Finacial poster

The most obvious cause for different borrowing and lending rates are differences in opinion between the lender and borrower. To think about this particular assumption violation, we must work in a world of uncertainty—it would be absurd to believe that such differences in opinion could exist if there is no uncertainty. So, what happens if the lender and borrower have different information or different judgment about the same information? Most prominently, they could disagree about the default risk! For example, if you have no credit history, then a lender who does not know you might be especially afraid of not receiving promised repayments from you—from the perspective of such a lender, you would be extremely high-risk. Your lender might estimate your appropriate default probability to be 20% and thus may demand an appropriate default premium from you of, say, 8% above the risk-free yield. On the other hand, you may know that you will indeed return the lender’s money, because you know you will work hard and that you will have the money for sure. In your opinion, a fair and appropriate default premium should therefore be only 0-1%.
When your potential lenders and you have different opinions, you then face different expected savings interest rates and borrowing costs of capital. That is, if you know that you are a low risk, then your borrowing cost of capital (the expected interest rate) would not only be much higher than the lender perceives it to be, but it would also be the case that your borrowing expected cost of capital is much higher than your savings expected rate of return that you would earn if you deposited your money in the bank. You might be able to borrow at a cost of capital (expected rate of return) of 12%, but save only at an expected rate of return of 5%.
It is not just that you must offer a higher promised rate of return than what you expect to repay. Instead, you must now offer a higher expected rate of return when you want to borrow, compared with the expected rate of return that you could earn if you deposited money in the bank. (The bank is unlikely to go bankrupt, and your deposit is probably insured by the government, which means that the bank may pay not more interest than the equivalent short-term Treasury. The bank’s promised rate of return is almost the same as the expected rate of return.) The difference in stated borrowing interest rates and stated saving interest rates at your local bank could just as well be the default premium—the difference in the returns you promise and which you expect to pay, although in a different guise. The bank quoting you a lower savings deposit interest rate than borrowing loan interest rate would just compare promised interest rates, not expected interest rates. Instead, the novel issue discussed in our blog is that disagreements and information differences are now causing differences in expected returns. The borrowing and lending expected rates of return are no longer the same.Perfect Market Default Spread Assume you have a 5% objective probability of total default. In this case, a risk-neutral bank would ask you for a return of 5% · 0 + 95% · x = (1 + 10%) · $1, 000 ⇒ x ≈ $1, 158 . (6.1)
This 15.8% interest rate is not a market imperfection. It is merely compensation for your probability of defaulting. Both you and and the bank would realize that you are paying a 10% cost of capital.
Imperfect Market Credit Spread Now assume that you believe you have a 3% objective probability of total default, and the bank believes you have a 9% objective probability of default. In this case, the bank would quote you an interest rate of 20.9%. You, in turn, would consider this $1,209 in payment to be equivalent not to the 10% expected rate of return that the bank believes it is, but equivalent to a 97% · $1, 209/$1, 000 ≈ 17.3% interest rate.
You would consider the 7.3% to be the extra spread due to friction—but, of course, who says you are right and the bank is wrong?