Monte Carlo Simulation and Sequencing Risk

Monte Carlo Simulation and Sequencing Risk

Further to the companion pieces on Robust Portfolio Construction and Expected Return Process, we now delve into the idea of putting the pieces together to customise portfolios that can adapt to personalised requirements. The idea here is not to replace the portfolio construction process, but to blend existing growth and safe portfolios together for each individual to minimise their chances of running out of money. By doing this at a household level, we can create bespoke portfolios based on specific customer needs rather than placing them in generic on the shelf target date like funds.

Why use Monte Carlo?

As the old saying goes, prediction is hard. Predicting the future is harder still. No matter how well we do our analysis, the future is inherently unknowable – at least in the specifics – and the further into the future we try and look the less clear the path is. Using a Monte Carlo simulation technique allows us to accept the fact that we may not know the exact future path, but we can model a range of paths that are possible. Like all modelling techniques, the devil is in the detail and the better we set our environmental parameters – and the more simulations we do – the more likely we are to get an idea of how well the portfolio may perform in a range of different circumstances.

The chart below illustrates this point by comparing what did actually happen (orange line) to the S&P500 versus what could have happened based on the historic statistical experience of the index. While the S&P 500 returned a pretty healthy 8.6% annualised return over the period, it could have been a lot better (13.3% per annum) – or a lot worse (1.2% per annum). When thinking about portfolio construction, we don’t have the luxury of knowing what WILL happen – only what could happen – and our portfolios need to be built with that in mind.

Monte Carlo Estimation

The first part of generating a Monte Carlo simulation is to build a statistical model of the way the portfolio behaves. Traditional approaches have relied on the I.I.D. (independent and identically distributed) approach that a normal distribution requires. But years of evidence has shown us that markets behave in ways that violate this requirement and better techniques are needed.

If we track the performance of a standard balanced fund back to 1987, we get this kind of monthly return profile:

The October 1987 stock market crash clearly stands out as the worst monthly return a balance fund has experienced.

If we were to simply take that historic series and estimate future paths using a normal distribution (in this case looking ahead 350 months), the chances of getting an event like 1987 would be basically non-existent.

One of the parts of setting up the estimation process is to decide whether the model should have a “view” on repeatability of extreme events. Applying a non-parametric estimation process gives the ability to map the moments (basically skew and kurtosis) of the historic distribution with much greater precision.

This approach now gives us a similar frequency of extreme events as we have experienced historically. A big part of the process of building the expected distribution of asset returns is deciding what period of history should be used for reference. If it didn’t include the 1987 stock market crash in the non-parametric estimation period, then it would be very unlikely to be in the simulation path. The consequences of this will be more evident when we get to the sequencing risk consequences.

Some return series require an ARIMA process to be fitted to capture the fact that returns trend. This is particularly the case for inflation and cash rates. Simply applying a normal distribution to cash rates generates an abnormally volatile future return path.

When we apply an ARIMA model to the data, we capture the trending nature of cash rates in amore realistic manner.

The goal of building the Monte Carlo simulation process is to make sure that the parameters that will be estimated are approximately what markets should behave like. Monte Carlos are a classic case of being approximately right, rather than precisely wrong.

OnTrack uses a technique called Ensemble Empirical Mode Decomposition (EEMD) to remove historical trends across asset classes to better capture the shorter-term co-movements of markets and establish a process for introducing correlated “noise”. EEMD is an adaptive method to analyse non-linear and non-stationary signals. It effectively removes different trends at various “frequencies”. Here is an example of a signal that has been broken down into 9 distinct frequency trends:

In order to keep the pattern of asset class movements, we want to keep the higher frequency structures (IMF 1-6) but remove the general historic trend in the market (IMF 9). By removing this trend, we capture the way markets move, but re-centre the structure around a new trend (as determined by our Expected Return Process).

Once we have the structure in place to estimate potential return paths for the assets, all the assets need to be estimated in a way that holds historic correlation structures in place. This structure is maintained by using the EEMD approach. If central banks look to inflation as a guide to where cash rates should be, then estimating the future path of cash rates needs to be linked to the path of inflation. This is especially true of bond and property returns as well. 

Economic Regimes

Setting the environment in which the Monte Carlo estimation process works is more than just choosing the statistical techniques used to predict a path of outcomes. Ultimately when thinking about retirement, very long-term projections are necessary for the bulk of people (more than 20 years in almost all cases and sometimes up to 50). Over this period of time, the expected return of the asset will compound significantly, thus changing the impact of potential future loses. If the retirement liability is $100 in present value terms, and a collection of extremely positive expected return periods are experienced in succession, then the value of the portfolio may exceed the liability value substantially earlier than retirement. At this point different decisions need to be made by the potential retiree – do I reduce my savings now, increase my standard of living in retirement, or retire earlier? The interplay between the economic regime, the expected return of the asset within that environment and the consequences for diversification all become important over exceptionally long periods. Please refer to the companion pieces on how we handle these ideas at OnTrack Retirement.

One of the most significant variables to model that is linked to the economic regime is inflation. The rate of inflation has large consequences on the discounting of future assets and liabilities and can directly drive the return of assets the investor may have in their portfolio. At OnTrack, when we run Monte Carlo simulations, we run three specific inflation environments – a “most likely case” regime, a high inflation regime and a very low/deflationary regime. The values of assets and liabilities are assessed in each of these broad regimes, where we run a large number of individual return paths that are consistent with the expected broad trend in inflation.

Sequencing Risk

The idea behind sequencing risk is that timing of returns can matter as much as the compound long term return itself. Market falls are just a reality of investing. When your investment balance is small, and you have many years of accumulation ahead of you, your sensitivity to short term returns is greatly diminished. This doesn’t make them any easier to accept at the time – but it does have a reduced impact on your ability to pay for your retirement.

Total Household Capital is made up of Financial Capital, Human Capital and the Future Age Pension (which is a hybrid of the two). Financial Capital can be considered all the investments that the household has – cash, Super, investment properties and shares etc. Human Capital is the after-tax future earnings of the household. The Future Age Pension is like a bond investment but only pays for as long as you are alive – a lifetime annuity. As such it is linked to your lifespan – but not your future earning potential. You simply must be alive and qualify to receive it.

While the household is still earning an income – their Human Capital is still positive – there is a buffer to losses in Financial Capital. In theory, a loss in the investment portfolio could be made up by increased savings from Human Capital in the future. As Human Capital falls, the ability to make up for any loss in the Financial Capital part of the portfolio diminishes. This is what makes the household more susceptible to sequencing risk.

Minimising Sequencing Risk

Sequencing risk is bespoke. It is dependent on the individual’s Human and Financial capital values relative to the liability value of retirement spending. To minimise the sequencing risk, a portfolio needs to be created for each individual. Target date funds are an attempt to generalise the individual’s specific requirements to reduce administrative burden on the fund manager. The problem with them is that individual characteristics are too specific to successfully generalise – they are a poor compromise that suits the fund manager and not the investor.

OnTrack has developed an automated, individualised dynamic rebalancing strategy that draws details from the investor’s specific situation. On an ongoing basis it mixes safe and growth assets in a way that minimise sequencing risk for each investor. This product is an add-on to the core profiling tool that OnTrack offers.

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