Since I wrote *Get Rich Slowly *I’ve received a steady stream of questions regarding personal finance. The most common of those is: **should I prioritize investing or paying off my debts?**

*Get Rich Slowly *wasn’t meant to break any new ground, just summarize some of the best advice online in a clear way for my readers. So, I thought I could just look up the existing best advice on debt vs. investing. I did, it sucks.

A lot of places tell you to invest if the return you’re expecting is higher than the interest on your debt, but that completely ignores risk. Taking a loan at 20% to invest in a highly speculative venture with expected returns of 20.1% isn’t smart investing, it’s a reckless gamble that’s likely to leave you bankrupt. *The Balance,* one of the most popular personal finance websites, mentions the importance of risk-adjustment but is too lazy to do the math explicitly. It also recommends maxing out your Roth IRA (expected return 6-7% with a fair bit of risk) before paying off credit cards (20%+ interest rate), which is utterly insane.

Risk adjustment is difficult and subjective, but there’s no escape from putting a number on it ourselves.

## Anti-investment

I like to think of debt as an anti-investment. Let’s say you have a $10,000 loan which charges 5% interest, and you also have $10,000 invested with a risk-free after-tax** **return of 5%. The two would cancel each other out – your cash flow is the same as if you had neither one, namely zero. So, if you pay off the loan, you can think of it as **gaining a risk-free investment** with the same after-tax return as the loan’s interest rate.

What if instead of paying off the loan you invest the money? Then instead of the risk-free investment, you gain a different one. For example, if you invest the money in an S&P 500 US stock index, you will gain an investment that should return 7% (or 6% after paying capital gains tax), albeit with quite a bit of risk.

Thus, the question of paying off the debt becomes a comparison between a risk-free investment and your best alternative investment option. The question becomes: **what risk-free rate of return is equivalent to your best available investment?** If you pay a higher interest on your debt than that, you should pay it off. If the rate you’re paying is lower, you should invest. In our example, if you like holding a risky 6%-return stock fund about as much as a risk-free 3%, you should pay off any loans that charge you more than 3%.

This may not seem like an easier question to answer, but we can attack it from several angles. At the core of this decision is a consideration of how much the *risk-free* part is worth to you, which is going to be different for each person. I will use the S&P 500 as the example of investment under consideration, but you should consider your own considerations instead.

## 0. Better loan

If you can get a loan for a lower interest rate than your current debt, you should just take the new one out to repay the old one. Duh. You could have an opportunity to borrow at lower rates for any of the following reasons:

- You improved your credit rating.
- You married someone with a better credit rating (I should add that to the matrix).
- You got into a degree program and can get student loans (which are cheaper because they’re not dischargeable).
- You bought/inherited/stole an asset that can be used as collateral.
- You got over yourself and borrowed the money from your parents.

Remember to calculate the interest rate on an after-tax basis too, so a 6% mortgage can really only cost 4% if you can deduct the mortgage interest from your taxable income. Taking a mortgage to pay off worse loans is a smart thing to do.

And with that out of the way, here are some reasons why a risk-free investment (which is what you’ll “gain” by paying off the loan) may better than the S&P 500 even with a lower rate of return.

## 1. Arbitrage

Whatever your preferred investment option is, there’s probably one with a higher return that’s just too risky for you. This can be something like junk bonds, an emerging markets index fund, or even simply a levered S&P 500 fund (which multiplies the risk and return). If you had a risk-free investment, you could invest part of it in the high-risk high-reward option and end up with a better overall deal.

Here’s a numerical example that may or may not make this clear:

The S&P has a yearly volatility of 15-20% (call it 17%) and a return of 6%. Let’s notate this [6,17] The MSCI world index (global stocks) has higher returns but is also riskier, perhaps [8,25]. In a vacuum, you may prefer the former. But what if you had a risk free 5% return [5,0]? You could invest 40% of that in the MSCI and end up with 60%*[5,0] + 40%*[8,25] ~ [3,0] + [3.2,10] ~ [6.2,10], or 6.2% returns with 10% volatility. That’s certainly a better deal than [6,17].

If you didn’t follow the example or you don’t like using yearly volatility as a measure of risk, you’ll just have to trust me that this principle holds. Back in our original formulation, paying off some *part* of your loan and investing the remainder in something with a higher yield can result in better returns and a lower risk than investing the whole amount in the S&P.

## 2. Utility of money

A good reason to be risk averse is that the value you derive from every extra dollar diminishes with every dollar you have. Going from $100,000 to $200,000 (whether in wealth or income) will give you a bigger happiness boost than going from $200,000 to $300,000. This means that a guaranteed $200k is better than a coin flip between $100k and $300k. There’s research showing the happiness depends on the log of income, so you’d need the coin flip to be between $100k and **$400k** to equal a safe $200k.

(I previously used this fact to propose a new measure of economic inequality.)

If you invest $100,000 in the S&P 500, after 16 years (at 6% return) you’ll have $250,000 on *average*. But it could be a lot more or a lot less, somewhat like a $100k-$400k coin flip. But to get to $200,000 you only need a risk-free investment at 4.6%.

## 3. Planning

This is closely related to the point above: a guaranteed return is better than a volatile one because it allows you to plan ahead. Whether you’re planning hit the milestone number for retirement, buy a house, or get that last bit of uranium ore from Amazon you need for your “peaceful” nuclear program, knowing how much money you’ll have in the future makes it easier to plan. If your future returns are volatile, you will probably need to aim for a higher number to guarantee you have enough to reach that all-important critical mass.

