Stats and Personal Finance: Oh My!


Lions and Tigers and Bears… Oh my! Wikipedia user: Wulfstan; Wikipedia user: Dibyendu Ash

Last time, I wrote about volatility in one’s expenses.  I kept it pretty generic.  On purpose.

Today, I’m going full nerd.  We’re going to look at expenses and how much volatility there really is.  And, we’ll quantify that volatility.  I’ll do my best to keep it accessible, but it will involve a smidge of math.

If you’re still trying to get started tracking your expenses, is a great way to start.  You can probably get everything set up in about an hour.  After that, it’s almost entirely automatic.  You get all the charts and graphs that most normal humans would ever want to look at.  And, for us nerds, everything is downloadable so you can do extra analysis when no one else is looking.  OK, back to the task at hand.

Before we get too deep in the proverbial muck, a question: why would you want to look at expense (or income) volatility!?

Answer: so you can plan better for long term things like financial freedom, retirement, house purchases or pay-offs, and budget risk.

In my last post, I showed a time series plot of our monthly expenses:

And because I'm a nerd, I also track spending within each pay period to ensure I don't go over budget.

And because I’m a nerd, I also track spending within each pay period to ensure I don’t go over budget.

So that I can work with our actual data in the public domain of the internet, I’m going to convert all of the expenses to a standard normal distribution so I’m not sharing the actual values.  You’ll still be able to see each monthly value expressed as a z-score relative to the average of all the others.  (That translates into the following: expensive months will have big numbers.  Cheap months will have small, possibly negative numbers.)   If that leaves you confused or angry, you can watch Psy dancing Gangnam Style again and feel a little bit better.   Or, you can just skip the conversion when (if!) you try this at home with your real data (and not post it on the internet).

std_expense-varianceA couple of things jump out at me based on these two views.  Lets start with the time series plot:

  • There’s a whole lot more volatility in the past 3 years than in the first 3 years.  Lifestyle inflation, buying and renovating a rental property, and having a little one will do that.
  • Baseline expenses are going up.  And, we probably have more increases to look forward to in the future.  That’s even after accounting for the “unusual” expenses of starting a rental property
  • The histogram shows two humps: the main one centered on 0, and a second one centered on 3 sigma.  Given the relative sizes, that says to me that we’re pretty good about sticking to our budget.  But, when we overspend, things really come off the rails.
  • As with so many things in life, “Average” doesn’t tell the whole story.  That’s the crux of this post, so I’m going to break out of bullets and expound.

A lot of conventional wisdom is centered around the idea of working to an average.  Average home prices, sales figures, time to commute to work, heights, salaries, etc.  The list goes on and on.  We’re taught from a very young age that in order to summarize a data set, we should add up the numbers and divide by the number of numbers.  That’s the average.  It’s a useful statistic to start with, but it doesn’t tell the whole story.  Check it out.  Each of these lines (H, S, and P) all have the same average.  What’s different?  The spread.


There’s more to data than just the average. If your head is in the freezer but your feet are in the fire, on average you’re fine! Right?



Enough stats for a minute.

Back to personal finance.  If I were to plan my 2017 monthly budget around last month’s expenses, I might pick up an outlier where we paid all the fees for an au-pair (and ate nothing but peanut butter and jelly to compensate.)  If I take a 6 year average, I might overlook the fact that my recent baseline expenses seem to be increasing.  So, let’s only look at the past 3 years.  That might have a more representative sample.

The past 3 years of standardized expenses

The past 3 years of our standardized expenses

Now I have a range of expenses to plan for in the future.  Picking the average and planning for that level of spending would result in having enough money allocated to cover 54% of months!  I’m dipping into my savings or emergency funds almost half the time.  If I want to be more confident that I’ll be allocating my budget appropriately, I should plan for a higher level of spending: enough to cover 80% of months.  That means I need to be budgeting at the 1 z-score level and not the average  (Or, we could slash our expenses by eating nothing but Ramen noodles).

Even if I upped our budget to cover an 80% level of spending, we’ll still be short in approximately 2 months of each year!  I have more confidence that the financial plan I’m building will get us where we want to go.  Is it relevant for 20 years from now? Probably not.  But, for the next couple of years, yes.  This model is probably relevant and can give me a good idea of what life will cost, including some pretty major surprises.  With this new information, I can set new thresholds for my emergency funds to ensure that we’re as prepared as we can be if/when disaster strikes.

Has anyone else looked at their spending (or income) with an eye towards variation?  What insight did you draw from the analysis?

Would You Bet Your Life On It?

Look Out!

Look Out!

I’m betting that I won’t live to see my 55th birthday.

