# New Research on How to Choose Portfolio Return Assumptions

Care must be taken with portfolio return assumptions, as small differences compound into dramatically different financial outcomes over a lifetime. My research shows just how big those differences are and how they vary in the pre- and post-retirement phases.

Though Monte Carlo simulations are the methodology of choice for projecting most financial plans, advisors often use simple spreadsheets for lifetime financial plans. Those spreadsheets typically use a fixed portfolio return assumption. After reviewing some of the basics for making the portfolio return assumption — which can provide valuable insights for clients — I will explore relatively new ground with respect to how sequence-of-returns risk should impact the assumptions.

I find empirical support for the idea that portfolio return assumptions for the post-retirement period should be more conservative than for the pre-retirement period. In turn, assumptions for the pre-retirement period should be more conservative than when simply applying a compounded return to a lump sum investment.

### Basics for choosing a portfolio return assumption

 Table 1 Summary Statistics for U.S. Market Returns, 1926 - 2011 S&P 500 Intermediate Term Government Bonds (ITGB) Average (Arithmetic) Return 11.8% 5.5% volatility (stocks: 20.3%; bonds: 5.7%) -> Compounded Return 9.8% 5.4% inflation (arith. mean: 3.1%, volatility: 4.2%) -> Real Compounded Return 6.6% 2.3% asset allocation (client uses a 50/50 portfolio) -> 50/50 Portfolio Real Arithmetic Return 5.6% 50/50 Portfolio Real Compounded Return 5.0% 50/50 Annual Volatility 11.0% Source: own calculations from Stocks, Bonds, Bills, and Inflation data provided by Morningstar and Ibbotson Associates. The U.S. S&P 500 index represents the stock market, and intermediate-term U.S. government bonds represent the bond market.

For a lifetime financial plan, the most intuitive way to express a portfolio return assumption is as the inflation-adjusted compounded portfolio return. Unfortunately, this is generally not the most common way returns are expressed. It is worth a quick review of the steps needed to arrive at a real compounded return.

For someone seeking to develop portfolio return assumptions based on U.S. historical data, Table 1 shows the basic steps. This table is based on the Stocks, Bonds, Bills, and Inflation data since 1926 from Morningstar and Ibbotson Associates. Historically, the S&P 500 provided an arithmetic return of 11.8%. This is the number one gets by adding up all the annual returns from the historical data and then dividing by the number of years in the data set. For intermediate-term government bonds, the arithmetic return was 5.5%.