Kling On Mankiw On Banks And Modigliani-Miller

A comment I posted on EconLog, "Banks and Modigliani-Miller" by Arnold Kling:

The Fisher separation theorem says that the investors (shareholders, depositors) are not concerned with the investment choice opportunities (the fruit trees) of the bank, as long as the bank invests in positive NPV (net present value) projects. Investors choose their own positive NPV investment opportunities for their own funds separate from the bank's investment opportunities.

MM [Modigliani-Miller] says that the value of the firm, and consequently, the NPV (net present value) of the projects, is independent of the way that the projects and the firm (bank) are financed.

To the extent that a firm can take a tax deduction for interest payments, the deduction is a government subsidy to firms. It allows borrowers to pay, and the lenders to demand, a higher interest rate due to the government subsidy, which by itself should offset the benefit of the tax deduction. If the lender is also taxed on the interest income, then the two taxes will offset each other. If the taxes are equal, then it will be as if there were no interest deduction and if the two taxes are different amounts, a new equilibrium supply and demand point (interest rate cost of borrowing) will occur depending on which tax is higher and by how much. If the two taxes are equal, as they most likely are, the interest deduction will have no effect on leverage. Likewise, if there is only a tax deduction there will be no effect on leverage due to the higher interest rate. It is only when there are different income and deduction tax rates, that there will be some minor leverage effect.

Deposit insurance is a put option (all insurance is a put option) given to the depositor through the bank by the FDIC. Because deposit rates do not risk adjust due to the put, the bank can invest in a greater number of projects with apparent positive NPVs due to low cost deposits. Some of these projects would have a negative NPV if the deposit interest rate adjusted for the riskiness of the project and the bank. The market, however will risk adjust the rate and treat some apparent positive NPV projects as negative NPV projects and decrease the value of the publicly trade stock of the bank.

Deposit insurance fools management, not depositors, as to their available investment projects.

The deposit insurance will have little or no value to the depositor as long as the market value of the assets of the bank is greater than the value of the deposits. The put option will be out of the money. As the market value of the assets declines, due to bad investments, and no longer covers the amount of the deposits, the put option (the FDIC insurance) becomes in the money and increases substantially in value.

Since the bank transfers its assets to the FDIC for the insurance (put) payment of the deposits to the depositors, the FDIC bears all the risk and monetary loss. The FDIC insurance is only paid when deposits exceeds assets. The FDIC pays the full amount of the deposits and loses the excess amount of the deposits over the value of the assets it receives, deposits minus assets.

The essential transparency that is lacking is the value of the FDIC insurance put by institution. However, the publicly traded equity of the bank reflects both the true NPV of the projects on a risk-adjusted cost of financing and reflects the decrease value of the bank due to the value of the put due to the probability of the exercise of the FDIC put and takeover of the bank by the FDIC.

In effect, tax deductions do not increase leverage because it will increase the cost of borrowing and are probability probably completely offset by the tax on interest income.

Deposit insurance allows banks to invest in otherwise negative risk adjusted NPV projects. While deposit insurance allows banks to invest in unprofitable and negative NPV endeavors, the market price of the asset will be independent of deposit costs or deposit insurance. This is the liquidity funding problem. Banks can have enough funds to invest in a positive NPV valued asset that does not have enough market value to roll over as collateral to fund the asset.

Long-term rates are just the (geometric) average of expected short term rates except for the short-term liquidity premium, and banks will on average just make a small liquidity premium spread. Since long-term rates are just expected averages of short-term rates, half the time the short-term rates will be less then the long-term rates and half the time more than the long-term rate [after adjusting for the short-term liquidity premium]. Half the time, the bank will have a positive interest rate spread and half the time it will have a negative interest rate spread.