I was talking the other day with a friend about a bunch of random topics, and retirement was one of them. More precisely, how to finance it. I guess I started thinking about that a while ago, but this was something that kind of bothered me during the discussions about the réforme des retraites here in France in 2023. What I found really amazing at the time was how few people did the math.

Okay, I’m not really sure how they arrived at that number, but financial advisors apparently think that in retirement, one should aim to have about 80% of pre-retirement income. I guess a bunch of that 20% gap is because people stop saving money when they retire, but there are a bunch of other things I don’t know how to factor in. On one hand, most people are not paying rent or a mortgage while in retirement. On the other hand, I guess that people have more time on their hands, and money can help fight boredom. Then, I have absolutely no clue how to account for things like medical care and such. Summing up: I have no idea how they arrived at the 80% figure, but let’s kind of accept it.

Now, both in the US and in Europe, there is social security. In Europe, it tends to be more generous than in the US, but in the US, it also exists, and if you look at it, it is not negligible. Anyways, I think of it as an annuity—a contract where you pay upfront some amount of money and which guarantees you a monthly/yearly payment for as long as you are around. Now, I know that this is a simplified description of what an annuity is, but let’s go with it.

There are differences between annuities and social security. For one, there is no legal contract guaranteeing you social security. In fact, the precise way that social security works is not set in stone, meaning that you are, in some way, dependent on politics and such. On the other hand, the entity with whom you sign an annuity can go bankrupt. As I see it, in purely financial terms—that is, assuming that one does not mess up and that one sees the world in terms of long-term statistics—social security is a kind of shitty investment. On the other hand, one has the security that one is not going to go temporarily crazy and gamble away one’s retirement money. One has the security that one is not going to have the temptation to use that money to buy a bigger car or phone, or to go on holidays more often than one can afford to. One also has the security that everyone else around you is in the same boat, meaning that there is friction if some politician comes up with a brilliant but risky idea, and that there is more pressure to keep pensions aligned with inflation and such. I guess this is more true in Europe than in the US, where social security is less important.

Now, right now, social security in France covers about 74% of the net salary at retirement time, but the calculation is pretty complicated because there are maxima and minima, because it depends on how long one has worked, and because there are 1,000,001 special rules for special groups—civil servants like me are in one of those special groups. Now, because of all that, my own numbers are not representative, but as things stand now, if I retire when I am 64, then I will get 55% of my final salary, 72% at age 67, and 80% at age 70. Here, 64 is the age I would be able to retire without being penalized for retiring early, 67 is when I would get what is called “full retirement,” and 70 is the age at which I would be forced to retire. The gap between 55% and 72% is due to the fact that I started late contributing in France.

Since I have no intention of retiring, as things stand, all of that makes it look pretty rosy. However, there is the issue that the baseline of all those percentages is the net salary, but one pays taxes on one’s pension. How much one pays depends on how much one gets, but it seems to me that something around 20% is a reasonable number. This means that the 74% average dwindles to 59%. In my case, it’s 44%, 58%, and 64%, depending on the scenario. As a consequence, there is right now a gap of about 20% to that desired 80% figure.

I personally expect a bigger gap, and honestly, it seems like lunacy to me not to do so. In France, there is no huge pot where your contributions go and are accumulated until you retire. What happens is that people currently employed pay into the system, and this money gets directly distributed to retirees. And here is how the ratio between the number of people paying into the system and retirees has changed over time:

Year Ratio
1960 ~4.0
1970 ~3.5
1980 ~2.1
1990 ~1.9
2000 ~1.8
2010 ~1.7
2020 ~1.5
2030 ~1.4 (projection)
2040 ~1.3 (projection)
2050 ~1.2 (projection)

Note that, barring a prodigious increase in immigration or a return of the Black Death—this time focusing only on older people—it is kind of funny to speak of “projections” for 2030, 2040, and 2050. I mean, it’s a bit like considering tide or lunar tables “projections.” Those numbers are baked in. So, if nothing changes, around the time I expect to be enjoying my retirement, the amount that salaried people pay into the system will have grown by 16% compared to now, when the system is already pretty strained. Now, given that already now the average retirement (pre-tax) is larger than the average net salary, it seems unlikely to me that workers are going to be willing to pay that extra amount.

There is a tendency to say that it should be other people who should pay for that. Right now, employers pay into the retirement system 18.5% of the gross salary they pay to their employees. If it were up to them to make up for the demographic change, they would find themselves paying 24.5%. You can believe or not believe in economic theory, but it is clear that this would have a real cost, either in job creation, or in the ability to invest, or you name it. Other people say that this 16% gap should be filled by the state, but this means it is paid by taxes, and France is already (behind Denmark) the country in Europe with the largest fiscal pressure (7% more than in Germany). Besides, France already has quite a big deficit. And there are all the costs that climate change and such are going to bring. So, it seems unlikely to me that the state is going to put the money on the table.

