9.5 Interest-Rate Risk #Notebook

 9.5 Interest-Rate Risk #Notebook

A Bank's profits highly rely on the difference between what it pays for its liabilities and earns on its assets. 

If interest rates increase +, the difference will decline -

*Because the value of its rate-sensitive liabilities exceeds that of its rate-sensitive assets.

For example, suppose a bank b pays 3% for your deposits and then receives 7% on the mortgages it lent. The difference is 4%, the amounts can be huge if they have billions of assets and liabilities on hand. The bank will be paying $100 billion * .03 = $3 billion to earn $7 billion.

If interest rates increase +1% on each side of the balance sheet, The bank will be paying $4 billion to earn $8 billion. 

Formally, this type of calculation, called basic gap analysis, is

 

Cρ = (Ar−Lr) × △i

Cρ = changes in profitability

Ar = risk-sensitive assets

Lr = risk-sensitive liabilities

i = change in interest rates

Duration, also known as Macaulay’s Duration, measures the average length of a security’s stream of payments. 

△%P = −△%i × d = △%MktV = −△%i × Dyr

Δ%P = % change in market value

Δi = change in interest (not decimalized, i.e., represent 5% as 5, not .05. Also note the negative sign)

d = duration (years)

So, let's get some practice...

Exp I. 

If interest rates increase 2% and the average duration of a bank’s $100 million of assets is 3 years, the value of those assets will fall approximately.....

△%MktV = −△%i × Dyr = −2 × 3 = −6%, or $6 million.

Then, at the same time..

If the value of that bank’s liabilities is $95 million, and the duration is also 3 years, the value of the liabilities will also fall, 95 × .06 = $5.7 million, effectively reducing the bank’s equity (6 − 5.7= ) $.3 million. 

If the duration of the bank’s liabilities is only 1 year, then its liabilities will fall −2 × 1 = −2% or 95 × .02 = $1.9 million, and the bank will suffer an even larger loss (6 − 1.9 =) of $4.1 million. If, on the other hand, the duration of the bank’s liabilities is 10 years, its liabilities will decrease −2 × 10 = −20% or $19 million and the bank will profit from the interest rate rise.

Apparently, we get the key point....

A basic interest rate risk reduction strategy when interest rates are expected to fall is to keep the duration of liabilities short and the duration of assets long. 

That way, the bank continues to earn the old, higher rate on its assets but benefits from the new lower rates on its deposits, CDs, and other liabilities. 

Quite the opposite, when interest rates increase +, banks would like to keep the duration of assets short and the duration of liabilities long.

Reference

Wright, R.E. & Quadrini, V. (2009). Money and Banking. Saylor Foundation.  Licensed under Creative Commons Attribution-NonCommercial-ShareAlike CC BY-NC-SA 3.0 license.