Saturday, July 10, 2010

Why the Poor Should Pay Higher Interest Rates

Try as I may, I've found that its become increasingly difficult to convince "I have a right to healthcare" folks that they're wrong. I've produced a few adherents, but in terms of conversion rates its been an abysmal attempt. I enjoy the formal disproving process, but it would be nice to produce some influence.

Adding to the amalgam of illegitimate rights-claims is the alleged right to credit, the idea that such a thing as a moral entitlement to loanable funds exists. Of course, the belief in such a notion lies behind everything the federal government has done within the last 40+ years to promote homeownership, particularly among the poor.

At the same time, left-collectivists have been lamenting the fact that poorer borrowers often pay higher interest rates than wealthier borrowers on loans of similar maturities. Intuitively, this seems unjust: shouldn't wealthier borrowers pay higher rates given that they are more capable of paying them than poorer borrowers? Does this not prove that the market allows for the existence of exploitative, financial arrangements? Hardly.

A comparison of two credit transactions with similar maturities, one involving a wealthier party and one involving a poorer party, will help to legitimize the disparity. Let's assume that Simple Loan Inc., an institutional saver/creditor, unveils its willingness to offer $10,000 loans to potential borrowers. In other words, Simple Loan is willing to form loan contracts with potential borrowers. A loan contract is a voluntary agreement between two parties where one party, the creditor or lender, agrees to transfer ownership over an amount of money to the other party, the borrower, in exchange for a promise (usually expressed in written form) from the borrower to receive the exact same amount (the principal) back on a future date plus an additional amount (the interest) as a fee to compensate the lender for the time he/she spends without the principal.

Now, a lender in a loan contract cannot know with complete certainty that his respective borrower will repay him with the entire principal and interest fee. The future, as far as specific human conduct is concerned, is uncertain. We can only form probabilistic conclusions with statistics and inductive reasoning regarding repayment. Thus, if Jack borrows $10,000 from Simple Loan, Simple Loan cannot know with certainty that he will reimburse them. He can either repay or not repay; to use probability jargon, these are "mutually exclusive events."

Using the probability calculus, the situation involving Jack and Simple Loan would look as follows:

P(reimbursement v non-reimbursement) = P(reimbursement) + P(non-reimbursement) = 1,

meaning "the probability of reimbursement plus the probability of non-reimbursement equals 1." The sum of each is 1 because the probability that either will occur is 100%. Moreover,

P(non-reimbursement) =
default risk (r),

the default risk being the probability that Jack will fail to reimburse Simple Loan.

The trouble for Simple Loan, and any lender for that matter, is quantifying the default risk associated with a potential borrower, including Jack. This is done by mathematically assessing Jack's ability to remunerate the loan. While Jack's ability to repay is expressed in quite a few ways, it's done so essentially through his productivity. The more productive Jack is, the more money he'll have, hence the greater probability he'll repay; the less productive Jack is, the less money he'll have, hence the lesser probability he'll repay.

Let's assume that Simple Loan's credit assessment of Jack unearths that he is fairly productive and, as a result, earns $100,000 annually. He pays his bills on time and has not failed to repay past loans. Let's further assume that given all of this information, Jack and Simple Loan agree to a $10,000, 7% simple loan contract.

Now assume that Adam is interested in borrowing money from Simple Loan as well. However, according to his credit assessment, he is approximately half as productive as Jack, earning only $50,000 annually. He's been shown to be delinquent at times when it comes to paying his bills and has delayed the repayment of his debt in the past. Given all this information, Simple Loan may agree to extend a simple loan of $10,000 to Adam, but only at a 10% interest rate. Is such discriminatory lending justified? Absolutely.

The reason why Simple Loan is justified in charging Adam with a higher rate than Jack for a loan of the same amount and maturity is because the default risk associated with Adam, who is less productive and therefore poorer than Jack, is higher than the default risk associated with Jack. This means that the probability that Adam will fail to reimburse Simple Loan is greater than the probability that Jack will fail to reimburse Simple Loan. Risk, any risk, is bad. If the risk associated with an investment increases, then the probability that the investment in question will yield a profitable return decreases.

The argument for such discriminatory lending is simple: Risk is a bad thing. Things that are bad ought to be mitigated. Therefore risk ought to be mitigated. The default risk associated with a risky borrower can be mitigated by increasing the interest rate charged to the borrower in question. In this case, the difference between Jack's rate and Adam's rate is an example of a default risk premium. A default risk premium is an increase in an interest rate charged by a lender to a borrower as compensation for incurring greater default risk on a debt instrument. Thus if Jack's rate is 7% and Adam's rate is 10%, then the default risk premium in this case is 3% (default risk premium = Jack's rate - Adam's rate). With a default risk premium attached to Adam's rate, Simple Loan can mitigate the default risk associated with Adam, i.e., the probability of a loss, by increasing the probability of a profitable return. The mathematics of Jack's loan and Adam's loan would look as follows:

The equation demonstrating the return on a simple loan is:

FV = PV(1 + i), where

FV = future value or the amount earned by the lender
PV = present value or the amount initially given by the lender to the borrower (also known as the principal)
i = interest rate or price of temporary ownership of the principal


PV = $10,000
i = 7%
r = 3% (default risk premium attached to Adam's loan), then Simple Loan's return on Jack's loan (should he reimburse) would look like this:

FV = PV(1 + i), $10,700 = $10,000(1 + 0.07)

Simple Loan's return on Adam's loan (should he reimburse) would look like this:

FV = PV(1 + (i + r)), $11,000 = $10,000(1 + (0.07 +0.03))

The addition of a default risk premium may prima facie seem opportunistic, but after thoughtful analysis it should be understood that a default risk premium benefits both the lender and the borrower. The benefit to the lender is obvious; it allows the lender to mitigate against default risk and earn a higher return. However, a premium benefits the borrower as well by enabling the borrower to become creditworthy. Without default risk premiums, most lenders would refuse to lend to riskier borrowers. Default risk premiums effectively incentivize lending to such borrowers. Thus, default risk premiums increase the potential for positive-sum transactions.

Furthermore, default risk premiums increase the potential for third party benefits as well. By incentivizing lending to riskier borrowers such as small, fledgling businesses, such premiums increase the amount of financial capital and, therefore, the potential for profitable investments. Risky businesses that otherwise would not have financial capital now can acquire capital and use it to acquire more labour (i.e., create jobs), acquire more or better capital goods, or invest in R&D - business decisions that all serve to increase productive capacity and therefore the broader economy.

Risk is an omnipresent phenomenon. Default risk premiums allow lenders to cope with risk, risky borrowers to get their hands on financial capital, and other economic agents to benefit from investments in riskier firms. Abolishing such premiums reverses these trends, making lenders unnecessarily conservative, risky borrowers unnecessarily cash-starved, and third parties unnecessarily less well-off.

Picture via
George Eastman House Collection

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