## 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 Inputs 401(k) balance at beginning of 15 year period \$200,000 \$200,000 Monthly Contribution to 401(k) \$500.00 \$500.00 Annual Return First Period 0.07 -0.04 Annual Return Second Period -0.04 0.07 Length of First Period in Months 90 90 Length of Second Period in Months 90 90 Analysis FV of initial sum in 401(k) at end of first period \$337,576 \$148,089 FV of monthly 401(k) contributions to end of first period \$58,961 \$38,933 FV of funds at end of first period funds to  end of second period \$293,615 \$315,672 FV of second period contributions \$38,933 \$58,961 FV all funds after 15 years \$332,548 \$374,633

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: