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.
Some might argue that the variability discussed above is automatically taken care of by running Monte Carlo simulations, but that is not the case. The problem is that, even though Monte Carlo simulations build in variability, the particular point estimate of ERP (and stock return) used makes a big difference as the following chart shows.
|
ERP impact on financial planning projections
|
|
|
|
ERP description
|
ERP
|
Median bequest
|
Failure rate
|
|
lower end of 95% confidence interval
|
1.61%
|
$127,153
|
41.5%
|
|
lower end of 67% confidence interval
|
3.93%
|
$400,221
|
28.0%
|
|
historical average 1928-2014
|
6.25%
|
$790,088
|
14.5%
|
|
upper end of 67% confidence interval
|
8.57%
|
$1,264,324
|
6.4%
|
|
upper end of 95% confidence interval
|
10.89%
|
$2,040,866
|
2.1%
|
Source: Aswath Damodaran and author’s calculations
This chart is based on a 65-year-old with $1,000,000 portfolio split 60/40 stocks/bonds taking 4% inflation-adjusted withdrawals (the 4% rule). A planner meeting with a client would likely focus on the 14.5% probability of failure and the $790,000 median bequest. However, a conversation that fully recognizes uncertainty should go like this:
Your results will be heavily dependent on the extra return of stocks over bonds. Unfortunately, we have limited statistical evidence and don’t know what to expect. The best I can do is tell you that I’m 95% confident that you can expect a bequest in the $100,000 to $2 million range and that the probability of plan failure is somewhere between 2% and 40%. For an asset allocation recommendation, it could be anything from 10% to 90% stocks.
Obviously this response, which is intended to reveal the true uncertainty, will be totally unacceptable to clients. In light of this uncertainty, we need to look for better ways to do financial plans and communicate with clients.
But first it’s worth asking whether there might be ways to reduce the uncertainty.
Alternative approaches
Here are several alternative methodologies for computing the ERP:
Demand model – One approach to estimating the ERP involves determining what return premium investors demand for taking stock market risk. The most straightforward demand approach involves comparing historical stock and bond returns as above. The assumption is that the average past ERP reveals what investors have demanded and will continue to demand for taking risk. However, as demonstrated above, data limitations make it impossible to be very precise with this approach.
Another version of the demand approach involves the application of utility theory to produce an estimate of how much consumers should demand for taking the additional risk of stock investing. Rajnish Mehra and Edward Prescott were the first to attempt this in 1985. They estimated the impact of stock market volatility on the utility of consumption and produced an ERP estimate of 0.35% – orders of magnitude lower than the historical average of around 6%. This huge discrepancy became known as the “equity premium puzzle,” and a number of researchers have since attempted alternative approaches that have produced higher ERPs. But given the variety of results produced, there is no way to judge reliability.
Supply model: The approach that holds the most promise for narrowing the range of ERP estimates focuses on what stocks can supply in terms of a dividend payout rate and a dividend growth rate reflecting the growth in earnings. The formula is ERP = D/P + G – Y, and I define Y as the yield for intermediate-term government bonds. (An additional nuance in the use of this simple formula is adjusting for changes in shares outstanding.) This approach produces a geometric rather than arithmetic estimate of the ERP, so it’s necessary to make an adjustment to produce an arithmetic ERP comparable to other estimates discussed in this article. Larry Siegel, along with co-authors Richard Grinold and Kenneth Kroner, produced a detailed supply analysis as a contribution to the 2011 CFA publication, “Rethinking the Equity Risk Premium,” and came up with an arithmetic estimate of 4.63%. Similar estimates of the ERP have been produced by others using the supply approach. This is lower than the historical average reported above of 6.25% for the period 1928-2014. Researchers applying the supply approach do not expect past effects to continue in the future and cite the long-term historical decline in PE ratios being as a prime example.
Expert opinion: The CFA publication mentioned above was preceded by another on the same subject 10 years prior. Both versions provided perspectives on the ERP from well-known researchers associated with universities or investment management companies. The 2001 edition listed 19 separate estimates of the ERP ranging from 0% to 7%. For the 2011 publication, fewer of the experts produced forecasts and those who did, tended to be in the general vicinity of Larry Siegel’s 4.63% and reflected the growing popularity of the supply approach.
Time varying ERP: So far we have focused on estimating the “true ERP,” but there is also research suggesting that the ERP varies over time. This research has been popularized by economist Robert Shiller, who developed the measure known as PE10 or the CAPE ratio, and demonstrated that ERPs over future 10- or 20-year timeframes have been heavily influenced by beginning market valuations. His PE measure uses 10-year trailing earnings to reduce business cycle effects.
In the 2015 Forbes article “Is a High CAPE Cause for Alarm?” Wade Pfau updated the regression equation Shiller used to relate CAPE ratios and future 10-year returns. Based on the current CAPE of 26 (compared to an historical average of 17), the regression predicts real stock returns of about 3%. With 10-year TIPS yielding 0.5%, which translates to an ERP estimate of a dismal 2.5%. But like the other estimates, predictions based on the CAPE ratio don’t have a lot of data to support them. Although the data goes back to the late 1800s, it only covers 12 non-overlapping 10 year periods. There is also much debate about the current applicability of Shiller’s approach. Arguments challenging Shiller and pointing to more optimistic results include: (1) the current low level of interest rates should be incorporated in the measure, (2) changes in accounting practices have biased the measure upward, and (3) investors are getting smarter and will adjust more quickly to market mis-pricings.
What can we conclude?
Despite the confusion, planners must make an ERP assumption to produce financial projections for clients. So it becomes necessary to evaluate a variety of sources of information and make subjective judgements. My own view is influenced by a combination of the supply approach, CAPE ratio, and recognition of uncertainty.
I start with an arithmetic ERP of 4.5%, based on the supply approach, and shave this back to 3.5% to partially recognize the current CAPE. To factor in uncertainty, I would not simply run Monte Carlo projections based on this 3.5% point estimate. I’d also do runs based on ERPs 2.5% lower and 2.5% higher than 3.5% and come up with spending plans and asset allocation recommendations based on these “what-if” scenarios.
The choice 2.5% is quite subjective and based on my view that the supply approach can help tighten the variability compared to relying on historical data. The key point is to give the “what-if” scenarios the same prominence as the best estimate to better reflect the uncertainty in the ERP estimate.
Additional implications
Recognizing the uncertainty in the key ERP assumption should influence the way planning is done. The benefits of building consumption floors through the use of bond ladders or single-premium immediate annuities (SPIAs) become more apparent; those strategies do not rely on equities and are immune to ERP assumptions. For the funds used to support discretionary spending, variable withdrawal strategies that recognize emerging investment experience will perform better than strategies where target spending is fixed at plan inception, such as the classic 4% rule. For overall portfolios, recommended stock allocations are likely to decrease, particularly if we consider SPIAs or similar annuity products as part of the fixed income portfolio.
Compared to the popular approach of assuming a point estimate for the ERP, an approach that admits we don’t know what number is may seem counterintuitive. But what has been truly crazy is assuming we know a precise number when the evidence clearly indicates that we don’t.
Joe Tomlinson, an actuary and financial planner, is managing director of Tomlinson Financial Planning, LLC in Greenville, Maine. His practice focuses on retirement planning. He also does research and writing on financial planning and investment topics. He thanks Gordon Irlam for sharing his research on the ERP and for helpful comments on this article.
Read more articles by Joe Tomlinson
