You can now fly nonstop from London to Australia, taking 17 hours and traveling 14,500 kilometers. Imagine it is your responsibility to load the right amount of fuel on the aircraft and chart the flight path. Too much fuel means a higher weight, so fewer miles per gallon, and less capacity for passengers and cargo. Not enough fuel could be disastrous. At best, there will be complaints if the plan is forced to make an unscheduled stop. Depending on weather and other factors you might want to adjust the flight path and flight speed to arrive safely and on time.
Investing for retirement can be considered in a similar fashion: given a pre-retirement savings rate and a desired spending rate in retirement, what is the allocation to stocks most likely to achieve my goals? The example we consider in a recent paper assumes our investor saves $20,000 per year for 30 years and then withdraws $40,000 per year for 30 years1. Clearly, we require an allocation to the stock market to generate a sufficient return over the 60 years to make this achievable.
A conventional approach would be to invest in a fixed allocation to stocks (60% stocks, 40% bonds, for example) and to see what happens. Over an investment period of 60 years there are a huge possible range of outcomes, including running out of money at one extreme and leaving a large and unintended bequest at the other. Most investors, given the option, would prefer the experience offered by a Defined Benefit Pension Plan where the level of income in retirement is guaranteed and there is no possibility of running out of money. For those without a Defined Benefit Pension Plan, the conventional approach offers a very uncertain outcome. Can we do better?
An alternative to a constant allocation is to define a stock allocation that varies with the age of the investor. This is the approach of target date funds, that pre-define a glide path, and other rules such as the stock allocation should be 100 minus the investor’s age. Perhaps surprisingly, this type of approach does not appear to provide better ending values of wealth compared to a constant allocation strategy with an equity allocation equal to the glidepath average over time.
A more radical approach is to not pre-specify the stock allocation at all, but to allow it to adjust to maximize the likelihood of achieving a desired outcome. The stock allocation is now not an input to the problem but an output. In a recent paper2, we showed dynamic stock allocation reduced the risk of missing a wealth target by 50%, compared with a constant stock allocation.
The latest work3 extends this dynamic approach through the complete lifecycle from savings to spending. A natural goal is to minimize the likelihood of running out of money, a subject of concern to retirees. This proved to be rather sensitive to input assumptions. Going back to the flight analogy, such an approach would consider getting to within 100 meters of the runway after flying 14,500 kilometers to be an absolute failure and running out of fuel as the wheels touch down, to be an absolute success. In reality, a more graduated approach is desirable. Efforts to include the cost, as well as the likelihood, of failure did not offer much improvement.
A more robust approach, quadratic shortfall, was to target a positive surplus at the end of retirement and to minimize the risk of missing this target and is described in more detail in our paper Management of Withdrawal Risk Through Optimal Life Cycle Asset Allocation. Compared to a constant stock allocation, quadratic shortfall had a significantly lower likelihood of running out of money and the average amount of shortfall in dollars was also significantly less. For retirees who are homeowners, their property can act as a contingent asset to borrow against, as a last resort.
The figure below highlights one aspect of the very different outcomes from a constant stock allocation compared to the dynamic stock allocation. The figure plots the distribution of probabilities of possible outcomes, so the area under the curves is always unity. The variable, p, refers to the stock allocation so curves for a stock allocation of 40%, 60% and 80% are shown corresponding to p values of 0.4, 0.6 and 0.8. The horizontal axis shows the terminal wealth in thousands of dollars. The constant stock curves show a broad range of possible outcomes while the quadratic shortfall strategy provides a much more predictable outcome. This is important because, while we assumed a 30 year retirement period, our retirees could live longer and want to be sure that there is sufficient residual to fund additional years. While this strategy doesn’t absolutely guarantee retirees won’t run out of money, it does reduce the odds of ruin significantly compared to a constant stock allocation, at the expense of forgoing the chance of a very large bequest.
Why are we pursuing this research? Our experience is that clients are much more interested and committed when discussing specific wealth goals than notions of risk focusing on short term market volatility. We have shown that goals can be achieved with greater certainty if the allocation to stocks is not prescribed but allowed to vary to continually maximize the likelihood of achieving those goals.
Algorithmic approaches to investing also have the advantage of consistency. Investment professionals are no different from other professional groups such as doctors and credit rating agencies in demonstrating inconsistency: the decisions from the same person can change at different times and professionals with the same experience can offer materially different decisions4. An algorithmic approach is a useful check against this noise and provides a more reliable client experience.
1 We assume that we are investing in real dollars so the nominal value would increase with inflation.
2 Target Wealth: The Evolution of Target Funds, Peter A. Forsyth, Kenneth R.Vetzal, and Graham Westmacott. PWL White Paper, June 2017 or https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2980952
3 Management of Withdrawal Risk Through Optimal Life Cycle Asset Allocation, Peter Forsyth, Kenneth R Vetzal, and Graham Westmacott, May 2018, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3180333
4 Noise: How to Overcome the High, Hidden Cost of Inconsistent Decision Making, Daniel Kahneman, Andrew M. Rosenfield, Linnea Gandhi, and Tom Blaser. Harvard Business Review, October 2016.
