The path really matters – Part II
Posted on 02-03-2011 | 0 comments
This is a continuation of Part I
Consider (again) savings accumulation over a long horizon – 30 years – where we assume an individual saves €1000 each month. Now, let’s assume that we have a fixed set of returns available for the 30 years. The returns have an (arithmetic) average of 7% pa and a volatility of 16.5% so they are in line with the sort of assumptions that practitioners might make for a financial planning exercise. Suppose we now experiment with the order in which the returns are delivered but leave the magnitude of returns unchanged. What difference does this make to results – to the sum accumulated at the end of the 30-year period?
The chart below plots some possibilities for the growth in the underlying investment asset price. You can see that all paths start and finish in the same place for a unit investment. The top (green) profile shows the path where we place returns in order from best to worst. The bottom (red) profile shows the reverse with returns ordered from worst to best. As we have already seen (see blog part I) accumulation strategies benefit from ‘late returns’ as under the red path. In this case, for the same set of returns, the ‘late return’ red path delivers a final fund of €3.7M (IRR of 12.7% pa) whilst the worst ordered outcome (‘late damage’) produces €0.3M (IRR of -1.4% pa). These striking differences are exactly reversed for de-accumulation problems.
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Two additional random-ordered paths are also plotted on the chart. In the chart below the full distribution of possibilities is shown for the accumulated fund where we randomise the order of the same fixed set of 30 returns and simulate a large number of possibilities. There turns out to be a 1-in-5 probability of achieving either more than €1280K or less than €680K. Given how much investors focus on both returns and measures of asset volatility it is striking how, when we nail down both these properties for a fixed set of returns, the outcomes for accumulated fund fall over such a wide range.
The lesson is that the path really matters and so advisers and savers need tools and strategies in order to understand and control these risks.
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