Answers to the recent question "Why don't bond makers just get loans?" Seem to take it as a given that lending someone money at a 12% interest makes sense when there is already doubt about their ability to pay back the same loan at a 5% interest.

That strikes me as counter-intuitive, so I would like to know how that works.

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    Your question represents a fundamental misunderstanding of personal finance. Interest rate is rarely the problem in paying loans, instead it is behavior. Over spending, not budgeting, etc... inhibits people's ability to repay. – Pete B. Aug 15 at 16:52
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    @PeteB. That might be a worthwhile answer, if you can flesh it out a bit. – HAEM Aug 16 at 11:27
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    What's not to understand? The same doubt about their ability to pay is there, but the incentive to take the risk is more than double. – John K Aug 17 at 16:28
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    The top answers take the perspective of a reputable financial institution trying to amortize risk. However by just changing the numbers, you can turn this into a question about predatory lending such as payday loans where suddenly it is the interest rate that's inhibiting the debtor's ability to repay. I assume the theory and motivations there are fundamentally different, but people are conditioned to think about loans from the perspective of a reputable bank? – Mike Ounsworth Aug 20 at 19:57
up vote 218 down vote accepted

It starts to make more sense when you consider a pool of borrowers rather than an individual.

For example, consider a pool of 100 borrowers with a 1 in 100 chance of default, if they all borrow $1,000 for 1 year at 10% APR, you can expect to receive ~$100 interest x 99 borrowers = $9,900 minus the $1,000 from the defaulter. Leaving you with about $8,900 in "profit". (Obviously this is greatly simplified - we're ignoring principal repayments, compounding, the chance of a borrower making a few repayments before defaulting, etc., etc., but hopefully you get the point).

Now consider a scenario where the risk of default is 1 in 10. If you charged the same 10% interest to those 100 borrowers, you could expect to receive $9,000 in interest payments, but you'll lose $10,000 in defaults, so you'd want to charge a higher interest rate to all members of that higher risk pool so that you can still turn a profit.

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    I assume there's some factor to account for non-linearity, specifically I think the point OP is asking about is the idea that charging a higher interest rate would increase the risk of default regardless of the borrower, as you're increasing the incentive to default. For example your 1 in 10 default borrowers might increase to 1 in 9 if you charge more. – poompt Aug 14 at 16:04
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    You are most probably right that the higher interest may itself cause slightly more defaults. If I were to guess, I would posit the relationship between default risk and interest rate resembles a slight upward curve rather than a straight ascent. I'd be very surprised if there hasn't been any academic research on the topic, but I'm not a mathematician, so I wouldn't trust myself to accurately interpret studies for this audience. Perhaps there is a scientist out there who can provide a more definitive answer. – CactusCake Aug 14 at 16:35
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    @BlueRaja-DannyPflughoeft It is, though this is also just how banking works. The specific problem there was that lenders did not realize how their changes in policies were affecting the likelihood of default—they calibrated their numbers based on historical data of default rates, but historically, no one had ever given out so many loans to so many people who were so blatantly unable to repay them. The strategies used to mitigate the risk/damage of default were therefore wildly insufficient for the amount of defaulting that took place. – KRyan Aug 14 at 16:42
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    @Daniel, while a government may appear to be a single entity on paper, it represents all the people of its sovereignty and is backed by taxpayers; that would be the pool in this example. Probability of default can still be estimated based on the government's ability/history of collecting taxes and paying its debts. Governments with less corruption and political unrest get higher credit ratings because lenders feel more comfortable that they will be able to continue servicing their debts; this allows them to borrow more and pay less interest than unstable governments that might be overturned. – CactusCake Aug 15 at 13:03
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    Not only will higher interest rate increase the incentive to default; it will also select for borrowers who are likely to default who were not able to get cheaper credit elsewhere. – R.. Aug 15 at 16:05

It's not that their ability to pay increases with higher interest rates, it's that the lender is compensated for taking on additional risk.

If I lend you money, and have some concern (not a lot, but some) that you won't be able to pay me back, I'm going to charge a higher interest rate, so that I get more return on my money sooner.

Note that a difference between a 5% interest rate and a 12% interest rate represents a very small difference in the probability of default. If I think there's a 50% chance that you're not going to pay me back, I'm not going to lend you money at only a 12% interest rate. It's going to be high enough that I get at least my initial money back before you go bankrupt.

