[660] some boring stuff

Disclaimer, I am not a professional financial adviser so don’t take this post or any my opinions on financial matters as anything you can rely on for your own financial planning.

I am about to dive deep into some numbers on retirement planning because it is a topic dear to my heart (other than running) and recently I had a flash of insight that prompted me to write this. I have been thinking about it for several years.

I started planning for my retirement when my manager told me about the company’s retirement matching about 15 years ago and I have been consistently putting money in.

Initially, I did not know how much to put in but over time, started enjoy everything on the topic and developed my own opinion. (see my second post on the topic at the end of 2021, where I was trying to figure out over how much to contribute, now I have mature much).

I faced with the same question everyone is facing.  How much should one contribute?  Of course, there’s kind of maximum (capped by law for 401k and one’s income) that almost no mortal can reach.

I know if I “max” my contribution, I would be in good hand. But what about minimum?  Zero is an answer but we want a partical answer, a sweet spot.  This is a much harder question to answer.

(1) How much do I need to save now annually? (also how much I need to save by now is a good question too). There are some online guides, of how many times one’s salary by certain age.

(2) Related to this is how much I need to save by retirement (e.g. 10x one’s salary)

In order to know that, the third question is (3) How much do I need annually at retirement? (future)

(4) How do I plan to withdraw? (future)

These questions are what can keep me up at night regarding retirement.  This post is about answering Q3 and Q4, specifically Q4.

The answer of how big a nest egg needed is different for everyone, depending how early one start, how much to contribute, their tolerance of risk, and how far away is the retirement date (they call this the time horizon).

I am going do some hand waving.  Experts estimate we (millenials) need between 1.5 million to 3 million dollars saved up for retirement.  That is a lot of money, especially at the upper range. 

I agree that if I have that much I will be set.  Many don’t even know if they can save up for 1 million dollars. I think 1 mil is about the ball park for my case.

There’s also social security for those in the US, which is a government entitlement program. What about it? The prevaling thought is it won’t be enough for retirement and likely won’t be available when my generation is about to retire. But we won’t talk about that for now. We will assume it will still be around.

A few people have a pension.  We won’t talk about that either. Those have it, would be better off than the rest, because it means, they need to depend less on one’s own savings. However, usually pension like social security is also not enough either (or it can go bankrupt too, which we have seen, such as when Enron went under, it almost took many pensions with it).

To find how much to save, I used the 4% rule.  Note, we are working backward here.  That you should only withdraw around 4% from your retirement account each year to ensure your savings will last through your retirement. 

 Whatever the dollar amount needed annually at retirement, say $60,000, subtract off what social security or pension plan will provide, say $15,000-20,000 for our optimistic case, $60000-$20000 -> $40,000 (to make the math easy). 

Then we do some math magic here: 1 / 4% is 25x (inverse of 4% is 25), multiply 25 with the amount you think you need (for our example, it is $40,000 x 25 gives 1,000,000).  I know it’s a lot of math.  At retirement, you will need $1 million because 4% of $1 million will give $40,000.  We were working backward. 

As long as you have 1,000,000 in the bank (or the retirement account), you can withdraw $40,000 each year.

For most, this is the ideal case where each year they withdraw 4% from the account and it will grow back by the following year. It’s a money generating machine.

 As long as the growth rate is above 6.2%, money will not run out.  Why 6.2%? 2% for inflation, and 4.2% for recovering the $40,000 taken out. 

This doesn’t account for what if one year there is less than a 6% growth, or even a negative growth (i.e., a recession). 

There is always a risk of a recession, putting at risk that the capital would not be able to recover back to 1 million dollars. It is safe to assume every decade, there will be a recession.

However, know that it would take a period of 25 years of 0% growth to draw down the balance of 1 million to zero (because 25 x 40000 is a million). 

Someone ran a simulation thousand of times, and 4% rule is good enough to have the money last on majority of the time.

What I concern about is the 4% rule being too conservative — that I will die with a lot of money left over (like a million dollars or even half a million).  I don’t mind having money left over, but if I could put less into retirement right now and use the money for other things while I am alive, why not.

 Note the following is not be a good idea for most people.  This is my insight. It goes that if you don’t want to die with a lot of money left over, the idea is to draw down enough so when you pass away, you have just right amount. The key assumption is you know exactly when you will die.

Leaving the assumption aside, the math is pretty easy (at least easier than I have thought).  I have been thinking about this on and off and over the weekend I came across someone who wrote that retirement withdrawal can be considered as a mortgage payment.

