# Is putting money in the 1st pillar profitable?

tl;dr: Normally not

I wanted to know, if putting money into OASI was profitable in any way. If you control how money flows to you, you also control OASI contributions. E.g. a salary vs company invoice (with or without dividend payout).

## Sources

I didn’t find all sources I wanted. The calculations are difficult and riddled with exceptions. But I found enough to make an educated guess:

• The relevant average annual income (de: massgebliches durchschnittliches Jahreseinkommen) is calculated from the sum of all contributions. (German) That means it doesn’t matter how much you paid in what year. It matters that you contributed every year, though.
• The relevant average annual income is translated to a monthly pension. There is also an algorithm for that in the above document, but you can also just use their current table (page 14). It is important to note that up to half the maximum you get more per contribution than after. See table below:
• A single man without kids and no special circumstances is assumed. If you are anything else: Congratulations, not being a such man gives you many benefits. The law gives you more money, for longer, whilst paying less. It’s free real estate.
From To +Δ Annual average (a) +Δ Pension per month (p) +Δ Pension per year per contribution (g)*
14700 1470 0 0.000
14700 44100 1470 ~32 0.056
44100 88200 1470 ~19.5 0.034
88200 1470 0 0.000

* According to my formula:

g = \frac{p * 12}{a * y * r}

where:

Target contribution years (men) y = 44
OASI on gross salary r = 10.6\%

## Is OASI profitable?

tl;dr: No

I built some crude model with taxes, other social security contributions, and live expectancy. It was never worth it. Not if your other investment opportunities returned +0%. Not if you hypothetically don’t pay any (progressive) taxes. And with a return of 8.84% (50/50 US/ex-Us global stocks, portfoliovisualizer.com) it is worse even if you could top it up the day before retirement and then live forever whilst investing all pension payments into the market.

Let’s do just that and see why:
Since we make no contribution to society except for a one-time payment to top up OASI we have the choice between:

• (A) 1 CHF in the market
• (B) 0.056 CHF per year into the market

The total returns are:

t_A = A*r^y
t_B = b*A*\frac{r^y-1}{r-1}

where:

Years till death y
Market return factor r
Substitution B = b*A

So when is t_A > t_B?

If we assume:
r\ge1
y>>r,b

Some elementary math will give us:
r-1\gt b

We already calculated b in the very first table.
Our investment needs to beat an average of 5.4% and 3.4% respectively.

tl;dr: Maybe

Minimum contribution is 514 at the moment. You will still get the minimum pension of 1225.
If you could do as before then:
A=44*514=22616
B=12*1225=14700
b=65\%

No investment could beat that. But we can’t contribute only at the end here. If we need to spread the contributions over 44 years there will be missed market returns. Therefore:
A=c*\frac{r^{44}-1}{r-1}
b=\frac{B}{A}=\frac{14700}{c*\frac{r^{44}-1}{r-1}}
r-1\gt \frac{14700}{c*\frac{r^{44}-1}{r-1}}

where:

Annual contribution c

If someone wants to solve this exactly, feel free. Plotting gives:
r-1\gt 8\% for c=514 and
r-1\gt 5.5\% for c=3*514=1552, above which we start to get additional pension for additional contributions according to the first table.

## Final remarks

• I am happy to be corrected on my calculations and reasoning.
• The point of OASI is probably not that it is profitable. It is a continuous debt that was signed into reality last century to secure a living for elderly people.
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I haven’t dived into the math yet but, to me, OASI is an insurance. It insures us against disability, it insures our spouse and children against our death and it insures against longevity risk (with potential high inflation since there is some sort of inflation adjustment baked into it).

You seem to conclude that no amount of life longevity makes one benefit more by having OASI than by it not existing (provided someone financially literate, which many are not), is my understanding correct?

When comparing with stocks/bonds, I’d keep in mind that the 7%-10% long term averages that we often see are in USD. The USD has mostly lost value to the CHF since it got depegged from gold in the seventies so expected returns in CHF would be less. I personally have 5% memorized as the average of long term returns for global stocks in CHF. That means that for someone with a stomach for anything less than 100% stocks (which is probably most people), getting upward of 3.4% returns on a portfolio isn’t a given. Averaging 5.4% would be outstanding returns.

Question : would your results be the same if you did your comparison with real (inflation adjusted) CHF and some range of hypotheses for inflation during the given period? The average stocks returns used may have benefited from periods of high inflation whereas it doesn’t seem to me (but I could be wrong) that the inflation adjustment in OASI is taken into account when estimating its benefits.

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