The Challenge of Defining Time Horizons

Murali Ramaswami, vice president of risk management services at Bankers Trust, explains how the risk of various assets can dramatically change when viewed through the prism of time perspectives.

On the face of it, defining and holding to an investment time horizon is a no-brainer for a pension fund. By definition, pensions are a long-term investment, so why do anything more than match defined horizons with the liability structure and take the rest of the day off? But in the real world this seeming non-issue is quite complex. It requires a grasp of the underlying dynamics of risk and its tie-ins with the horizon choices managers make.

In plain language, the size and shape of risk can change dramatically when it is measured from investors' varying positions on the time line. Consider the following example.

You are a pension fund manager, trying to assess the risk of holding the S&P 500 index. You are particularly concerned because your board of directors has declared that it wants an appropriate annual volatility figure to attach to this popular, passive investment. Say your investment policy, for the past five years, has been to simply hold the S&P index, and you do not anticipate changing this policy or want to do so. Yet volatility statistics, measured from two different investment horizons, tell two very different risk stories. This may not only confuse the board of directors, but could ultimately force them to change the strategy you think is best. For while the volatility inherent in holding the S&P 500 index for five years at a stretch over the past 35 years would average out to 5.9 percent per year, the same investment held for one year would have produced a much greater volatility of 15.4 percent per year.

Which strategy should the board pick, and why, and how can you, the fund manager, advise them appropriately? That is the question this article will explore. We will then create two "optimal" model portfolios, one for the tactical investor and one for the longer-term, strategic investor.

First of all let's face the fact that while pension funds may be long term in an ideal world, in the real world they must attend to short-term returns and levels of volatility. Why? One, manager performance is typically measured according to yearly, quarterly, sometimes even monthly returns. Naturally these short-term numbers have to be respectable or the pension manager could quickly be out of a job. Two, some funds are underfunded. Since they are strapped to make their payment obligations, they must invest with a significant part of the total portfolio oriented to the short term.

In sum, there are three critical factors which can affect the selection of an investment horizon: 1) asset allocation; 2) risk management; and for pension funds, 3) surplus or non-surplus management issues.

Returns Differ

The institution thus has to chose between a strategic (long-term) or tactical (short-term) investment approach. Not only do long-term versus short-term returns differ significantly for any given asset, but the correlations between the assets themselves can change remarkably as a result of the investment horizon. If left unmonitored, these correlations could get out of hand and undermine the investment strategy.

For example, the U.S. equity market (S&P 500) investment cited above would have fetched an average return of 10.5 percent per year over the past 35 years if held for five years at a time. If held for only a year at a time, the S&P 500 would have earned an average return of 11.15 percent per year.

The correlation between the S&P 500 and the plain vanilla corporate and government bonds frequently found in pension funds also differs depending on the investment horizon. This correlation shrinks from a positive 0.8 to a positive 0.5 when the horizon changes from 10 years to 1 year. In short, over the past three decades, the longer you held blue chip stocks and bonds, the greater the apparent correlation between them.

The distinction between strategic and tactical asset allocation strategies is not perhaps as simple as it seems. For example, there are some extremely well-funded pension funds today that are monitoring returns on a monthly or quarterly basis, changing money managers who do not measure up. Many of them ought to be long-term investors and therefore conducting reviews no more often than annually. "Tactical" behavior carried out by what ought to be a "strategic" plan often carries unperformance penalties for which no amount of "mix and match" of managers can compensate.

The next critical component of a pension's investment horizon is whether its investment strategy more closely resembles rapid "in-and-out" trading or the traditional "buy-and-hold" approach. Trading portfolios are typically characterized by short-duration volatility (i.e. daily or intra-day), making them very sensitive to short-term fluctuations in volatility, so they should be monitored frequently.

The selected investment horizon should impact not only the periodicity of risk calculations but also the volatility measurements used. While traders with rapid investment turnover may wish to focus primarily on the last 20 to 30 days' market performance, perhaps incorporating these numbers into an exponentially weighted average, long-term investors should evaluate volatility of market returns over an investment horizon of 10 years.

Generally speaking, a comfortable surplus means that a fund can adopt a longer-term strategy, because the surplus makes it possible to "ride out" near-term volatility. Conversely, a marginal surplus or deficit coupled with heavy obligations may force management horizons to the near term in response to surplus erosion and/or corporate funding risk. This, ironically, leads to expensive higher transaction costs and volatile shorter holding period and investment-horizon strategies.

Okay, now we come to the nitty-gritty: how a pension fund should construct optimal portfolios to meet short-term and long-term objectives. Consider the following example: using asset return information for stocks (S&P 500), bonds (Lehman government/corporate index) and cash (1-year T-bills) over the last two-and-a-half decades, I have constructed illustrative strategic and tactical asset allocation schemes. The differences in the investment portfolio composition is due to the long-term versus short-term holding period. Optimal portfolio expected returns presume that the past returns of two decades are realized, on average, in the future as well.

Notice how allocation to equity assets increases from 34 to 55 percent as the investment horizon lengthens. This is due to a reduction in the risk (volatility) of equity investments when held over a longer period. Based on the historical returns of the past, a short-term-type asset allocation strategy would have produced poorer returns (10 percent versus 12 percent annualized for the long-term-based strategy) with higher risk (9 percent versus 3 percent annualized for the long-term strategy).

Another practical application of the investment horizon concept lies in the way it forces the updating of outdated investment guidelines. For example, as many firms replace instrument-based guidelines (e.g, triple-A securities, corporate bonds) with risk measurement-based guidelines, they may wish to formulate different risk-based guidelines for money managers with distinct investment horizons.

Clearly, too, the logic of my argument suggests the need for different controls for different types of managers, based on their investment horizons. When measuring a short-term investor's value-at-risk, for instance, it may be appropriate to use a geometrically weighted volatility figure, whereas for a long-term investor an evenly weighted average volatility may provide a more accurate risk measurement.

The growing popularity of 401(k) plans is likely to put a greater focus on investment horizons. Where it is employees who often set their own investment allocations, the administrators of their non-401(k) pensions will have to adjust to the movement of funds from, say, the fixed income portfolio to the equity portfolio, and vice versa. The increased popularity of 401(k) plans is likely to increase the fraction of pension funds devoted to short-term investments because employees will be reviewing returns relatively frequently.