## 4. The Beta of your life

A risky investment isn’t just bad in itself, it also contributes to the overall risk of your economic life. If you live and work in a developed economy, almost everything you can invest in will be positively correlated with everything else, and with your career as well: US stocks, global stocks, corporate bonds, real estate, natural resources, even government bonds (especially during crises).

This means that in the worst-case scenario everything can turn sour at the same time: the economy tanks, your investments lose value, your job is at risk, etc. A risk-free investment can isolate you from that pain, or, conversely, debt will make that pain much worse. This again should make risk-free investments more attractive even at lower return rates, especially if the rest of your eggs are in the same few baskets.

There are some possible investments that aren’t positively correlated to everything else, such as cryptocurrencies (maybe). But if you’re reckless enough to take out loans for the purpose of buying crypto, I have a bunch of JacobCoins to sell you.

## 5. Risk aversion

Humans have evolved to be averse to risk and unnecessary gambles. Some of this risk aversion is rational in the case of investments – see points 1-4. But even the irrational part is still part of you, and having volatile investments will fray your nerves and cost you sleep regardless of the math you do.

## Summary

I know it seems weird to compare existing choices to an option you don’t really have (a risk-free investment with arbitrary return), but that’s exactly what debt is. Or rather, that’s exactly the opposite of what debt is.

Different people will give different weights to the five factors I listed, but it’s important to remember that they’re additive, not exclusive. The more you care about any of them the lower the return you would be happy with if you could get it risk-free, and thus the lower rate of interest on your debt that you’ll hold.

Most of my own money is in stock index funds. I expect a 7% return from my retirement savings (401k and IRA) because they’re tax-free, and 6% return from my medium-term savings. I’d be happy to replace those with a 4% and 3% return, respectively, if I could get it risk-free.

This means that I:

- Don’t hold any debt at above 4%. If I had any, I would sell some short-term investments to pay it off right away.
- Will happily borrow money at 2-2.5% to invest in stocks, and will consider borrowing at 3-3.5% only if it goes to retirement (for example, if I need it to max out the yearly Roth IRA cap).
- Will happily lend at 5-6% for something close to risk-free, such as a short-term loan to a close family member or friend, because that’s a better deal for me than my investments.

And finally, since good investments with returns above 6% are very hard to come by, if you have any debt at 5-6% or more you should almost certainly pay that off before investing a single penny. It’s a very un-American piece of advice to hand out on July 4th, but it’s the truth.

Another factor that weighs against paying off debts is the value of flexibility.

Suppose I put some savings to work in an index fund. If I have an unexpected expense (or, more optimistically, an unexpected high-quality investment opportunity), I can tap that investment for cash. But if I spend the same amount paying down student loans, I can’t exactly call Sally Mae six months later and say “Can I take back that payment? I found a better use for the funds”.

Basically, every dollar you put into index funds becomes part of your safety-net / flexibility-fund, while money paid to creditors disappears into a black hole.

Also, shouldn’t our standard for “risk-free” be US bonds? In any situation where the US isn’t paying its debts, I doubt that creditors will have a means to enforce their contracts anyway.

My personal heuristic is to only pay off loans when

(1) the interest is substantially higher than treasury yields and

(2) I don’t assign much value to the option of re-allocating the funds later

I think it makes particular sense for recent graduates (with negative net worth) to pay the minimum on their student loans as long as possible while they build up a safety-net, as a form of self-insurance.

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I love this comment! I saw this point raised in one of the advice articles, but I ignored it to keep the article focused. I decided to just hope that one of the commenters will spell this point out clearly.

One caveat: both opportunities and emergencies are less likely to occur the greater the sum involved is, while the interest you pay scales. Keeping $100,000 available as “dry powder” isn’t 10 times as useful as keeping $10,000, but it costs 10 times as much.

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I never realized that the ability to add variances of sub-samples had a financial application!

I feel like this realization and the EMH suggest a bound to expected returns and risk. In particular, suppose you have 3 investments with return/variance (A, V_a), (B, V_b), and (C, V_c) and suppose A < B < C and V_a < V_b < V_c.

Now, we know we can get B returns by investing x% in A and (1-x) some in C. This will yield an investment opportunity with variance

V_d = V_a * (B-C)/(A-C) + V_c*(A-B)/(A-C)

Now, if V_b > V_d, then no one would invest in B, so we know that

V_b ≤ V_d.

I don’t have time to try to prove anything, but I feel like this suggests that expected variance must increase linearly or super linearly with expected returns.

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For long-term investment purposes, it’s probably worth mentioning the Kelly Criterion. Assuming returns in each timestep are independent, the long-run rate of growth is maximized by maximizing the expected log return at each timestep.

The Kelly criterion naturally handles the “hey why not leverage everything up the whazoo” problem, without artificially inserting risk bounds.

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The method I would use is to bung it into a Monte Carlo and compare to a load of other alternatives – each chucked into their own Monte Carlo.

I use https://www.getguesstimate.com but Excel can work. A

simpleexample is: 10k loan with a yearly interest of 5% gives 10.5k at the end of the year. If that was invested into something with a return of 10% then you would get a profit of £500 and it seems worth it. But if the 90% confidence interval is -10% to +30% then the confidence interval for the profit come out to be about £-1500 to +2500. This is a very different result, and seeing it on a graph can help you decide if the expected value (£500) is worth the risk – if you are an “econ” it just depends on your ability to cope with the losses if they occur.Which is all a bit unfair: if losing £1.5k isn’t a big deal for you then you make an expected £500, if losing £1.5k would be very bad then you don’t get the £500, even though you need it more and the utility of the extra £500 is worth a lot more for you (the poorer person)!

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