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    I'm not convinced that higher interest rates are intended to recoup the loaned amount sooner. What if the debtor goes bankrupt immediately? The interest rate in that scenario is more or less irrelevant - the lender has lost money whether they were charging 5% or 12% or 50%. It makes more sense to consider the pool of debtors, so that the probability of default for an individual is balanced by the interest from those who do not default. – Nuclear Wang Aug 14 at 16:07
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    But that's looking at what has happened rather than the possibility of what could happen. If a lender knows that the borrower will go bankrupt immediately, they will not loan money at ANY interest rate. In any case, @CactucCake's answer is clearer and better fits the probability model. – D Stanley Aug 14 at 16:16
  • I would argue that loan sharks are trying to get their money back before their client (victim) goes bankrupt. It might not be the mainstream lending model, but it does exist. +1 – CactusCake Aug 14 at 16:37
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    @nuclearwang while this Q&A only addresses interest, with a very high risk of default, nobody will lend without some collateral. See mortgages. They are only possible because the house will become the collateral. Sometimes the collateral can mitigate risk so well that the interest rates go back to a sane level. Without a collateral in a high risk situation, you fall into 'money shark' as CactusCake mentioned. – Mindwin Aug 14 at 17:02
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    I'm not convinced by the "very small difference in the probability of default". With compound interest, 5% doubles the capital in 14 years, 12% doubles it in only 6 years. If you miss a few months, it becomes really hard to avoid a snowball effect at 12%. – Eric Duminil Aug 14 at 23:24

... there is already doubt about their ability to pay back the same loan at a 5% interest.

Another way to think about this is, "If a lender would offer someone with a good credit rating a loan at 5%, why would that same lender offer someone with a poor credit rating the same loan at 12%?"

It's because it's not the "same loan".

The important distinction is that your credit rating determines the interest rate you will receive, whereas your income determines how much you can afford per month (or year).

For example. Based on your income, suppose you can afford to pay $500/month towards a new loan. You wish to purchase a car with a 60 month term. (At 0% interest, the max loan you could afford is a $30,000 loan.)

  • If your credit rating is such that you are eligible for a 5% loan, then the max loan amount would be adjusted to $26,500.
  • If your credit rating is such that you are eligible for a 12% loan, then the max loan amount would be adjusted to $22,490.

In both scenarios the person is paying $500/month. The end result is that for the person with a lower credit rating, the total amount loaned is reduced, the bank's risk is mitigated, but the ability of the person to repay the loan is not affected.

The difference in this case is that you, the bond buyer, are now the lender and you must assess if lending money at 12% is worth the additional risk based on the lendee's credit rating. As long as you feel the lendee is not spreading themselves too thin based on their income, then it might be an investment worth considering.

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    This answer misses the point. Why are people with good credit ratings eligible for that 5% loan? As the other answers point out, the reason is the lower expected losses from (partial) defaults. – MSalters Aug 15 at 7:08
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    @MSalters - I felt that the question already assumed that, other answers already covered that thoroughly, and I also mention it in passing ("the bank's risk is mitigated"). My point is that once the lender (or bond purchaser) has established a risk point, what matters more is the ability to repay the (presumably lesser) loan amount, which is based on income rather than interest rate. – TTT Aug 15 at 13:30
  • I see some of the logic in this answer, but if we assume the borrower only wants $10k, this analysis doesn't make sense. – AndyT Aug 15 at 13:36
  • @AndyT - in the case of $10K (less than what the borrower can afford), then the ability to repay is still not affected, even though the payments are more with the higher interest rate. Lender's risk is still mitigated by the higher rate. You could argue (and I would agree) that if the borrower takes on additional debt in the future, or their income is decreased in the future, then the higher rate could in fact make it more difficult to pay the loan off compared to the lower rate, however, lending decisions are usually based on what's known now, not future speculation. – TTT Aug 15 at 14:07
  • This is a critical point, and the reason I would suggest a better question would be why rates would go up for a borrowing in trouble repaying. For instance, a credit card company might raise interest from 15% to 29% in the event of missed payments. But if the borrower is at the brink of marginal cash flow the increased interest could push them into a debt spiral they couldn't get out of. – Michael Aug 18 at 5:19

Stop thinking like a consumer and start thinking like a lender. You would lend less money to a lower quality borrower at a higher rate than you would a higher quality borrower for a variety of reasons.