I expect—and actually, I hope, because anything else would be immensely unfair to younger people—that what will happen is that retirement benefits are going to get smaller. I hope that it is done in a socially responsible way, with my benefits getting reduced more than those of people who are less well off than I am. I also hope that creative ways are found to keep people useful for longer. Indeed, to reduce benefits, you can not only reduce the pensions but also increase the retirement age. I expect that both things are going to happen. And yes, all the ratios above were calculated for France, but I think it is a pretty universal phenomenon because the demographic development in France is actually not as bad as in other countries. We should all be voting for parties who want to encourage immigration. Just sayin’.

Anyways, it is totally unclear how all of the different levers are going to be moved, but for myself, I decided to count on getting a pension of about 40% of my salary. Since I will not want the being to pay for me—if she is in France, she will already be paying into the system, and in any case, she will need money for things like a mortgage, kids, or enjoying life herself—this means that I have to count on closing the gap between 40% and something close to 80% myself.

All calculations from now on are made with a 1000 EUR per month basis, to be scaled as desired. That is, 12,000 EUR per year. How much money does one need to have saved to be able to take out 12,000 EUR per year? First, right now, you can’t buy annuities in France (why would you if the retirement system works as it does now?), but if you buy an annuity in the US at age 67, it seems that to get 1,000 EUR a month, you would need to pay in between 180,000 EUR and 260,000 EUR, depending on whether you are male/female and if it is valid just until you die or until both you and your partner die. Now, when you are 67, you have a life expectancy of about 20 years, but it could be more or less–the price of an annuity is closely linked to life expectancy, and hence to your age. In any case, with an inflation rate of 2%, 1,000 EUR now are worth 667 EUR in 20 years, something to be taken into account. Generally, annuities are not indexed by inflation—you can also buy those, but they are much more expensive.

An alternative is to keep the money under the mattress, or rather in something like a money market fund that basically keeps up with inflation. On average, this is about as expensive as buying an annuity: to take out 1,000 EUR a month for 20 years, you need to put in 244,000 EUR. From your personal point of view—that is, if you ignore possible heirs—annuities are also more secure because you continue getting your 1,000 EUR monthly even if you live to 120.

Now, if you put (some) money into the stock market, things are less predictable. There is the 4% rule, saying that if you have a portfolio of X, then you have a safe withdrawal rate of 4% of X. This means that every year you can take out 4% of your initial capital X, and with 90%+ probability, you will not ever exhaust your money. This rule is kind of controversial, partly because it is considered too optimistic—some people speak of the 2.7% rule—and also because it is kind of unrealistic. I mean, you would be kind of an idiot to always take the same sum out. If the stock market crashes, then you will probably have a cheaper holiday, or delay some expenditure, and make up for it when it booms. This would be especially true if you already have some baseline income coming from social security. Anyways, I think that this 4% gives a decent approximation, and that means that to be able to count with getting 1,000 EUR/month forever, you need a 300,000 EUR porfolio.

Now, let’s calculate as a percentage of your salary and suppose you wanted to get 10% of your salary per year. The calculation above suggests that you need a portfolio worth 2.5 years of your net salary. To get 40%, you need to have a portfolio worth 10 years of your net salary. That’s a lot of money.

Now, you would tell me that this calculation is wrong. I mean, what you might care is not about your salary, but you salary minus savings. At the end of the day, this is what you are used to spending. Now, if you count you will get 40% of your (final) salary from the retirement system, and you still want 80% of what you are used to spending, then you need to save

$$x=\frac{10}{20+comp(n)}$$

percent of your salary, and \(comp(n)\) is the “accumulated saving over \(n\) years”. If you just avoid inflation, then \(comp(n)=n\) and this means that if you want to for it in 10 years, you need to save 33% of your (final) salary, in 20 years 25%, and in 30 years 20%. That is pretty grim.

For me, the alternative is to get some additional return, in my case by investing in the stock market and expecting a modest 4% long-term inflation-adjusted return. If you have 0 savings and start investing now at a 4% rate then after 10 years \(c(10)=12\) and that means that you need to save 31% of your salary. If you do it for 20 years, then \(c(20)=30\) and you need to save 20%. If you have 30 years, then \(c(30)=56\) and you need to save 13%. On the other hand, if you have saved 4.5 years’ worth of monthly salary and still have 20 years to go, you don’t need to put anything in.

Now, all of this is kind of approximated because for the calculation salary is your final salary and not your current salary. Also, I am not taking into account the taxes you are going to pay on what ever stocks appreciate (in France, between 18.5% and 30%, depending on how you arrange things). It also does not take into account that maybe you are buying a house, that you could trade it for something smaller, and that you could move somewhere where life is cheaper, but actually, there is no reason why the calculation is fundamentally different because how much do you expect your house to increase in value each year?

The upshot for me is that (1) in Europe, already now, most people who live off their pension take a solid cut in their standard of living, (2) that while we will get significant retirement, the cut is going to get larger, (3) that unless one wants to exploit younger people, it is for us to make up for it, and (4) that to do that one actually has to do the math, at least approximatively, to see how much one has to save and how. But I don’t give financial advice. Neither life advice. And we all should be grateful about this.