Download Part B: Examining the possibilities of future 401K balances

Fin 408
Final Project—Fall 2016
Problem A: Testing the 4% Rule
You have $1million in a 401K account and plan to live for 30 more years. The 4% rule tells us you can
withdraw $40,000 immediately and then withdraw $40,000 every future year (adjusted for inflation).
1. Set up a spreadsheet with $1,000,000 near the top. Withdraw $40,000 immediately and grow the
remaining balance by the return for that year. Annual returns will be in an adjacent column. Start out
with returns of 3% every single year.
Note: Instead of growing the $40,000 by some average inflation rate, we will use REAL returns.
Real returns are LOWER than nominal returns and exactly compensate for not increasing the
withdrawals.
2. Go to the T Rowe Price Retirement Income Calculator. Enter the following:
Spouse?
No
D.O.B.
12/1951
Career Status:
In Retirement
Social Security?
No or $0.00
Pension?
$0.00
Account Balance:
$1,000,000
Asset Allocation:
50% stock/50% bonds
Monthly Spending:
$4,000
Report their estimate of the percent chance your savings will last until age 95 (that’s 30 years). Also,
report their recommended monthly spending. Is it consistent with the 4% rule?
3. Go to the spreadsheet of returns made available on Canvas. Copy 30 consecutive returns (100% stock
or 50%-50%) and past these returns into a COPY of the columns used in #1 above. These returns will
replace the 3% returns you used initially. You are experimenting just like T Rowe’s calculator.
Note: A few years ago, a student wrote a Visual Basic macro to insert all possible 30-year returns
sequences into the spreadsheet and tabulate the % of times we ran out of money.
Excel Warm-up Exercises:
Put “=rand()” in a cell. You get a random draw which is a percentile.
Copy this formula down a bunch of rows and see that each percentile is different.
We don’t know what %-tile our next investment return will be in! It might be in the 95th
(great!!) or the 5th (NOT great) or the 50th (average).
Excel has a function that takes the percentile and provides an investment return for that %-tile.
You need to tell Excel the AVERAGE return and STANDARD DEVIATION of return too.
“=norminv(rand(),average return, standard deviation of returns)” does this.
Set up this function, type 0.50 in place of rand() and see what you get. Change 0.50 to
0.25 and look again. Get the idea.
Note: The norminv function takes a %-tile using the normal distribution and
finds the number corresponding to that percentile. The average and standard
deviation depend upon the asset allocation choice you make.
For your next set of 30 returns, copy the columns in #3 above but replace each return with the
norminv() function so that you get a random return for each entry.
Windows users can hit F9 a bunch of times and watch a new set of 30 returns show up. Try this
and see how many times you run out of money (the last balance will be negative). Apple users
can need to use something different from F9 and I don’t know what it is. Changing an empty cell
usually forces a recalculation.
To repeat the procedure used by the T Rowe calculator, you only need to hit F9 1,000 times and
count the number of times you did not (or did) run out of money by checking the last balance.
We are going to write a macro to copy the last balance 1,000 times and see how many of them
are negative (or positive).
Let X be the row number of the last balance. Observe this on your spreadsheet.
Let Y be the column number of your ending balance.
Cells(X,Y) refers to the cell with the ending balance in Excel’s macro language.
Here is the macro program:
For i=1 to 1000
Cells(i,16) = cells(X,Y)
Next i
The “=” says take the right-hand side and put it in the cell on the left-hand side.
The “i” will start at 1 and go to 1,000.
I arbitrarily chose the 16th column to put these 1,000 ending balances
All that remains is to do a bunch of simulations:
4. Withdraw $40,000 a year and show me the column of 1,000 potential balances for BOTH a 100%
stock portfolio and a 50%-50% stock/bonds allocation. You might want to sort the column and report
the % of times you succeeded (did NOT run out of money) for each. Repeat this for $50,000 a year.
Part B: Examining the possibilities of future 401K balances
1. Give yourself 40 years of salary (age 25 to 65) in a column. Save 15% of that salary in a 401-K account.
Grow your account at 3% and see what you have at age 65. Then replace the 3%’s with the norminv()
function (use average and standard deviation for either all stock or 50%-50%) and run 1,000 simulations.
Sort your 1,000 ending balances and report the 10th %-tile, 25th %-tile, 50th %-tile, 75th, and 90th.