Interest is calculated by applying the rate to the principle outstanding in some periodic interval, usually monthly. For back of the napkin calculations you take the annual percentage rate divided by 12. So 0.05 divided by 12 is 0.00416667. So if I borrow $10,000 my first payment will include ($10,000 * 0.00416667) $41.67 of interest. Many loans are amortized over a period of time to make the payment level and predictable for the borrower. If the loan term is 3 years the payment will be $299.71 but $41.67 of the first payment is still interest the difference in payment only changes the amount of principle that's paid.

At 12% the first payment has (10,000 * 0.01) $100 of interest in it. If this is amortized over 3 years the payment is $332.14. For more than double the interest the three year amortization table costs the borrower about 11% more, $332.14 versus $299.71.

Without getting too technical, for the lender this rate change materially changes their income. Again considering the three year repayment terms, when you make your first payment at 5% the lender receives $41.67 of income and $258.04 of returned capital. At 12% the lender is receiving $100 of income and $232.14 of returned capital. The lenders rate of income is ramped up significantly and if you default the principle outstanding at the time of default is a tax deductible loss. If you default after 10 payments in on the 3 year repayment plans in the case of 5% the lender has made $367.74 in interest payments and will write off $7,370 as a loss; at 12% the lender has made $892.70 in interest and will write off $7,571. The loss risk to the lender has not changed much but the income is dramatically different.

Interest rates are a function of your perceived risk in the lending market. If you look more risky, you pay more in interest and can't borrow as much money. Now it should come as no surprise that in order to be successful in lending you must have a large pool of borrowers. If you only have $10,000 to lend you'd be wise to lend $100 to 90 high quality borrowers and maybe the remaining $1,000 is split between 20 lower quality borrowers.

Additionally, your risk as a lender changes depending on the type of loan as well as who the borrower is. A secured car loan is lower risk than a credit card because the lender can come get the car. A personal credit card may be lower risk than a corporate credit card because a fictitious entity can just disappear, but Apple corporate cards probably have more favorable terms than a college student with no credit history could get.

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    Having worked in the 2nd chance auto loan industry myself, your analysis is spot on. +1 – Pᴀᴜʟsᴛᴇʀ2 Aug 14 at 21:59

Excellent answers above (by CactusCake and TTT, respectively) that explain the two key points that:

1) The interest rate for a group is based on probability of default. It's a group characteristic, calculated based on historical data.

2) The interest rate doesn't increase the probability of default, because if they give you a higher interest rate they also approve a lower loan amount. Your burden is the same whichever interest rate you get and doesn't affect your ability to repay.

I would just like to tie them in.

The key thing to understand is the difference between the individual and the group. It's really a bit as if the single customer is invisible to the bank. This is counterintuitive, because he/she provides so much data upon application. Yet despite all that, the bank cannot figure out whether he's going to default or not. The only thing the bank can do is try to match the individual to a segment of existing customers with known historical default rates. So the bank will say (simplified): "OK, this guy is 25 years old, so he's in our 20-30 year-olds cohort, which has a default rate of 10%. For that group to be profitable to us, we have to charge them 8% each." (See CactusCake reply for a simple calculation.)

People think, mistakenly, that when a bank examines their application it is focusing on them and trying to figure out whether they will default. It's not really true. Imagine a bank with zero customers. No matter how many data points about a person it had, and how hard it looked, it simply could not arrive at something like "this guy is 35% likely to default". Only after having historical data can a bank try to match the new customer to an existing group and derive the probability of default from that.

So the sequence is:

Look at customer --> figure out which group he belongs to --> check historical probability of default of that group --> set the interest rate --> adjust and approve the loan amount

It is not:

Look at customer --> reject or approve the loan amount --> set the interest rate (and thus increase/decrease probability of default)

  • Only after having historical data can a bank try to match the new customer to an existing group and derive the probability of default from that. ... FICO, Equifax, Experian and Transunion all very cleverly managed to capitalize on that truth. – CactusCake Aug 14 at 20:26

Counter to the other answers, I'm going to approach this from the perspective that some people who offer loans expect those taking the loan to not be able to pay them back. Reprehensible as it may seem to some, the practice has been in place for centuries of intentionally getting someone into debt so that you can essentially own them as a slave or indentured servant. While today's society technically forbids things like "debtor's prison" or forced servitude, in many countries a lender can still use the legal process to garnish wages, seize property, and generally ruin a debtor. This predatory lending, sadly, is at the basis of many "payday loan" and "check cashing" businesses, as well as some credit cards. Thus, someone may specifically target the person who can't pay back the loan, knowing that they will be able to recoup their initial sum several times over.