  You can use the same loan amortization schedule to calculate the withdrawal amount needed to have the a zero balance left over. Eureka!

Imagine you have a mortgage of $1,000,000.  The number of years to pay off is the number of years in retirement.  The interest rate is the growth rate (minus inflation to be conservative). The payment would be the retirement withdrawal amount.

For our example, the retirement term is 30 years, interest rate is 4%, to find payment, I used a financial calculator (or Excel formula), pmt: 4%, 30+1, -1000000, 1 -> $56,855. This is the amount to withdraw per year until the nest egg becomes zero. (It’s a lot of math/financial terms, sorry, but that is the idea of how to determine the withdrawal amount).

Without social security, $56,000 won’t be enough if one were aiming for $60,000 for retirement. But with income from social security too, it is more than enough (we assume social security can provide 20,000).

Is this better than the 4% method? No, because it is riskier.  It withdraws more than 4%.  Actually starting at 5.8%, and it increases each year until the balance is reaches zero (withdrawing at 100% on the final year)!

The cool thing is the balance gets to zero at a predetermined period, and in our example, at the end of 30 (or 29) years (note to self, the off by one error). 

Why use this way to withdraw?  If one is comfortable with the risk, one can have a lower balance to save up. 

The question then is how much to save up if I want to withdraw $40,000 per year using this method instead of $56,000. This is just the reverse of how big loan I can take out if I my repayment is $40,000 per year. Excel function: pv(4%, 30+1, -40,000, 0) ~ $703,000.  This means instead of trying to save up to a million, we can save to about $700,000, which is 30% less than 1 million.  This is the answer to question 2.

As for finding the answers to Q1, one can use a financial calculator.  Search the internet on how to save a million dollars or $700,000, would be bring to a schedule of how much to save per year.

One can use the pmt formula in Excel again (or any financial calculator), for our example, e.g., i=4, n=30, pv=0, fv=-703000, answer: $12,534 (about $1,000 a month). (Q1)

Note how high the payment is. For some, this is 15-20% of their income.  This assumes a low interest rate (4%) of return.  Most investors though are aiming for a 7-10 % annual returns by investing from the stock market.  Also the time horizon (period of investment, which is how long before retiring) is longer than 30 years, say 40 years.  This would reduce the amount one need to contribute to retirement. Start early, and put in regularly is the key.

Summarizing, I don’t recommend calculating withdrawal using the amortization schedule because it is more risky of running out of fund earlier than anticipated.  But it is a way to know, it is possible to have a smaller nest egg and still can have the same amount for withdrawal during retirement.

My second insight that kept me up this week is a bit embarrassing to describe.  I have not found how other people calculate this. But it came to me like a eureka moment when a friend shared how her coworker passed away right before her retirement. I have wrestled with this for some years (mostly on the math part).

We all know we won’t live forever and there’s a chance we die before we even retire.  And so what?  How does that factor into how much to save.

The chance we going to die before retirement date, e.g., age 65, can be estimated with one of those life insurance charts. 

The thinking is: if we sure 100% we will live beyond 65, then we need the full amount.

If we know there’s a 50% chance we won’t live past 65, some say we still need the full amount.  I say, we need less.  Maybe we only need to cut back a bit on the savings.

If we know definitely we are not going live pass 65, then no need to save for retirement. Or maybe still save a little bit, like 5-10%.

Majority though it is not as extreme as 50% but maybe at 5-10% likelihood we won’t live past 65, I think we should save less than what the actual need is (I would peg 3-5% reduction), because the chance we are going to die before 65 is not zero.  If we live pass the age, we beat the odds, and we should be glad to live with what we have (less), say 5% less in the balance is probably an acceptable tradeoff.

Also the odds of dying increase each year. So in a sense, we could/should contribute less and less instead of more and more as we head into retirement (note, our tax system seems to encourage people to do the reverse, i.e., to save more to do a “catch-up contribution” as we near the retirement date).  There is also special points in life we our bodies age significantly (such as 50, 60, 70).  I think those are times we should evaluate how much (less) to contribute into the retirement account.

This is controversal. I am not advocating everyone to avoid doing catch up contributions. However, there might be logical sense to not do so. 

As for the amount to reduce, I used the expect value (no math is shown here because I don’t want people to follow this idea).  Just putting out here of the broad idea that one should not be in dismay of not having 1.5-3 million saved up, because there are various reasons, we can contribute less and not feel being not adaquate prepared.

For some, a 5-6% reduction is not worth the risk (plus too much math to arrive here).

Again, I posted this because of how far my thinking has changed since a few years ago. I will post again maybe in a few years from now on the topic.