EC203 CH 6: Different Interest Rates and Risk

Nominal Interest Rate

interest rate in dollar terms showing how fast a dollar amount grows

Real Interest Rate

nominal interest rate adjusted for expected inflation showing growth of purchasing power

Formula with nominal and real interest rate

1+r = (1-i)/(1+expected inflation)

Approximate Formula for real interest rate

r = i - expected inflation

Ex-ante real interest rate

Real rate based on expected inflation

Ex-post real intrest rate

real rate based on actual inflation

If expected inflation increases, what happens to real interest rate?

falls

when nominal interest = real interest, what is expected infaltion

0

Zero Lower Bound (regarding nominal interest)

nominal interest rates cannot fall below 0 because people would hold cash instead

Real Interest Rates can be negative and as low as?

Negative expected inflation

Liquidity Trap

when the economy is stuck at ZLB and monetary policy cannot reduce interest rates further

Risk Premium (z)

extra interest charged on risky bonds compared to risk free bonds

Formula for interest rate on a risky bond

i + x

Why must risk and risk free bonds have the same expected return?

Arbitrage

Formula for expected Return on a risky bond

(1-p)(1+i+x)

What happens to borrowing cost for firms when risk premium rises?

investment falls

Investment Function in Extended IS-LM model

I(Y, r+x)

Extended IS Equation

Y = C(Y-T)+I(Y, r+x), + G

What is the relevant interest rate for firms? (real borrowing rate)

= r + x

How does an increase in risk change the IS curve?

IS shifts left

How does monetary policy offset a rise in the risk premium?

Lower the policy interest rate (i) to keep r+x constant

Why may monetary policy fail to offset a risk shock?

The ZLB prevents lowering nominal rates enough

Non Conventional tools central banks use at the ZLB

• long term bonds purchases

• Buying MBS or corporate bonds/stocks

• negative nominal interest

• raising inflation targets

• helicopter money

Helicopter Money

Direct monetary transfers of new printed money to households

How doe negative interest rates help at ZLB

allow real interest rates to fall below zero by lowering nominal rates below zero

How does raising inflation expectations affect real interest rates?/

higher expected inflation lowers real rate

Bank Capital

funds provided by bank owners and absorbs losses

Capital Ratio

Capital/Assets

Leverage Ratio

Assets/Capital

High Leverage means what?

more borrowing relative to equity and thus higher expected return,s but higher insolvency risk

What happens to highle leveraged bank when asset values fall?

Capital becomes negative - bankruptcy

Return on Capital Formual

return = cost of liabilities + (Assets/Capital)(return on assets-cost of liabilities)

Why do banks prefer high leverage?

increases expected return on equity

Why is high leverage dangerous?

small losses in asset values can wipe out capital

Liquidity

how easy an asset can be sold

Why are banks vulnerable to liquidity risk?

They fund illiquid longterm loans with liquid short term deposits

Fire-sale prices

extremely low prices from forced asset sales during liquidity crises

Why can banks cause isolvency/bankruptcy?

Banks must sell assets quickly at low prices to meet withdrawals