• How Large an Emergency Fund?

    Conventional wisdom is that we all should have an emergency fund (EF), a chunk of cash (or equivalent) set aside for use when financial trouble strikes. When employment prospects are good, I’ve seen recommendations for EFs as low as three months of salary. In times of high unemployment, some recommend EFs as large as one year’s worth of salary.

    These are seat-of-the-pants estimates. If anything they’re based on how long it might take you to regain employment after loss of a job. But income replacement isn’t the only purpose of an EF. One might tap it in the event of any financial emergency (e.g. unexpectedly high health care costs, urgent home repair, etc.). My interest in this post is to explore a rational means by which to set one’s EF size. It is based on the work by Charles Hatcher, summarized in a prior post. (See also the Bogleheads Forum discussion of Hatcher’s methods.)

    In Should Households Establish Emergency Funds? Hatcher compares the opportunity cost per year of having an emergency fund (the difference in rates of return between a more aggressive investment and that of the EF cash equivalent holding, denoted by the liquidity premium) with its per-year benefits if an emergency occurred (the avoided borrowing costs). The result is a simple expression for the minimum probability, p,  of an emergency in a given year such that holding an EF is rational: p=(r2-r1)/rb, where r2 is the rate of return on investments, r1 is the rate of return of one’s EF, and rb is the borrowing rate (Hatcher suggests a APR/2 is a good estimate of the borrowing rate).

    Hatcher assumes that the EF is equal in value to the cash needed in an emergency so the expression of the probability of rationally holding an EF given above is independent of EF size. That provides an opportunity to use it to determine a rational EF size as follows. If we interpret p as the lower bound on the annual rate of emergency such that an EF is rational we can ask: what is a typical size for an emergency that occurs with at least that frequency? The answer to that question provides some guidance to the rational EF size.

    Let’s use a concrete example. Suppose borrowing costs are 18% APR, which is typical of some credit cards but much higher than a home equity loan. Then rb is about 18%/2 = 9%. Suppose also that the liquidity premium is r2-r1 = 2% then the probability of an emergency must exceed about 22% to justify an EF. That’s about one emergency every five years. Based on one’s own experience one might have a general sense of the size of an emergency that’s likely to occur at that rate. I certainly do. For me this would suggest that an EF no larger than two months of salary ought to be sufficient. Of course, my borrowing costs may be even lower and liquidity premium may be higher. So maybe I could get buy with an even smaller EF.

    Instead of relying on my own intuition of typical emergency size over some time period, I’d love to see a study of such a thing. For example, an analysis of variation in monthly household outflow relative to income as a function of important variables like household size, age of head of household, education, and other relevant economic and demographic variables would be useful. From such a study one could estimate various measures of the likely largest emergency that would occur over an interval of time.

    I think the foregoing approach is one reasonable place to start in determining a rational EF size. But I wouldn’t end here. I’m not convinced one can know one’s borrowing costs and liquidity premium at the time of an emergency. The former could be higher and the latter lower, suggesting an even higher EF is rational. That’s one reason to increase one’s EF beyond the size suggested above. Another reason is peace of mind. There is no law against being irrationally conservative. Sleeping well at night is worth something.

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    • While I generally favor the ‘on paper rationality’ academic approach, optimizing the size of our emergency fund is not as much about rational analysis as it is about sleeping well at night and having the financial freedom to take risks.

      • @Jay – That’s a common notion and I share it to a degree. But one should consider how much our gut feeling of what is prudent is based on culture. In this case, for those who are into the personal finance culture, there is a general sense in that community that a certain number of months is reasonable. But, other than the work I’ve cited in my posts on this topic, I’ve seen nobody back that general sense up with something, well, sensible and quantitative.

        I have to admit, that what helps me sleep at night is not rational and is largely driven by what the community has taught me is right. I think it is important to be honest about that. Nothing wrong with a rational perspective. One can choose to ignore it if one wishes. I just think one should know why.

    • I was thinking about this subject this morning. Trying to figure out how much of an emergency fund I should save before I started paying debt down. Honestly, it has been very difficult for me to even get to $1000. So, I am just setting it at $500. With two weeks, and motivation to not starve, anyone can make it through a financial crisis. You learn what’s really important at that moment. 🙂

    • For home owners with significant equity, another option that costs nothing to keep on reserve but can be extremely helpful in a larger-than-expected emergency is an open but unused HELOC. It is an open well of cash. Our household depends on a % of investment income: when the equity markets tanked in 2008/2009, we activated the HELOC and invested it in fixed income securities to keep on hand as a backup. To this day, as a result of the interest deduction, we’re not actually losing money–just holding extra cash at no cost in case it’s needed for minimum expenses while the main portfolio recovers. We also drastically cut expenses, to avoid accessing the HELOC, but it’s a comfort knowing it’s there.