Tuesday, May 22, 2018

The path of returns and financial risk for 401(k) investors

The path of returns and financial risk for 401(k) investors

Question Eighteen:  A person has $200,000 in her 401(k) plan.   She contributes $500 per month to her plan. She is planning to retire in 15 years.  Investment scenario one involves 7 percent returns for 90 months followed by -4.0 percent returns to 90 months.  Investment scenario two involves -4.0 percent return for 90 months followed by 7.0 percent returns for 90 moths.

What is the difference in the FV of funds in the 401(k) plan between the two scenarios?  What does this result tell us about impact of path of returns on financial risk for 401(k) investors?

Methodology:   The final balance in the 401(k) plan can be calculated with the future value function.  It is a five-step procedure.

Step One:  Take the future value of the initial $200,000 to the end of the first period.

Step Two:  Take the future value of all first period contributions to the end of the first period.

Step Three:  Find funds available at end of first period (This is the sum of steps one and two.)  Take the future value of these funds to the end of the second period.

Step Four:  Take future value of all second period contributions.

Step Five:  Add results of steps three and four to get FV at retirement.

It is important to use monthly returns and monthly holding periods.   It is also important to input contributions and initial balances as negative numbers so you obtain a positive future value balance. 

Results:    The future value calculation for the two market scenarios is presented in the table below.

The timing of the bull market
401(k) balance at beginning of 15 year period
Monthly Contribution to 401(k)
Annual Return First Period
Annual Return Second Period
Length of First Period in Months
Length of Second Period in Months
FV of initial sum in 401(k) at end of first period
FV of monthly 401(k) contributions to end of first period
FV of funds at end of first period funds to
 end of second period
FV of second period contributions
FV all funds after 15 years

Observations about results:

The return in the overall market is R=(1.07/12)90 x (1-0.04/12)90 for both scenarios.

Even though market returns in the two scenarios are identical the final 401(k) balance is larger when the bull market occurs at the end of the period rather than the beginning of the period. 

The difference in portfolio outcomes is non-trivial.  The difference is around $42,000 or around 12 percent of the average of the two portfolio outcomes.

Analysis and Discussion:  The timing of the bull market matters for 401(k) contributors because more money is exposed to the market at the end of the holding period than at the beginning of the holding period.

Interestingly, timing or returns does not matter when the investment is a lump sum.   For example, the timing of returns does not alter the future value of the initial $200,000 investment.

Financial analysts argue that people need to invest in their 401(k) plan and place funds in equities at the beginning of a career because in the long-term stocks out-perform other asset classes.  However, the long-term performance of stocks will not protect investors from substantial losses when a bull market occurs near the end of a career.

Market timing is a significant risk factor!

Many financial analysts argue that end-of-career financial risk can be mitigated by investing in life cycle funds, which increase allocation of assets towards fixed-income assets as the investor ages.  But if returns are low after the first period should the investor maintain a risky position or reallocate assets as planned under the life cycle account. 

The rebound in the second ninety months is not a sure thing in advance.

 This is question eighteen in my Excel Finance tutorial:

Saturday, May 12, 2018

Resume for David Bernstein


David Bernstein
1786 Grape Street
Denver Colorado

202 413-5492 (cell)


Purdue University, Ph.D. Economics, 1988.
Arizona State University, M.S. Economics, 1982.
Rutgers College, B.A. Mathematics, 1979.


Researcher, Author and Publisher, June 2012 to the present
Wrote articles for several blogs on finance, public policy, health care, and mathematics.

U.S. Treasury Department, Economist Office of Economic Policy, 1989 to 2012.
Provided management of the U.S. Treasury with economic briefings and analysis on several issues including health costs and policies, gambling and bankruptcy, the North American Development Bank, and Housing.   Presented papers at conferences and submitted economic articles to academic journals.

Analysis often involves evaluating data from government surveys including the Survey of Consumer Finances, the Current Population Survey, the Medical Expenditures Panel Survey, and the National Health Interview Survey. 

Substantial experience with STATA and SAS

Energy Information Administration, U.S. Department of Energy, 1987 to 1988.
Reviewed models and papers that were used to generate official forecasts.

Purdue University Teaching Assistant 1983 to 1986,
Taught both introductory macroeconomics and microeconomics.

Kansas State University, Instructor Department of Statistics,
Taught introductory statistics for business students

Selected Health Insurance Research

“Health Care Reinsurance and Insurance Reform in the United States: A Simulation Model” The Geneva Papers on Risk and Insurance, October 2010.

“Intergenerational Transfers and Insurance Policy Design,” The North American Actuarial Journal, July 2008.

“Factors Impacting Emergency Department Use” (October 14, 2008) 

The State Child Health Insurance Program Debate: Background and Insights

Selected Financial Posts:

An Excel Financial Function Tutorial
Teaches how to use Excel financial functions with interesting problems.

Portfolio Price Earnings Ratios When Sone Firms Have Negative Earnings 
Develops a method to obtain a PE ratio for a portfolio when some firms have negative earnings.

Comparison of Microsoft and Apple PE Ratios on July 4, 2017.
Post asks why Apple has much lower PE ratio than Microsoft on July 4, 2017.

The Choice Between ETFs and Mutual Funds:
A discussion of the difference between ETFs and Mutual Funds

Six Vanguard Funds
Post analyzes six funds offered by Vanguard

Investment Fund Performance Measures
Post shows how to measure investment fund performance when fund is purchased and sold on multiple dates and there are several potential holding periods.

Systematic Risk of Three U.S. Stock Funds:
Post measures and compares systematic risk of a large-cap, mid-cap and small cap U.S stock fund.

Asset Allocation and the Four Percent Rule:
Post discusses how retirement start date and portfolio mix affects outcomes under the four percent rule.

Selected Policy Posts:

Ways to Provide Student Loan Debt Relief:
Post originally published by NASFAA discusses different ways to provide debt relief to borrowers with excessive levels of student debt.   Proposals include modification of the IBR loan program and alterations to bankruptcy law.

An ACA Reform Proposal
This post describes two changes to the ACA, which if enacted could stabilize state exchanges and reduce health insurance costs.

Selected Publications:

Trade Concentration, Openness and Deviations From Purchasing Power Parity, (With Michael Melvin) Journal of International Money and Finance, 1984.

“Three Essays on Corporate Dividend Policy,” Ph.D. Dissertation, Purdue University, 1988.

"A Note on the Effects of Equity and Non-Equity Variables on Mortgage Default," Journal of Housing Economics, 1991.

"Property-Casualty Insurance Markets," Treasury Working Paper No. 9203, Office for the Assistant Secretary for Economic Policy (with Lucy Huffman), 1992.

“Imperfect Information and Agency Cost Models: Further Empirical Evidence,” International Review on Economics and Finance, 1994

"Asset Quality and Scale Economies in Banking," Journal of Economics and Business, 1996.

“Do Fuel Efficiency Improvements Really Increase Travel,” World Resources Review, 1998.

“The Past and Future of U.S. Fuel Efficiency Policy,” Book Review, World Resources Review, Vol. 13, No. 3, 2001.

“The Impact of Gambling on Personal Bankruptcy Rates,” (With Lynda de la Vina) Journal of Socioeconomics, 2001.

"Fringe Benefits and Small Businesses: Evidence From the Federal Reserve Board Small Business Survey." Applied Economics, 2002.

“An Assessment of Corporate Average Fuel Economy CAFE,” Journal of Environmental Policy & Planning, 2003.

Household Debt and IRAs: Evidence from the Survey of Consumer Finances,” Financial Counseling and Planning, 2004.

 “Intergenerational Transfers and Insurance Policy Design,” The North American Actuarial Journal, July 2008.

“SAMs: A Better Approach to Mortgage Lending?” The RMA Journal, October 2009.

“What is the Appropriate Tax-Base for President-Elect Obama's High-Income Household Tax?” Tax Notes, January 2009.

“Bankruptcy Reform and Foreclosures” in Housing Loans and Mortgages (editor S. Ravi) ICFAI University Press, 2009.

“Should the U.S. Congress appropriate funds for the repurchase of older vehicles?” Applied Economics Letter, 2010.

Issues Impacting the Decision to Tax Part of Employer Health Benefits, Tax Notes, September 2009.

Health Care Reinsurance and Insurance Reform in the United States:  A Simulation Model,” The Geneva Papers on Risk and Insurance, October 2010.