Interest Rates

• Present (discounted) value


  The value today of a payment that is promised to be made and that will be received in the future
• Simple loan


  1. Receive loan £100

  2. Repayment at maturity £100+interest
• Present value


  Today's (present) value
• Cash flow (CF)


  Future cash flow (payment)
• Interest rate (i)


  The interest rate
• Credit market instruments


  • Simple Loan
  • Fixed Payment Loan
  • Coupon Bond
  • Discount Bond (zero-coupon bond)
• Yield to Maturity


  The "interest rate" that equates the present value of cash flow payments received from a debt instrument with its value today
• Yield to Maturity - Simple Loan


  1. PV = £100

  2. CF = £110

  3. n = 1

  4. Solve: £100 = £110 / (1 + i)^1

  5. i = 10%
• Yield to Maturity - Fixed Payment Loan


  1. LV = £1000

  2. FP = £120

  3. n = 25

  4. Solve: LV = FP / (1 + i) + FP / (1 + i)^2 + ... + FP / (1 + i)^n

  5. i = 11.15%
• Yield to Maturity - Coupon Bond


  1. P = price of coupon bond

  2. C = yearly coupon payment = £100

  3. F = face value of the bond = £1000

  4. n = 10 years

  5. Solve: P = C / (1 + i) + C / (1 + i)^2 + ... + C / (1 + i)^n + F / (1 + i)^n
• When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate
• The price of a coupon bond and the yield to maturity are negatively related
• The yield to maturity is greater than the coupon rate when the bond price is below its face value
• Consol (or perpetuity)


  A coupon bond with no face value and no maturity, that pays a fixed coupon, periodically, forever
• Yield to Maturity - Discount Bond


  1. F = face value = £1000

  2. P = current price = £900

  3. n = 1 year

  4. Solve: P = F / (1 + i)^n

  5. i = (F - P) / P = 11.11%
• Rate of Return


  The payments to the owner plus the change in value expressed as a fraction of the purchase price
• Current Yield (ic)


  C/Pt
• Rate of Capital Gain (g)

  (Pt+1 - Pt)/Pt
• The return equals the yield to maturity only if the holding period equals the time to maturity
• If the time to maturity is longer than the holding period, a rise in interest rates is associated with a fall in bond prices (capital loss)
• The more distant a bond's maturity, the greater the size of the % price change associated with an interest-rate change
• The more distant a bond's maturity, the lower the rate of return when the interest rate increases
• A bond with a high initial interest rate can still have a negative return if interest rates rise
• Interest-Rate Risk


  The riskiness of an asset's return resulting from interest rate changes
• Prices and returns for long-term bonds are more volatile than those for shorter-term bonds because long-term bonds have higher interest rate risk
• There is no interest-rate risk for any bond whose time to maturity equals the holding period
• Nominal interest rate


  Makes no allowance for inflation
• Real interest rate


  Adjusted for expected changes in the price level
• Ex-ante real interest rate

  Adjusted for expected changes in the price level
• Ex-post real interest rate

  Adjusted for actual changes in the price level
• When the real interest rate is low, there are greater incentives to borrow and fewer incentives to lend
• The real interest rate is a better indicator of the incentives to borrow and lend
• Countries with high nominal interest rates

  Tend to have high inflation