Ugh, that was a tough sentence to write.

But, in a way, it’s true: now that my wife and I have a little girl, we’re thinking about buying life insurance.

Which really makes me grouchy!

Why on earth would I dump money into something where I hope I never get paid back!?  Shouldn’t I just put money into an asset that may appreciate?  Won’t my family be better off just cashing out my investments once they’ve had a chance to grow?


Unfortunately, there’s a lot of buses out there, and you just never know if one has your name printed on the front of it.  And, that’s why we carry insurance: to protect us from low probability, high risk events.

  • The house burning to the ground.
  • Someone smashing into our beloved (parked) Scion xB.
  • A sudden stop to the journey we know as life.

Unless you’re already loaded, it’s tough to be completely self-insured (not us, by the way).  So, we’re back to buying life insurance.

More specifically, I’m looking to buy a 20 year term policy.  Let’s keep the math simple and say that we’ll buy a $500,000 policy (we don’t want her to grow up wanting).  I’m almost 35.  With a term policy, the bet that I’m making is that I will die sometime in the next 20 years.  If I do, my girls get $500,000 (assuming my path to the Big Dog Park in the sky met the predefined criteria).  Some really smart mathematicians have figured out the risk (or probability) of someone within my demographics suffering a similar fate.  Using some complex statistics and math, the insurance companies have figured out what premiums (small, routine payments) each person in the population would need to make in order to work out to a profitable business for them.  Their goal is to have more money coming in through premiums than money being paid out in claims.  For an insurance company the aggregate difference between the two is called the loss ratio.

Back to my bet against the insurance company’s…  I received a quote from an insurance company for monthly premiums.  They quoted roughly $20/mo for the first 5 years, and $25/mo for the remaining 15.  In exchange, were I to meet an untimely demise within the 20 year period, the insurance company would pay out the benefit value of $500,000 to my family.  And that’s the bet we’re each making.  The insurance company is betting I’ll outlive my policy so they don’t have to pay up.  I’m making sure my family is covered in the unlikely (I hope!) event of an early ascension (or a bus ride to someplace warm).

So, what are the odds in this particular bet?  In my mind, the insurance company knows the odds of an individual passing, and they set the premiums accordingly.  So I’ll assume that the:

 Payout x Probability Of Dying can be no more than the Cumulative Premiums.

What I think that means is that:

The Probability of Dying <= Cumulative Premiums / Payout

I said I was going to keep it simple.  That’s all the math I’m going to throw at you for this post!

What are the odds? In whose favor are they?

What are the odds? In whose favor are they?

The less than condition is there to cover profit, overhead, etc. that the insurance company factors in to their math (and I don’t have access to that stuff).  Let’s look at the “best” case where I’ve spent the least and receive the payout: tomorrow.  I’ve paid my first month’s premium, and wham!  Fortunately for me that works out to a 0.004% or smaller chance of occurring.  But it could happen, and that’s exactly why I want to “invest” in life insurance.  Our investments haven’t had enough time to grow to cover the costs of raising our daughter, paying for college, etc.  It’s tough to find a $500,000 return for on an investment of $20 anywhere else (25,000:1).

Now fast forward to the last month of the 20 year term.  I’ve successfully dodged buses, riots, airplane crashes, and all other manner of unexpected hazards.  I’ve paid in $5,700 in cumulative premiums (without adjusting for inflation).  Then a slip in the shower and wham!  That < 1.14% chance of death somewhere within the 20 year term worked out in my favor … I guess.  My family still gets the payout, but it cost me the full premium amount.  That’s still almost an 88:1 return.

Let’s look at the most likely case: everyone lives happily ever after.  This is the one that keeps insurance companies in business.  It’s also the one that feels like a warm blanket.  My girls were covered for some of the most vulnerable years of our lives.  I slept better knowing that they would be taken care of in case of unlikely events.  And that’s well worth $5,700 spread out over twenty years to me.


I should mention that in no way should you use any of this to make any life insurance decisions of your own!  Do you homework.  That said, what do you think?  Are the odds worth the expense?  How much insurance do you carry?  What type(s)?

How to Prepare for a Layoff

With the Great Recession officially ending in June 2009, the US economy is almost 7 years into its recovery as of May 2016. Based on recent history, that’s a long run of good times a rollin’. How far in? It’s tough to tell.  The Bureau of Economic Research keeps track of US economic cycles.  Because their announcements tend to lag a peak or a trough (by up to 21 months!), let’s take a quick look at recent historical cycles to get a crude sense of where we might be in this cycle.  If you’re an optimist, you can make a case that the US economy may still be peaking:


If you’re a pessimist, you can argue that the economy is already in decline and we’re heading for the bottom of our next economic cycle:


Regardless of whether you think the economic punch bowl is half empty or half full, if you work for an employer, you have some risk of a layoff to contend with. So, what is a well-intentioned employee to do!?

