How to think about a self-financing emergency fund

There are two major kinds of events that can pose a significant financial challenge to a person as well as their dependants or supporters.

The first kind of events affect more than one person at once. A pandemic such as the present COVID-19 pandemic or an earthquake that hits a town are some of the examples.

The second kind of event affects an individual person alone. Included in this category is a devastating car accident to one’s relative. These events may occur not only in isolation or at the same time but may occur more than once during one’s lifetime.

Whether they occur once or more than once, more than average financial resources, though not the only ones, need to be expended, which in certain circumstance may drive one into permanent poverty in addition to severe mental or psychological burden. The effect may extend to many more other people who are related to the affected individual in one way or the other. However infrequent such events are, they can cause much physical, psychological as well as economic stress.

We would like to come to a sustainable way of dealing with emergencies such as those mentioned above that might affect some of us. And we would like to do this when there isn’t yet an emergency. Precisely, we would like to set up a special fund through which we could effortlessly finance the emergency and carry on with our life journeys.

We would like to set up a special fund through which we could effortlessly finance the emergency and carry on with our life journeys.

To operate the fund, we would need to raise enough funds, some of which would be available for the emergencies which we might face in the near future and some of which would be invested and be ready to solve emergencies in a farther distant future. We would also like the fund to eventually self-finance.

Concretely, the expected cost of emergencies in a given period, say a year, determine the size of the fund while the prevailing interest rate determine the expected number of years until when the fund becomes self-financing.

To make it work, the expected interest earnings must be greater than or equal to the expected cost of the emergency in any given year. For instance, if we expect the cost to be €500, then we should put in the fund €10,000 if the interest rate is 5% annually. With compounding, it would take about 14 years for the €10,000 to double to €20,000. Can you work out the arithmetics?

To make it work, the expected interest earnings must be greater than or equal to the expected cost of the emergency in any given year.

Once it doubles, the fund would become self-financing, meaning no additional contributions would be necessary after that period. It would be up to us what we do with that initial €10,000. For instance, it could be given back to the members of the fund. Suppose instead of investing the necessary €10,000 the members contribute €15,000, then the fund would become self-financing after about only six years. All monetary figures expressed in real units of currency so that an emergency that costs €500 today, costs the same amount in all future dates, everything else constant.

For those unfamiliar with terminologies, the expected cost is not the cost you will actually incur. In fact, you will almost never incur it. However, you might incur a cost much larger or smaller than you expected. Rather, it is the average of the costs of all types of emergencies. The rate of interest here refers to the percentage amount per one unit of currency (e.g., euro (€)) many people are expected to accept in order to lend money to other people. Therefore, you would want to be able to account for the fact that you might be significantly far off from the expected value. All these aspects are left out in the interest of brevity.

While we reason, what are the odds of an emergency on any day? Virtually zero. How about over a year? Likely. And over two years? Very likely.

So, how should we think about a self-financing emergency fund?

First, the obvious, emergencies rarely occur, but when they do, they cost a lot. Therefore, an emergency fund should be financed by more than one person. The contribution of an individual member of the fund is smaller than that which the individual would incur alone. Further, it depends on the rate at which the expected number of emergencies hit the group as a whole. The expected contribution to the fund for any member increases with the number of members not because the cost per emergency increases, but because the expected number of emergencies increases with the number of members. Can you derive these results yourself?

An emergency fund should be financed by more than one person.

Second, the expected time until the first emergency occurs saves as the time to build the fund. While it is longer for any one individual, it is much shorter when more than one individual are considered. Why?

Third, the size of the fund equals the expected cost of any emergency divided by the rate of interest.

Fourth, we need to have a perspective on the time until the fund becomes self-financing. However, until the fund becomes self-financing, we need to have an additional buffer should we make a mistake in evaluating the expected cost of the emergency. I would suggest that the buffer should be about 25% – 50% of the expected cost multiplied by the expected time until the fund becomes self-financing. And we would need to keep a perspective on this buffer even after the fund becomes self-financing. Further, we would have to finance it during the time it matures to sustainability. But this is likely to be covered by the buffer.

Until the fund becomes self-financing, we need to have an additional buffer should we make a mistake in evaluating the expected cost of the emergency.

Last but not least, the fund would have to be professionally managed such as via a bank or insurance company.

Please do not create an emergency fund without professional support.