### Stash Rate

Financial Independence, simply defined, is when your passively produced income is enough to pay for your life’s expenses.  But how do you get there?  When at the beginning of the path, it can seem daunting.  Even imaging enough wealth to generate that kind of passive income is a challenge.  However, the good news, and the real point of this blog, is that the decisions we make along this path drive non-linear results.

A mathematician would tell you that a linear function is defined by the output being directly proportional to the input.  Your elementary school teacher would say they make a straight line on a graph.  Fortunately, on the quest for Financial Independence, we leverage the power of non-linear mathematics.  Maybe the most powerful, the exponential effect of compound interest when investing, we will get to later.  However, it starts with the disproportional effect of saving versus spending.  Let’s explore that now.

A useful metric to track is the Savings Rate, commonly defined as the amount you save in a year divided by the total amount you make in a year.  So, as an example, let’s say you had take-home pay of $50,000 in a year and spent$40,000 on expenses that same year.  That gives you $10,000 left over, which by definition you have saved since you didn’t spend it. $Income\ per\ Time\ -\ Expenses\ per\ Time=Savings\ per\ Time$ Your savings rate would then be calculated as: ${10,000 / year \over 50,000 / year} = 0.2 = 20\%$ One thing I like about this function is that it is dimensionless; the and are both in dollars per year and cancel out so the result has no units. We interpret it in this case as a percentage: the percentage of your take home pay saved. In fact, as long as the time period is the same between the income and savings, you could evaluate the Savings Rate over any period of time, from a single paycheck to years. A year is a common choice because many of our life’s expenses come in chunks that repeat annually. For example, looking at the first few months of the year might not give a clear picture if a bunch of tax payments, insurance premiums, and holiday spending skews the result later in the year. So more generally, the equation is: $Savings\ Rate={Savings\ per\ Time \over Income\ per \ Time}$ Being dimensionless makes it easier to compare. Two people with different incomes may have very different savings goals, but they can compare savings rates to give them a common language to discuss Financial Independence. However, there are some issues with this calculation. Is it before tax or after-tax income? Where do 401k contributions go? Ask these questions of different experts and you will get different answers. It’s also not immediately clear what effect different saving rates have on your path to Financial Independence. A related calculation I use is the Stash Rate. Much like the savings rate, this is a dimensionless number. It is defined as: $Stash\ Rate={Savings\ per\ Time \over Expenses\ per \ Time}$ Notice in using this equation that we have eliminated the income term. When looking at a year, for example, you now take the total amount of money you stashed away in any savings or investing vehicles (we will dig into the different types in future articles and why they all count) and divide it by your expenses for the year. The result can again be interpreted as a percent, but it may be more useful to think of it as a multiple. Let’s look at some numbers to see what I mean. Using the same example as before: $Stash\ Rate={Savings\ per\ Time \over Expenses\ per \ Time} = {10,000 / year \over 40,000 / year} = 0.25$ This time, instead of$50,000 of income in the denominator, you have $40,000 of expenses. The important result is that you have saved 0.25 of a year’s worth of expenses. This is meaningful on the journey to financial independence. If you can save 0.25 of a year’s worth of expenses, then the message is simple. You can work for 4 years and afford to take off (0.25 + 0.25 + 0.25 + 0.25 = 1.0). Some people with aspirations to take a year to travel the world or dive into a startup may do exactly that. The rest of us may instead choose to work many years and take the remainder off. But the numbers here aren’t very promising yet. In the example, you would have to work 40 years just to take 10 off. The compounding returns of investing our savings will certainly help, but compounding takes time. For those of us looking to reach financial independence earlier, there must be a better a way. Fortunately, non-linear math comes to our rescue! The way to accelerate this path is to Grow the Gap. To grow the gap, we must put as large a gap between our income and our expenses as possible. To continue with the example in this article, let’s say your income is fixed (a common scenario of W-2 job where we expect modest raises, just keeping up with inflation over the years) so we focus on your expenses. In other articles we will tackle different methods and life hacks to do this. For now, let’s just focus on the numbers. Let’s say you can reduce your expenses by 10%. What happens? Expenses were$40,000, now they drop to $36,000. By definition, that means your savings now increases to$14,000.  Therefore, your Stash Rate climbs to:

${14,000 / year \over 36,000 / year} \approx 0.39$

Now that’s interesting: you reduced our expenses by 10% but your stash rate went up .  Instead of working four years to have one free, we’ve brought it down to just over two and half.  Let’s try another example.  What if you can decrease our expenses by 25% all the way to $30,000? ${20,000 / year \over 30,000 / year} \approx 0.67$ The stash rate tells us how many years of freedom we’ve bought. In this case, you’ve bought a full two-thirds of a year in just one year. If you can get your savings to match your expenses, then not surprisingly you have bought yourself a year of freedom in just of working. As we approach and then cross a stash rate of 1.0, the impact flips. We can now take more than a year off for every year we’ve worked. If we can save 3 dollars for every dollar we spend, we can work a year and then take 3 off. You could work 15 and take 45 off, flipping traditional retirement on its head! Remember the Stash Rate definition: the vertical axis can also be interpreted as years of expenses saved per year worked. Note the crossover point at 50% Stash Rate accumulating one year's worth of expenses. What’s your financial situation? Can you save a dollar for every dollar you spend? Can you save three? It might be hard in our$50k example to imagine spending only $12,500 per year, but it’s not impossible. More realistically, we’ll pull both levers of Grow the Gap and try to increase our income at the same time. Making$100,000 and spending $25,000 so we can save$75,000 doesn’t seem as farfetched.