Research

Financial simulation

Anyone who has invested on the sharemarket knows there are no guarantees about future returns. The rapid turnover of the top 20 stocks by market capitalisation year in, year out, is evidence enough of this truism. That said investors must have a process by which they can "reliably" attempt to predict future returns. While many factors are involved, two are fundamental: evaluating past returns to determine any trends and how they interrelate and then selecting a simulation method to use these past trends to predict future returns. There are two simulation methods used to estimate future returns - historical or Monte Carlo. This report, a summary of a detailed Vanguard paper on the issue, examines the pluses and minuses of historical and Monte Carlo stimulation.

Defining historical and Monte Carlo stimulation

Historical: Predicts future returns by assuming past events will occur again in some chronological order. It also assumes that potential changes to an asset's future return will not exceed past changes over a set period.

Monte Carlo: Similar to historical, Monte Carlo (yes, its name does come from that famous principality known for its casinos in southern France) relies on historical data to predict an asset's future return. But it rejects the assumption that the past represents the full range of future returns. Instead, the computer randomly selects annual returns based on certain statistical guidelines. This process is then repeated over and over to give a range of possible outcomes for an asset's future return.

Timeframe

Data collected over a long period improves the likelihood of improving the "results" because there is a fundamental relationship between investment returns and the broader economy. But how long is long? Analysts argue 30 years provides data over several economic cycles (cycles have historically lasted between five and six years) and as such captures key macro-economic events as sharemarket crashes and recessions. (Australia between 1974 and 2004 had two bull markets (and crashes), two property booms (and one crash), widely fluctuating interest rates and inflation, two oil price shocks and two recessions (the second 1990-92 the worst since the Great Depression) But even a 30-year cycle comes with certain caveats. First, huge political or economic structural change might exclude a certain period (ie. war or revolution). Second, the actual data over the 30 years might be inadequate.

Historical simulation methods

Three methods fall under the umbrella of historical simulation. They are:

• Looping time-path analysis: Assumes clients begin investing at a certain time (eg. 1960) and do not make withdrawals. It then applies the asset/assets' returns for each subsequent year to the client's cashflow for a 30-year cycle to create the first time path (ie. 1960-89). To create the second time path it begins the initial investment the next year (1961) and repeats the process (ie. 1961-90). It continues this process for the entire period being reviewed, in this instance 1960 to 2002. This means there will be 43 time paths, the last being 2002-31. It is the 43 time paths that then allow investors to "assess" their portfolio risk.
• Rolling time-path analysis: A more restrictive version of looping-time path analysis in that it only uses data from complete chronological sequences. This means there are only 14 paths, the last being 1973-2002.
• Bootstrap re-sampling: Assumes the same 30-year buy-and-hold portfolio over the same timeframe (1960-2002). But this method chooses years at random so the first 30 years' of annual returns could include any years of this 43-year period. Obviously, this data can be assembled in many ways, generating a bigger number of future scenarios of an asset/assets' returns.

Limitations of time-path analysis

It is not difficult to appreciate the major problem with historical stimulation. The same set of past returns is used to determine any scenarios about future returns. The time path approach, in particular, makes this problem worse by relying on chronological sequences, with the inevitable consequence that it understates investment risk. The other limitation with time-path analysis is that the simulated asset returns are limited to the extremes that occurred during that historical period. It cannot include good or bad returns that might have occurred in that period. For example, a period that looked at S&P500 index that omitted the 2000-02 bear market would have severe implications for simulated worse case scenarios.

Monte Carlo: One of the most widely used tools to generate possible scenarios about future returns in the finance industry. It is an analytical technique that samples an asset's returns from an imposed probability distribution instead of taking them chronologically from historical data.

Like historical sampling, the Monte Carlo method has its shortcomings. They are:

• It is assumed the asset's return will be distributed symmetrically around the mean return - the bell-shaped phenomenon. But for certain types of assets, historical returns tend to deviate from the mean in ways that are not reflected by a bell curve.
• It is also assumed that an asset's returns are not correlated over time. This assumption can distort the simulation depending on the type of asset, how often the data is observed and the historical period being examined.
• Finally, this method assumes there is a fixed correlation between assets, such as shares and bonds. However, empirical evidence often contradicts this assumption. For example, the correlation between bonds and shares has varied widely over time.

How the relative drawbacks of historical simulation and Monte Carlo ultimately affect assessments and potential future returns depends on how several factors interact. As a rule, these two approaches will be more reliable if:

1. Investment horizons are kept short.
2. The longer sample of the historical data.
3. The more stable the cross-asset correlation.
4. The more closely a portfolio's historical asset returns resemble the norm.

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