I was never exposed to this kind of education when I was younger, so I thought re-posting this might help some people one day. Matthew Heaney wrote an awesome preso called The Essentials of Investing. (I dug this up at work recently.) He did a good job explaining investing and its importance. In Part 2, he covers one portfolio of investments to consider.
Disclaimer: I’m not a financial advisor. Investments can go both up and down. No guarantees in life!
Why Invest?
- We begin our career with no financial assets, but lots of human capital. We use our human capital to work in exchange for financial assets (money). When we end our career, we will have no more human capital, but hopefully lots of financial capital.
- Investing is just way to systematically replace human capital with financial capital. The only way to get from here (US$0) to there is to take risk. A portfolio is simply a mechanism for investing in accordance with our stated risk. The purpose is not to eliminate risk, but rather to manage it.
- Once we have accumulated the amount of financial capital needed to provide our desired retirement income, then we can dial back the risk. If you’ve already won the game, then stop playing.
- If you’ve already won the game, then stop playing.
How Much Do I Need To Save For Retirement?
- Suppose you have a 40-year career, e.g. start saving at age 25, and stop at age 65.
- Assume a retirement salary of US$100,000. (Inflation, housing, travel, etc.)
- Per the 4% withdrawal rule (Bengen, Trinity), you need to save about 25x salary as capital, or US$2,500,000.
- The real question is: How much do I need to save from each biweekly paycheck, to accumulate US$2.5M by the time I retire?
One Equation To Guide Us
We can use Mathematica’s Annuity, TimeValue, and NSolve functions to find this out (see footnotes to learn more about Mathematica). Annuities are basically just fixed payments over time, so we can use this to model retirement savings.
- Compute payments needed to achieve US$2.5M future value: (* 40 years, 26 intervals per year, 4% real return *)
Input: NSolve[TimeValue[Annuity[pmt, 40, 1/26], 0.04, 40] ==
2500000, pmt, Reals]
Output: $993
- Or compute present value:
In: NSolve[TimeValue[Annuity[pmt, 40, 1/26], 0.04] ==TimeValue[2500000, 0.04, -40], pmt, Reals]
Out: $993
- Check your work:
In: TimeValue[Annuity[993, 40, 1/26], 0.04, 40]
Out: $2,500,000
- Answer: $993 per paycheck
TL;DR Version
- So, you have to save about US$993 from each paycheck, for the next 40 years, or about 26 * 993 = US$26,000 per year.
- Making additional contributions to your Roth IRA and after-tax 401k, means that you can either retire early, or have more retirement income, or merely have a buffer in case you need to reduce your savings rate later.
Suppose I Delay Saving For Retirement? (Or, Suppose I Want To Retire Early?)
- Suppose you wish to retire at age 65, but don’t start saving until you’re 35.
- Alternative framing: Suppose you want to retire at 55 instead of 65?
- How much do I need to save from each paycheck then, to accumulate US$2.5M?
Mathematica
- Using future values (* 30 years, 26 paychecks per year, 4% real return *)
In: NSolve[TimeValue[Annuity[pmt, 30, 1/26], 0.04, 30] ==2500000, pmt, Reals]
Out: 1682
- Answer: 1682–993 = US$689 more per paycheck… Moral of the story: Start saving as early as possible!
Are My Retirement Savings On Track?
- Suppose you’re age 35, and have been saving for a while.
- You want to retire at age 65.
- How do you know whether your retirement savings are on track? Are you behind in your savings, or ahead?
Mathematica
- Let’s use present values this time (* Retire in 30 years, with US2.5M, using 4% discount rate *)
In: TimeValue[2500000, 0.04, -30] -TimeValue[Annuity[993, 30, 1/26], 0.04]
Out: 315,824
- Answer: You need to have saved about US$315,824 at age 35, to be on track for retiring at age 65, with US$2.5M of savings. If you have less
than that at age 35, you need to save more going forward, or plan
on working beyond age 65.
Will I Be Able To Retire Early?
Suppose I have accumulated US$500,000. When can I retire?
- First let’s use future values:
In: NSolve[TimeValue[500000.0, 0.04, t] +TimeValue[Annuity[993.0, t, 1/26], 0.04, t] == 2500000.0, t, Reals]
Out: 25.6
- Answer: Which means you can retire in about 26 years from now, assuming you maintain the same savings rate going forward.
Read Part 2 here: Basic Portfolio
Footnotes
What Is Mathematica? A computer algebra program, used in many scientific, engineering, mathematical and computing fields. It was conceived by Stephen Wolfram and is developed by Wolfram Research.
What is NSolve[expr,vars]? Attempts to find numerical approximations to the solutions of the system expr of equations or inequalities for the variables vars.
Why Annuities? An annuity is just a stream of equal payments, occurring at equal intervals. We can use the annuity formula to calculate the performance of our retirement withdrawals.
