Insurance: Emergency Funds As Self-Insurance

For anyone starting out on their personal finance journey, a common piece of advice is to set up an emergency fund. That is, save until you have 6 to 12 months of expenses or salary in the bank for rainy days. And that is before thinking about putting any money into investments. In How much cash or liquid assets should I hold in my investment portfolio?, unemployment can last for at least 6 months. Hence, this seems like a prudent approach for someone just starting off. But beyond this, nobody really tells you what to do as you accumulate other assets: Do you still need 6 to 12 months of cash in your emergency fund? Or do you need it at all? We can find the answer to this if we look at the true reason for holding cash in this way, that is, using emergency funds as self-insurance.

Emergency Funds as Self-Insurance for a Rainy Day

How does Self-Insurance work?

Let’s start by understanding how insurance works. In our previous post Insurance: When to get insured, and when not to, we linked expected utility theory to insurance. As before, the thick white line depicts how our happiness or utility changes with increasing wealth. More wealth means more happiness or utility, but utility increases at a slower rate. In other words, the second million dollars we have is great, but not as awesome as the first million!

Living with Uncertainty: Expected Wealth and Utility

In the diagram above, there are two possible outcomes for end-state wealth, $A or $B, each with equal chance. Expected utility, or happiness, is the weighted average (weighted by chance of happening) of the utility in either state, and is lower than what it would be compared to having $C in wealth for sure.

We then show that in such a world where outcomes are uncertain, insurance can help to provide certainty (for a premium). And in turn, certainty gives us higher utility (or happiness) compared to living with uncertain outcomes.

Insurance as a means to providing Certainty

Insurance as a means of providing certainty

By paying an insurance premium of $(A-C), we can have the insurance company pay us $(C-B) when the bad outcome happens. This means that we will have wealth of $C regardless of how events turn out, and hence will have utility of c’ instead of c.

Now, let’s say insurance for this risk does not exist (and it is unlikely to, given the high chance of the risk occurring). And looking at the possible outcomes, we feel that a wealth of $B in the bad state is too low for us to be comfortable with. What can we do?

One thing we can do in this case, is to save a little money, just in case the bad state occurs. Suppose we save an amount of $(B’-B) in the emergency fund.This ensures that in the bad state, we will end up with wealth of $B’ instead of $B. This, in turn, raises the expected wealth to $C’ instead of $C. And, in turn, increase our expected utility and happiness to c’.

Partial Self-Insurance of the Bad State using an Emergency Fund

Now, as we can see, putting a small amount away in the emergency fund by cannot fully insure us against the uncertainty. But the amount put into the emergency fund illustrated here is far smaller than the insurance premium needed to insure ourselves. And it still manages to make the uncertainty easier to live with, and gives us higher utility. Moreover, we get to keep the emergency fund if nothing bad happens (unlike the insurance premium). So, the next time we face such uncertainty, we already have partial self-insurance, and can increase the amount of self-insurance by saving more as well!

When does using Emergency Funds as Self-Insurance work best?

So far, we can see that using Emergency Funds as self-insurance works quite well when the chance of the bad event occurring is relatively high, and when the loss in the bad state is quite high. In such a case, it turns out that saving a little in emergency funds does the equivalent of paying a lot in insurance premiums! Are there other instances where it is better to self insure using emergency funds instead of insurance?

We can use the same model or diagram to think about this, since we can represent the chance of the bad event happening by how near or far $C is from $A.

When does using Emergency Funds as Self Insurance work?

When expected wealth is at $C1, it means that the chance of the bad event happening is quite low. This corresponds to the case of term life insurance, which we show in Insurance: When to get insured, and when not to to be the case where insurance works very well. Conversely, it is also the case where self insurance does not do so well. This is easy to work out on the diagram above – a small amount of emergency funds (relative to the loss amount) does not change the expected wealth or utility very much.

If we instead look at the expected wealth at $C2, which represents a much higher chance of the bad state occurring, it is quite clear that even a small amount of emergency funds can make a big difference to the expected wealth and utility. So this is in line with the initial case, where there is a 50:50 chance of either good or bad state occurring. In such an instance, conventional insurance is unlikely to be available, or will be very expensive, and self insurance works much better.

Self-Insurance using Emergency Funds works best when the chance of the bad event occurring is relatively higher, e.g. 1ADL Disability, or Early Stage Critical Illness, and is less suited to cases where the chance of the bad event is low, e.g. term life insurance

Other instance of using Emergency Funds as Self-Insurance

Another instance where using Emergency Funds as Self-Insurance works well is when the possible size of the loss is small. As we show in Insurance: When to get insured, and when not to, when the size of the loss is small, paying the premium for insurance does not actually increase expected utility by much. Instead, we can use the amount of the emergency funds to completely offset these small losses. Since most conventional insurance of this nature is priced accordingly to how much the insurer actually has to pay out i.e. you pay a premium of $50 every year if there is a 50% chance of losing $100 per year. Self insurance will mean putting $100 aside (2 years’ worth of premiums) to cover this loss, if it happens. If it does not happen, the bonus is that you still retain the money, unlike insurance premiums!

Self-Insurance using Emergency Funds also works well when the amount of loss when the bad state occurs is small, e.g. travel insurance, Integrated Plan Riders. Unlike the emergency funds, insurance premiums paid are not recoverable!

Additionally, using emergency funds for self-insurance in such instances can be very cost efficient, if there is no collrelation between the bad events in question. For example, it is unlikely to have travel delays and lost luggage at the same time as the need for paying medical deductibles, all of which we can cover from the emergency funds. Hence, the same amount of emergency funds can self-insure for a wide range of events or risks, compared to paying separate insurance premiums for each type of risk!

Do we still need Emergency Funds when Wealth Increases?

Finally, what happens to the emergency fund as our wealth increases over time? To properly understand the need for the emergency fund, we need to see it as a form of self insurance, especially when our wealth is low (hence the undesirability of the bad states). When our wealth increases with savings and investment, then the emergency fund becomes less relevant for this purpose.

For example, suppose we have accumulated $2 million in financial assets, and still have monthly expenses of $10,000. Does it make sense to keep an emergency fund of 6 months’ worth of expenses, i.e. $60,000? Clearly, in this instance, the level of wealth even with a typical bad event occurring is likely to be far higher than the size of the emergency fund. As a result, it does not help with self insurance. So the answer is NO.

Once the level of financial assets is such that the minimum level, even in a bad state, is above what we start feeling uncomfortable with, there is no longer any need to keep an emergency fund

When the level of assets are at a level where the needed emergency funds are 10% or less of the assets. then the allocation to cash is more a matter of portfolio asset allocation according to risk appetite, rather than self-insurance.

Conclusions

Setting up an emergency fund is a common piece of advice for all those starting on their personal finance journey. But what is less common s an understanding of what it is for. And in reality, it is a form of self-insurance for the instances where conventional insurance is too expensive, or where there isn’t any insurance you can get. In particular, we identify 2 areas where it can come in handy:

Self-Insurance using Emergency Funds works best when the chance of the bad event occurring is relatively higher, e.g. 1ADL Disability, or Early Stage Critical Illness, and is less suited to cases where the chance of the bad event is low, e.g. term life insurance

Self-Insurance using Emergency Funds also works well when the amount of loss when the bad state occurs is small, e.g. travel insurance, Integrated Plan Riders. Unlike the emergency funds, insurance premiums paid are not recoverable!

In short, emergency funds are for self-insurance, and so we should use them when the need arises, for example paying for medical deductibles and co-payments, or covering losses when travelling. Stop wasting money on insurance premiums when you can self-insure!

You can read some of our other blogposts on insurance here: