A customer asks a bank if it would be willing to commit to making the customer a one-year loan at an interest rate of 8% one year from now. To compensate for the costs of making the loan, the bank needs to charge one percentage point more than the expected interest rate on a Treasury bond with the

Question

A customer asks a bank if it would be willing to commit to making the customer a one-year loan at an interest rate of 8% one year from now. To compensate for the costs of making the loan, the bank needs to charge one percentage point more than the expected interest rate on a Treasury bond with the same maturity if it is to make a profit. If the bank manager estimates the liquidity premium to be 0.4%, and the one-year Treasury bond rate is 6% and the two-year bond rate is 7%, should the manager be willing to make the commitment?

Accepted Answer

The bank manager is unwilling to make the loan because at an interest rate of 8%, the loan is likely to be unprofitable to the bank.

[latex]i^{e}_{t+n} =\frac{(1+i_{n+1t} -l_{n+1t} )^{n+1} }{(1+i_{nt} -l_{nt} )^{n} } -1[/latex]

where

[latex]i_{n+1t}[/latex] = two-year bond rate = 0.07

[latex]l_{n+1t}[/latex] = liquidity premium = 0.004

[latex]i_{nt}[/latex] = one-year bond rate = 0.06

[latex]l_{1t}[/latex] = liquidity premium = 0

[latex]n[/latex] = number of years = 1

Thus,

[latex]i^{e}_{t+1} =\frac{(1+0.07-0.004)^{2} }{1+0.06} -1=0.072=7.2\%[/latex]

The market’s forecast of the one-year Treasury bond rate one year in the future is therefore 7.2%. Adding the 1% necessary to make a profit on the one-year loan means that the loan is expected to be profitable only if it has an interest rate of 8.2% or higher.

Question 5.5: A customer asks a bank if it would be willing to commit to m...

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