Do you recall how in Pride and Prejudice they are always measuring how wealthy men are in terms of an annual rate?
[H]is estate there is a noble one. A clear ten thousand per annum.
— Mr. Wickham commenting on Mr. Darcy
Consider two ways to measure monetary status: total wealth and income. When talking about the super-wealthy, we often talk about wealth, but when talking about the rest of us, income is often more appropriate. A subtle but interesting aspect of quotes like this from Pride and Prejudice is that they are talking about someone who is quite wealthy in terms of income, but that income is a reflection of total wealth.
For a number of years now I have been trying to sort out the best way to determine an appropriate monthly budget for my family based on my assets and my present income. On one hand, you could just spend as much money as you earn (i.e., completely income-based). This is pretty common. One the other hand, you could try to spend based on your total wealth, which is less common because wealth is less common than income.
Interest Rate Conversion
Recently I was looking at a house I was considering and I wanted to get a better sense of the total cost of maintaining the property, so I took a look at the tax records for the property. Then the following question popped into my mind: if I wanted to buy a 30 year Treasury to cover the cost of these property taxes, how much would it be? Well, at the moment treasury yields are at around 4%:
So let’s say you have a house worth $1M, and property taxes are 1%, so you have to pay $10,000/yr in taxes. Right now you would have to buy treasuries worth $250,000 to cover the taxes. However, not that this is because treasury yields are quite high. If you did the same thing in 2020 when yields fell to 1%, the present value cost of the taxes would be $1M, same as the house!
This is interesting in itself, but it reminded me that once you have an interest rate, you can always convert a present value (i.e., a wealth number) to a rate (i.e., an income number). In fact, any wealth number should be seen as a representation of a stream of income over time.
This article about the economics of Pride and Prejudice mentions that the numbers in that book were based on an interest rate of 4%. And of course, that is the rate for treasuries now. But in fact, interest rates have been falling over time, so that is probably an anomaly.
Constant Rate vs. Present Value
So if we can simply convert from one to another, does it matter whether we express our wealth in terms of income or present value? Yes, but only if interest rates change.
As the Treasury graph above illustrates, interest rates have more than doubled in the past year. When interest rates change, the conversion between wealth and income changes. When rates go up, it means the same amount of wealth provides more income. However, it also tends to depress asset prices. Consider the impact of rising rates on the NASDAQ stock exchange:
Imagine that you had $1.5M in a NASDAQ mutual fund at the end of 2021. The value of your account would now be closer to $1M. This looks like a pretty substantial loss. But now consider that you converted all of your money to Treasuries at the end of 2021. What income would you have? At 2% interest, your $1.5M would get you an income of $30,000 per year.
What if you did the same thing now? At 4% interest, your $1M would get you $40,000 per year. So in present value terms your wealth has gone down but in terms of income your wealth has actually gone up!
This illustration shows that fluctuations in asset values tend to go in the opposite direction as changes in interest rates. Since the income number depends on both numbers, they can cancel each other out. So converting your wealth into an income number can give you a less volatile result than just looking at the stock market.
Combining Wealth and Income
Most of us have a combination of assets and income from employment. So how should we determine how much we spend? Should it be based on assets or income? I propose that one should combine both.
Step 1: Find the net present value of your (after tax) employment income.
Step 2: Combine the net present value of your income with your current wealth to find your total wealth.
Step 3: Convert your total wealth back to an income using current interest rates.
The purpose of step 1 is to ensure we take into account factors like where we are in our career and how much volatility there is in our income. Suppose you have a salary of $100,000, taxed at 25%, so your after tax income is $75,000 annually. If this was your last year of work before retirement, and that you had to live on your savings after that, you wouldn’t want to base your spending that number alone.
So make a guess about what your income will be for the next ten years or so, and discount each year by some discount rate (say, 5%) to account for uncertainty. If this was your last year of working, you would just use a present value of $75,000. If you expect to keep working, use a present value calculator.
If you expect to earn the same income year after year for a long time (say, more than 30 years) than you can get an estimate by simply dividing your income by the discount rate. Let’s do that here to get a net present value of $1.5M.
Now add this number to your wealth. Say you have $500,000 in assets. Add that to the present value of your income to get $2M. Then calculate how much income you would have if you bought bonds at the current interest rate (i.e., currently 4%). 4% of $2M gives $80,000 per year.
Note that this is the number you should spend if you want to smooth out your spending over time, not if you want to grow your wealth.
It’s also important to realize that this number is highly dependent on interest rates. If interest rates suddenly fell from 4% to 2%, and all else remained the same, your target spending would fall from $80,000 per year to $40,000 per year.
So does that mean you should base your consumption on what is happening at the Fed?
Not necessarily. The net present value of the employment income is based on a discount rate, and this discount rate should depend on the current interest rate. In the simplest model you could just use the same rate for both, but a better idea is to choose a multiple. In the example above we used a 4% interest rate and a 5% discount rate, so our multiple was 4/5 = .8. Thus, you can think of that $80,000 per year as resulting from $75,000 X .8 + $500,000 X .04 = $60,000 + $20,000.
If interest rates fell to 2%, our multiple would give a discount rate of 2.5%. The net present value of the employment income would rise to $3M, but converting that back to income based on the 2% rate would give us the same $60,000.
But what about the $500,000 in assets? Well, if prevailing interest rates fall from 4% to 2%, the value of stocks and other assets is going to skyrocket. Let’s say our stock portfolio goes up to $900,000. In a way this is phantom wealth because it is driven by interest rates. And we see that if we multiply $900,000 by the new interest rate of 2% we get $18,000, which is actually slightly lower than before.
The interest rate conversion shouldn’t impact how you think about your employment income too much, but it should definitely determine how you perceive wealth stored in volatile assets like stocks and bonds.
Interest Rates, Wealth, and the Fed
You often hear people accuse the Federal Reserve of keeping interest rates unnaturally low. This may be true, but realize that all evidence points to the fact that rates have been falling for hundreds of years.
If we use the process described above, it means that asset prices (including home prices) will naturally rise to higher and higher multiples of the value they generate. It also means that the amount of wealth you need to live comfortably is going up.
Think about that. If you want to retire on $100,000 per year, you need $2.5M in assets if interest rates are 4% and $10M if interest rates are 1%. The way the world is going, the bar for being comfortably wealthy is getting higher and higher! And although the Fed controls interest rates in the short term, the long term trends are entirely out of the Fed’s control.
One result of all this is that it will become harder and harder to become wealthy by saving money. For more and more people, employment income will be the only meaningful wealth they ever have. It’s like the WEF says:
Should we be concerned about this? Well, there probably isn’t anything we can do about it. Not even the Fed can reverse the trend. All we can do is budget accordingly.