### The Most Critical Planning Assumption – and How to Choose it

The expected premium that clients earn by investing in stocks, known as the equity risk premium (ERP), is the most important assumption in financial planning. The best planners take great care developing an ERP estimate to use in preparing financial plans. But by focusing on “a number,” planners overlook the fact that their ERP estimate is highly uncertain. I’ll show why it’s important to fully recognize this uncertainty in preparing financial plans.

The importance of the ERP has been recognized by a number of different researchers. In this 2005 article, Jeremy Siegel noted that more than 320 articles had been published over the previous 20 years with the words “equity premium” in the title. The ERP assumption is critical, not only for asset allocation, but also for decisions about how much to save during the working years and how to spend down wealth during retirement. The most up-to-date research on the ERP is provided by Professor Aswath Damodaran of the Stern School of Business, who publishes an annual report summarizing research on the subject.

I’ll give my recommendations for how advisors can incorporate the uncertainty in ERP estimates into their financial plans. First, I’ll look at developing an ERP estimate from the historical data and then at some alternative methodologies for deriving a reliable estimate.

Historical data

We need to define the ERP. I’ll use the difference between arithmetic average returns for stocks and intermediate Treasury bonds. This is the most appropriate measure to feed into Monte Carlo simulations that are commonly provided in financial planning software. There are other definitions such as using geometric (or compound) stock returns and using bills instead of bonds as the base component. Unfortunately, much confusion has been created by not making the definition clear.

Let’s look at the historical data. Based on Damodaran’s 2015 report, the average ERP over the period 1928-2014 was 6.25%. But he also provides results for more recent periods, and the result for 1965-2014 was 4.12%. There have also been attempts to go further back into history to gather more data, and Damodaran reports estimates from Goetzmann and Jorion of an ERP of 2.76% from 1792 to 1925.

Because those averages vary so much for the different time periods, it is clear that attempting to base a future ERP estimate on history is not a straightforward task.

Dealing with uncertainty

We can get a better appreciation for challenges in trying to use historical averages by applying basic statistics. When a sample average is used to estimate a population mean, a confidence interval for the mean can be calculated. For Damodaran’s 6.25% average for 1928-2014, he calculates a standard error of 2.32%. We can be roughly 95% confident that the population mean based on the experience of the past 87 years was plus or minus two standard errors from the sample average of 6.25% — or 1.61% to 10.89%— a shockingly wide range. Planners often discuss what return or ERP assumption to use in doing financial projections. There might be a discussion about whether to rely on history or whether to scale back and shave off a couple of percentage points. But there are never discussions of “what-if” testing based ERPs spanning a two standard error range as shown above.

The uncertainty about the ERP has implications for asset-allocation recommendations. In this recent paper, Gordon Irlam takes into account the uncertainty in the ERP and then uses his AACalc software to determine optimal asset allocations at age 65. His recommended asset allocations are based on the concept of maximizing the expected utility of lifetime consumption. He calculates 95% confidence intervals for recommended asset allocations and, similar to the ERP ranges, finds wide confidence intervals for the recommended asset allocations – 10% to 82% stocks for the particular example he studied and approaching a 0% to 100% range for some other client scenarios.

Again, this news will come as a shock to planners thinking in terms of tweaking asset allocations by 10% or 20% at the most.