3.4 Interest Rates

Interest rates and inflation are closely intertwined in finance. Nominal rates include both the real interest rate and an inflation premium, while the Fisher Effect explains their relationship. Understanding this connection is crucial for making informed financial decisions.

Real interest rates, calculated using expected or actual inflation, measure the true cost of borrowing. Positive real rates benefit lenders, while negative rates favor borrowers. This concept helps investors and borrowers assess the actual value of their investments and loans over time.

Interest Rates and Inflation

Nominal rates and inflation connection

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• Nominal interest rates consist of two components:
  • Real interest rate represents the true cost of borrowing determined by supply and demand for loanable funds in the market
  • Inflation premium compensates lenders for expected loss of purchasing power due to inflation increases as expected inflation rises
• Fisher Effect states nominal interest rate = Real interest rate + Expected inflation rate
  • $i = r + \pi^e$, where $i$ is nominal interest rate, $r$ is real interest rate, and $\pi^e$ is expected inflation rate
• When expected inflation increases, nominal interest rates tend to rise to compensate lenders for loss of purchasing power (higher inflation premium)
• When expected inflation decreases, nominal interest rates tend to fall as inflation premium decreases (lower inflation expectations)

Calculation of real interest rates

• Real interest rate measures true cost of borrowing after adjusting for inflation
• Ex-ante real interest rate calculated using expected inflation
  • $r = i - \pi^e$, where $r$ is real interest rate, $i$ is nominal interest rate, and $\pi^e$ is expected inflation rate
• Ex-post real interest rate calculated using actual inflation
  • $r = i - \pi$, where $r$ is real interest rate, $i$ is nominal interest rate, and $\pi$ is actual inflation rate
• Positive real interest rates indicate nominal interest rate is higher than inflation rate (lenders gain purchasing power)
• Negative real interest rates indicate inflation rate is higher than nominal interest rate resulting in loss of purchasing power for lenders (borrowers benefit)

Risk and Interest Rates

Risk impact on interest rates

• Default risk is risk that borrower will not repay loan
  • Higher default risk leads to higher interest rates to compensate lenders for increased risk (subprime mortgages)
  • Credit ratings assess creditworthiness of borrowers and help determine interest rates (AAA, AA, A, BBB, etc.)
• Liquidity risk is risk that investor may not be able to sell security quickly at fair price
  • Less liquid securities tend to have higher interest rates to compensate investors for lack of liquidity (corporate bonds vs government bonds)
• Maturity risk is risk associated with length of time until bond matures
  • Longer-term bonds typically have higher interest rates than shorter-term bonds
    • Investors demand higher return for locking up funds for longer period (10-year Treasury vs 2-year Treasury)
    • Longer-term bonds are more sensitive to changes in interest rates (duration risk)
• Market risk is risk of changes in interest rates due to economic conditions and market sentiment
  • When market interest rates rise, value of existing fixed-rate securities falls (bond prices move inversely with yields)
  • When market interest rates fall, value of existing fixed-rate securities rises (refinancing opportunities)

Time Value of Money and Interest Rates

• Time value of money concept states that money available now is worth more than the same amount in the future due to its potential earning capacity
• Interest rates reflect the opportunity cost of using money for one purpose instead of another
• Yield curve shows the relationship between interest rates and time to maturity for bonds of similar credit quality
  • Upward sloping yield curve (normal) indicates higher long-term rates
  • Inverted yield curve may signal economic slowdown
• Federal funds rate is the interest rate at which banks lend money to each other overnight
  • Influences other short-term interest rates and indirectly affects long-term rates
• Prime rate is the interest rate that commercial banks charge their most creditworthy customers
  • Often used as a benchmark for other types of loans
• Basis point is a unit of measurement for interest rates, equal to 1/100th of a percentage point
  • Used to describe small changes in interest rates