The path really matters - Part III: A de-accumulation example
Posted on 11-03-2011 | 0 comments
Previous entries have highlighted the sensitivity of savings accumulation to the path or order of a set of investment returns. We concluded that – for accumulation – savers benefit from avoiding poor returns late in the accumulation period and that these returns will do less damage early in a savings plan because the invested fund is small. The analysis presented below demonstrates that the reverse is true for de-accumulation. In the example we analyse the same set of returns (mean 7% and standard deviation / volatility of 16.5%) over a 30-year horizon where the initial fund is €100,000 and an annual withdrawal of €6,000 is made. As before we now experiment only with the order in which the returns are delivered but leave the magnitude of returns unchanged. What difference does this make to results? Let us examine the terminal fund and the probability and timing of fund exhaustion i.e. where the fund is wiped out before year 30.
The chart below plots some possibilities for the growth in the underlying investment asset price. As before, 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. In contrast to accumulation strategies, de-accumulation will benefit from ‘early returns’ as under the green path. In this case, for the same set of returns, the ‘early return’ green path delivers a final fund of €+389K whilst the worst ordered outcome (‘early damage’) produces €-1.3M (although this result rather unrealistically assumes we ‘borrow’ at the unit rate of return). These differences are the exact opposite of what we saw for accumulation. Two additional random-ordered paths are also plotted on the chart.
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Now consider two more obvious questions: firstly, what is the probability of the fund being exhausted before year 30?; secondly, what is the chance of the fund being wiped out in any particular year? The chart below helps to answer the question by analysing 10,000 possible (randomized) orderings of the returns. You can see that the assumptions suggest that the strategy delivers the €6,000 withdrawal over the full 30 years in approximately 70% of simulations. In the 30% of simulations where the fund is wiped out prematurely, there is a very high probability of the fund surviving beyond year 10 but around a 10% chance it is exhausted by year 20.
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In these past three articles, I’ve highlighted some of the problems faced by savers. In future articles, we’ll take a look at some of the strategies used by product designers to help tackle the questions raised.
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