (what the money is going to be used for), and (iii) the stochastic features of the assets held in his portfolio.”

And lo, the shepherds were beckoned to welcome stochastic life-cycle management into their herding tools.

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