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Why Murphy's Law Holds True - Emergency Fund Probability of Use Chart

Murphy's Law has many variations, but as Dave Ramsey likes to put it, "If you don't have an emergency fund, you're inviting Murphy to come in."  What he's referring to is Murphy's Law that simply states if something can go wrong, it will.  While we would all agree that we need an emergency fund, that doesn't necessarily mean that we all have one or that it is sufficient to cover life's emergencies - thus, Murphy and Dave are 100% right.

About the Chart

Since most of us are visual learners, we thought it a good idea to create a simple graph that shows what the probability of using an emergency fund would be.  In the graph above, we've illustrated this by showing the value of an individual's emergency fund expressed in the number of weeks worth of expenses and the percentage likelihood of having an emergency fund that would wipe it out.  It starts at 100% with no emergency fund and works down to about 3% at 52 weeks worth of expenses in reserve.

Interpreting the Chart

Another way, perhaps a better way, to think of this is that if you don't have an emergency fund, you are guaranteed to have an emergency come up.  However, if you have a full year's worth of expenses set aside, only once every 33 years would an emergency come up that would wipe out these reserves.  Thinking in this way is very helpful because understanding the probability of needing an emergency fund and of what size can be a big assist when it comes to ranking the need to set money aside for an emergency versus putting money towards other savings goals.

Finding the Sweet Spot

We all have limited resources and unlimited wants and because of this, the central question in personal finance is always applicable:  How should resources be allocated among competing needs and wants?  In looking at this chart, it's obvious that an emergency fund is necessary, but how much?  That depends on you, but here are some numbers to consider:

• 0 weeks = 100%, guaranteed to have problems
• 4 weeks or 1 month = 70% or every 17 months
• 8 weeks or 2 months = 49% or every 2 years
• 13 weeks or 3 months = 31% or every 3 years
• 26 weeks or 6 months = 10% or every 10 years
• 52 weeks or 1 year = 3% or every 33 years

Given these numbers, it becomes a little easier to determine how much you should set aside and where this need would rank against others.  In deciding where to put your money, there is a point that you reach where the probability of a cash killing emergency is low enough that you feel comfortable putting money into longer term goals like retirement.  This is different for everyone, as it's a question of peace of mind and individual circumstances, but for many, it will be between three and six months' worth of expenses.  For very conservative folks, it could be a year or more; for aggressive people, maybe as little as a month's worth of expenses will do.

Why Murphy's Law Holds True

Regardless of where your comfort zone is, the reason Murphy's Law hold true is because most of us live paycheck to paycheck with little money in cash reserves.  On the sample chart we've created, the majority of us would fall in the range of zero to eight weeks of emergency cash.  As a result, emergencies come up frequently, and this often leads to additional debt.  In short, without sufficient cash reserves, when things can go wrong, they will.

Critical Thinking

• How do you think comfort levels change over time?  How would your perception change from the time of being young and single to getting married and having young children to approaching retirement with an empty nest?  What steps should you take to prepare for these life stages?
• Unemployment rates typically rise as we age.  How does that impact the frequency and severity of emergencies?  What actions should you take to address this fact?
• If you have too little cash set aside and have to go into debt to finance an emergency, what are the long term costs associated with this?  Does it make emergencies more or less likely in the future?
• If you have too much cash set aside, what are the quiet costs that you must pay?  How much in the way of investment returns are you giving up by holding too much cash?  Is your added peace of mind worth the extra cost?

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Total Returns, Best and Worst, and Risk for Stocks, Bonds, and T-Bills from 1926 through 2009

When it comes to building a portfolio, there are three major asset classes - stocks, bonds, and cash.  The most common measures of these asset classes are the S&P 500 index (large cap stocks), Barclay's long-term government bond index, and Barclay's 3-month T-bills index.  Below is a table that shows the average annual total return, best year, worst year, and risk of each of these indices.

	Stocks	Bonds	T-Bills
Avg. Annual Return	9.9%	5.5%	3.8%
Best Year	60.0% 1935	42.1% 1982	14.0% 1981
Worst Year	-41.1% 1931	-12.2% 2009	0.0% 1940
Standard Deviation	19.2%	10.1%	0.6%

As would be expected, moving from left to right shows a declining level of return and risk.  In addition, it's helpful to know that inflation has averaged roughly 3.1% over the same period of time.  This means that the real return (total return minus inflation) are 6.8%, 2.4%, and 0.7% for stocks, bonds, and cash, respectively.

In addition to the standard deviation measure, the best and worst year ranges offer up some valuable information.  Investors have never lost investing in T-bills over the course of a year while stock investors have suffered through substantial losses over time.  Another interesting footnote to this table is that 2009 was the worst year on record for holders of long-term bonds.

What we would like for you to takeaway from this is that risk and return characteristics vary greatly among these three major asset classes.  For this reason, they are a great place to start when deciding how to assemble your investment portfolio.  As we'll see later, finding the right combination of these asset classes is perhaps the most important factor in determining your portfolio's level of risk and return over the long run.

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