Let’s set aside brown-nosing, jumping ship, and prayer as possible strategies to prepare for a layoff or other disruption to one’s primary income stream (This is a financial blog after all).

As I see it, there are two basic approaches: defense and offense.


Cold, hard cash (or in a savings account). There is no substitute for a well-stocked emergency fund.  Conventional wisdom says that when looking for a new job, plan for about 1 month for each $10,000 of compensation.  If you want a $100k/yr job, be prepared to spent ~10 months to find it.  …so, how big is your emergency fund?


As I understand it, a Home Equity Line Of Credit is like an open credit card against the equity you’ve built up in your home. Why would anyone be interested in such a critter?

  1. It provides a leveraged way to boost your emergency fund
  2. The interest costs are type far lower than a credit card.  On the order of 3 to 6 percent these days.

Unfortunately, there are also some downsides:

  1. You could lose your house as the HELOC collateral is your home.
  2. you need to demonstrate financial stability now. It’s tough to get a bank to approve a HELOC after you’ve suffered a financial perturbation already
  3. You will be charged interest on your outstanding balance until you pay it back
  4. There is an upper limit to how much of a line of credit you can obtain. How much equity you’ve built up in your home vs. market value is an influential factor.
  5. The interest rates are adjustable ~monthly, introducing volatility

Other Loans (e.g., Personal or Student)

There’s a couple of other loan options.  Personal loans are just that: loans for any personal use.  The lending office will be looking for verification of your income, so if you want to pursue this option (e.g., HELOC not available), get started while you still can show steady income.  Interest rates can vary but be between 6 and 9 percent currently (it’s good to be the bank, isn’t it!?).   If you are currently even a part-time student, you have a pretty cool option available to you: interest deferred student loans.  You’ll have to fill out a Free Application for Federal Student Aid (FAFSA).  Rates vary between 4 and 6 percent these days.

Credit cards

This is definitely a fall back option. I think an extra credit card that is largely unused, possibly with a single bill that auto pays each month, is a great idea. It can help boost your FICO credit score by lowering your percent of revolving debt. The minute you have a revolving balance at 10, 15, or 20% interest, you’re in trouble.  But, for a short term disruption, it might enable you to pay for essentials.


Cut Costs

If there is a pending disruption to your earned income stream, now is a great time to review your current expenses and trim what you can.  Cable, gym memberships, other monthly entertainment subscriptions (Netflix, Hulu, Spotify, Kindle Unlimited, gaming, etc.) are all candidates.  They may not be major drivers of your budget, but they’re easy targets, and they’re pretty quick to cut.  Reduce/negotiate your wireless data plan (we’ve cut ours from almost $130/mo to $85/mo!) Bigger targets of opportunity are certainly out there: housing, transportation, etc.  But, I’ll assume they’re roughly fixed for most folks in the short run.


Diverse Income Streams

Of course, this is one of my favorites (and a prime theme of this blog).  If 95% of your income derives from your day job’s paycheck, losing that income stream is highly disruptive.  If 20% of your income comes from your day job, it’s not such a big deal.  When you have enough income from other sources, you reach the F.U. Point ℠ (that’s “Freedom Uttained”).  Hustle.  Start a business.  Start a website.  Start now.

Unearned Income

Use a portion of your current net worth to generate unearned income.  We’ll revisit this topic in much more detail in future posts.  But, here’s a quick breakdown:

  1. No risk: Set up a CD ladder to earn a bit of FDIC insured interest income on a regular basis.  These days, this amounts to a pittance, but if you shop around, you can find rates a bit better than a high-interest savings account.
  2. Minimal risk: set up a bond ladder or buy into a bond fund (with quality bonds) directing interest payments to your checking account.
  3. Higher risk: buy & hold dividend stocks directing dividends to your checking account.
  4. Crazy risk: Peer to Peer lending where you become the bank to other folks (given that the context for this post is planning for a perturbation in your earned income, this may be folly).

Jump Ship

I said I was going to exclude this from the list, but I’m bringing it back anyways.  If you’re in the fortunate spot where you are finding out about a layoff before it hits, start looking for a new gig now.  Get that resume updated and tap your internal and external networks.

Yes, I said internal…

Not all parts of a company experience a cull in the same way.  You might be able to transfer or rotate much more quickly than finding a new opportunity externally.  In parallel, leverage your external network to see who can use your awesome skills.

A special shout-out to my friend, Dan for providing the inspiration and framework for this post.