How Big Should the Emergency Fund Be?

What it does

How much cash should this household hold, and should they add to it or free some up. Not whether a savings goal gets hit, which is a different template: what one income-loss episode actually costs. The model is conditional, and that is the decision everything else rests on. Every trial IS a job loss, so a percentile here means N in 100 job-loss episodes and not N in 100 futures.

There is deliberately no probability of losing a job inside the sizing, because putting one there makes the answer jump wherever that probability crosses the percentile you asked for, and hangs the whole number on the least defensible input in the model. The two optional chances near the bottom of the stack feed the judging line and nothing above it.

The household as loaded: two earners on $6,800 and $2,600 a month take-home, crisis-mode essentials of $5,200 plus $1,450 of health cover if the policy goes with the job, so $6,650 a month of burn, which is the number that matters and is not what they spend today. No severance, which is the common case and the conservative one, $2,400 of unemployment for six months, a $1,400 vacation payout.

Two unplanned expenses in a year, typically $900. They hold $9,000 in the fund and can reach another $2,000 inside a week. The sheet as loaded is drawn at 0.9 on the search curve, so before you click anything you are looking at the 90 in 100 episode they asked to be covered for: a 13-month search, a gap that opens in month 7, and $34,600 of cash needed.

Click Run. Across 20,000 episodes the middle one needs about $7,300, the mean needs about $14,500 and the 90th percentile needs about $38,400, and the distance between those three figures is the whole subject, because an emergency fund is not priced by the typical episode. The $11,000 they can reach today carries 65 in 100 episodes. Covering the 90 in 100 they asked for takes about $38,400 of reachable cash, so roughly $36,400 in the fund and about $27,400 more than they hold.

Now the month the gap opens, which is the finding this template exists for. The fan across the eight quarter-end outputs shows the P90 track at about $5,300 by month 3, $11,100 by month 6, $22,900 by month 9 and $33,900 by month 12, and it stops climbing after month 15. That steepening is the benefits cliff. Unemployment runs out at the end of month 6 and the monthly shortfall goes from about $1,800 to about $4,200, so the same household that loses ground slowly for half a year falls through the floor in month 7.

Reading only the end of the episode hides it entirely, which is why the answer here is the deepest point rather than the closing balance. The folk rule, priced. Three months of cover is $19,950 and buys 77 in 100. Six months is $39,900 and buys 91 in 100. Twelve months is $79,800 and buys 98 in 100. So on this household the old six-months-of-expenses rule lands within a point of the 90 in 100 they asked for, which is a better showing than the rule usually gets, and the step from three months to six buys fourteen more episodes in a hundred for another $20,000.

Those are the trades the rule of thumb never states. What moves the answer: the tornado puts the search draw at 0.98, the number of unplanned expenses at 0.12 and their size at 0.07, so how long it takes to replace income dominates everything else in the model. Earner 2 search draw comes back at 0.00, which is not a fault: in this episode earner 2 keeps working, so their job security does not move the fund at all.

Set earner 2 income stops to 1 and rerun and coverage falls from 65 in 100 to 31, and that bar becomes the second largest on the chart. Type in a severance package and rerun, because it is the single change that moves this sheet most. Two months at full pay takes coverage from 65 in 100 to 81, pushes the gap from month 7 to month 10, and drops what the loaded episode needs from $34,600 to $21,000.

Already laid off. Set earner 1 months already without income to 4 and rerun, because two things change and both are the point. The benefits are partly spent, so only two months of unemployment are left and the gap opens in month 4 rather than month 7. And the remaining search is drawn from the search curve conditioned on having got past four months, not from a fresh draw with four months subtracted.

That distinction is worth a sentence of its own: a fresh draw minus four months quietly mixes in every trial where they would already have found work, which puts the expected remaining search at about 3.2 months instead of 5.1. With this curve the conditional remaining search is shortest around month 4 and climbs back past the fresh average of 6.6 months after about a year, so the direction depends on how far in you are, while the size of the error from ignoring the conditioning does not.

Coverage falls from 65 in 100 to 57, and what is left of the episode needs $41,400. Someone four months into a search with 1.7 months of cover is in a different conversation from someone planning for one. If both lose income: always shown, never the headline. At the draws typed on the sheet the episode needs $65,800 instead of $34,600, and that line gives earner 2 no benefits of their own, which makes it a stress test rather than a forecast.

Leave the second earner block blank and every two-earner line goes quiet instead of printing zeros, and the same household on one income needs $65,800 with 25 in 100 coverage. With income intact, a year in which every unplanned expense lands at a 1-in-10 size costs $6,100 against $1,800 in a typical year, and that, not a layoff, is the call on the fund most households actually meet.

Reading across: what this episode needs in five years at 2.5% is $39,147, and every $1,000 held above the requirement gives up about $40 a year at the 4% in the return row. If this household held $40,000 rather than $9,000 the sheet would say free up $7,400, which is $296 a year of return, and their coverage would be 91 in 100 against the 90 they asked for.

It says free up rather than too much on purpose, because it is their money and their nerves. Set the percentile, not 90. The coverage cell is an input. It is capped at 99, and the cap is not arbitrary: at 20,000 trials, 90 in 100 leaves 2,000 trials behind the answer and 99 in 100 leaves 200, which is why trials in the tail is a row on the sheet rather than a footnote.

Past 99 you are insuring against the model's own assumptions rather than against unemployment, and the tail estimate rests on too few trials to be steady. If you push coverage above 95, raise the trials to 50,000 or more so the answer stops moving between runs. Where the shapes come from: time to replace income is lognormal, which is the honest default for a search length, because most searches end quickly and a few run very long and no symmetric curve can say that.

Two figures pin it, a median of 5 months and a 1-in-10 figure of 13, and the sheet solves the spread from the pair. The number of unplanned expenses is a Poisson count written out as its own probabilities, and their size is a right-skewed triangular whose own 90th percentile is the $3,050 on the sheet. Four things this cannot tell you. Severance often delays or reduces unemployment eligibility, and the rules vary by state, so if you type in a package, paying both at full value in the same month may overstate your support: check your own state and shorten the benefit months if it applies.

The unplanned expenses are spread evenly across the episode rather than landing in particular months, so the model prices how much they cost and not when they hit. Severance and benefits are taxed, so every figure you type should be after tax. And a fund in a fixed-term deposit is not an emergency fund, whatever the balance says. Last, and it is the part people get wrong about the whole exercise: none of this is a forecast that anyone will lose their income.

It is only what it takes if they do. To make it yours, put in your own take-home pay, the essentials you would actually run at, what your health cover would cost, and whatever your employer has told you about severance.

Next question

• Pay a little extra each month. How much sooner is it gone?How Much Sooner Does an Extra Payment End the Loan?
• Will you actually hit your savings goal?Will You Hit Your Savings Goal?
• Will your retirement money last to 95?Retirement: Will the Money Last?
• Should you buy the house or keep renting?Rent vs Buy a House
• Will this rental actually cash flow?Does the Rental Property Make Money Most Months?
• Which deductible really costs you less?Which Health Plan Costs Less Over a Year?

Every model like this one, and the method behind them: Monte Carlo simulation.