**Retirement Planning And The Impact Of Investment Market Performance**

**June 21, 2016**

**by Joe Tomlinson**

The major challenge in building a sustainable retirement plan is the combination of low interest rates and stock market risk. Amplifying this challenge is the prospect of lower future equity returns and uncertainty about equity risk premium (ERP). Researchers have developed a number of different retirement withdrawal strategies to help manage investment risks; however, such strategies have not been adequately stress tested. I’ll compare strategies under stress to determine which strategies will be the most resilient.

### Retirement Planning – Investment market background

Much has been written in the past few years about prospects for lower-than-historical future returns for both stocks and bonds. The most recent example is this McKinsey report projecting real (inflation-adjusted) stock market returns, including dividends, of 4% to 5% for a low-growth scenario and 5.5% to 6.5% under a higher-growth scenario. (These projections are for compound or geometric returns.) By comparison, stock returns for the past 100 years have averaged 6.5%. Laurence Siegel summarized the McKinsey analysis in this recent *Advisor Perspectives* article and included his own projections, which were in the 4% to 4.5% range.

Bond returns are easier to predict than stock returns because current low yields exert a strong influence. For government bonds, real yields are close to zero, and both McKinsey and Siegel project future returns near zero.

Predicting stock returns is more difficult because of uncertainty about the ERP, which I discussed in this November 2015 *Advisor Perspectives* article. I cited extensive research by Professor Aswath Damodaran on the historical variability of the ERP, and an SSRN paper by Gordon Irlam where he analyzed the impact on asset allocation recommendations. Although Monte Carlo projections are typically done with a point estimate of the ERP, the research from Domodaran and Irlam indicates that it would be prudent to recognize a standard deviation for the ERP of two percentage points.

For this analysis, my stock return projection is approximately 1% more pessimistic than Siegel’s. Monte Carlo projections use arithmetic returns, which exceed geometric returns, and I’m projecting an arithmetic average return of 5%.[1] If I apply a 2% standard deviation to this estimate, there is a 15% to 20% probability that the “true” ERP is actually 3% or lower. Therefore I have chosen 3% for purposes of running stress tests. For bonds, I’ve used current TIPS rates to estimate a real return of 0.5%.

### Example

This analysis will be based on a retired couple where the husband is age 65 and the wife is two years younger. Their life expectancies are 88 for the husband and 90 for the wife. They have $1.5 million in tax-deferred savings, which they wish to utilize to generate cash flow to support their retirement. The assumed stock/bond mix for these investments is 60/40. They also have a $400,000 un-mortgaged home, which will become part of their bequest. They will be receiving $40,000 of annual inflation-adjusted income from Social Security (or partly from bridge funds if they delay claiming) and their basic living expenses are $70,000 annually, also increasing with inflation. They will need to generate at least $30,000 of cash flow from savings to cover their basic needs. This will be an after-tax analysis assuming a 15% marginal tax rate.

I used these client characteristics and investment assumptions in Monte Carlo retirement simulations. I model both stock and bond returns as variable, as is typical for such simulations, but I also model the longevity of the husband and wife as variable, rather than assuming a fixed retirement period.

### Return assumption impact

We’ll first assess the impact of the return assumptions used in Monte Carlo analysis. Chart 1 assumes the couple takes retirement withdrawals in accordance with the venerable 4% rule, so their withdrawals will be $60,000 per year (4% of $1.5 million) increasing with inflation, or $60,000 level in real terms.

The first line of the chart is based on 10,000 Monte Carlo simulations and arithmetic average real returns of 9% for large company stocks and 2.4% for intermediate-term government bonds (1926 – 2015 historical averages), standard deviations of 20% for stocks and 7% for bonds, and an assumption of zero stock/bond correlation. For the second line, I kept the standard deviation and correlation assumptions and reduced the real return assumptions to my 5% estimate for stocks and 0.5% for bonds. For the third line, I lowered the stock return assumption to the stress test level of 3% and kept everything else the same.

For this chart and subsequent charts, I show some performance measures that are typical for financial planning packages, and others that are new. For each of the 10,000 Monte Carlo simulations, I calculate average consumption (Social Security plus withdrawals minus taxes) over the variable period until the last member of the couple dies. I then display the average of the 10,000 averages. (These dollar figures and all other dollar figures in the charts are based on real 2016 dollars without inflation.) The average consumption decreases as I lower the stock return assumption. With the 4% rule, real consumption stays level unless savings are depleted – due to poor investment performance and/or long life – so lowering the stock return assumption means there will be more cases where the couple depletes savings and lives their remaining years on Social Security only.