  • Research on payday lending at responsiblelending.org/research-publication/… – Bryce Aug 17 at 7:11
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    Nonsense. Lenders who have to resort to garnishing wages or seizing property will see a negative return on investment. In fact, generally they just sell the debt at a reduced rate (like .50 on the dollar) to collections and let them try to collect off of it. It's not a an investment tactic, its just a way to defray loss. Of course there is predatory lending, but that doesn't involve defaulting so much as charging exorbitant rates over long periods of time. – John K Aug 17 at 16:25
  • @JohnK: Payday lenders benefit most from borrowers who are able to make minimum payments for awhile, but never actually pay off the debt. Ideally the borrowers would keep making minimum payments forever, but if the minimum weekly payment is 20% of the original loan amount, the lender would fare better with a borrower that defaults after two months than one who pays back the entire loan in one week. – supercat Aug 20 at 15:25

Say I offer you a lottery ticket for $2.00. You have to guess a number between 1 and 300,000,000. If you guess correctly you win, and get a 5% return: $2.10. If you guess incorrectly you lose, and you get nothing. Would you buy this ticket?

What if instead of picking a number I toss a coin, and if it lands on heads or tails, you get $2.10. Only if it lands on the edge do you lose your money. (Wikipedia claims the odds of this are about 1 in 6000 with a US nickel.) Would you buy that ticket?

To a first order approximation, gambling and lending money are the same game. The lender is betting the debtor won't default. A high chance of default (losing) requires a high return on winning, such that the expected value of the bet is more than the cost plus overhead. Otherwise it's not profitable.

In cases where a debtor has a bit of bad luck and can no longer afford to make payments, often the lender will allow the terms of repayment to be renegotiated. This is called restructuring the debt. Often it involves amortizing the loan over a longer period such that the lender is still repaid eventually, just over a longer time. For the lender this is often favorable to bankruptcy, where the lender may not get a full repayment, or may get nothing at all.

As other answers point out, one of the main reasons for increasing rates to "unsafe" borrowers is compensation for the extra risk (and where the increased chance of default due to the higher rate is accommodated by pooling loans across a number of borrowers).

Another factor is that a higher interest rate raises the "cost of money" and may make a company decide that its plans are ill-advised or not worth the risk.

If the cost of borrowing is "too cheap" a company that is already "at risk" may nevertheless go ahead with what might be a risky, over-ambitious plan to try and turn its fortunes around. If the cost of borrowing is higher (as it will be for "riskier" companies), then this increased cost may make them pause and consider whether there are better (and cheaper) ways of solving their problems.

  • In some cases, there may be a less risky, probably slower, course they can take to reduce what makes them "risky" in the first place. If successful, they might then be able to adopt the original plan, but should now be able to do so at lower interest rates.

  • In some cases, they may decide that the risk of failure is low enough (and the potential reward high enough) that they are prepared to pay the higher price, and will proceed with plan. (Or, it may be that they are in a "do or die" situation, and that not proceeding will almost guarantee failure, so they will take the chance anyway.)

  • Of course, some companies would go ahead with their original plans anyway (at the higher rate of interest) and ignore the possibility of a better option.

For the lenders point of view, the higher rate will weed out some of the riskiest borrowers (they'll do something else). Of those that still proceed, some will succeed (and pay back the loan/bond), compensating the lender for the (hopefully small) number that proceed with the loan and then go on to default.

If there is doubt whether the borrower can pay, it’s a riskier investment than if the borrower has a good credit score, or better history of repayment. Because of this increased risk, the lender can charge a higher interest rate to help cover their risk and potential losses.

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    Welcome to money.stackexchange. Please try to avoid duplicating other people's answers. Please see a much lengthier and clearer explanation along the same lines by CactusCake. – AndyT Aug 15 at 13:38

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