Lecture 3 - Bond Valuation and Interest Rates Flashcards
Bond
Security that obligates the issuer to make specified payments to the bond holder
Face value (par value of principal value or nominal amount
Payment at the maturity of the bond
Coupon
The interest payments made to the bond holder
Coupon rate
Annual interest payment as a percentage of face value
Bond pricing
The price an investor is willing to pay for a bond depends on the present value of the cash flows expected to the received by holding the bond
Bond value =
Present value of coupons + present value of par value
(Discounted at the required rate of return)
Yield to Maturity
- Is the interest rate that makes the present value of a bonds payment equal to its price
- It is measure of the interest rate on a bond
- Interpreted as a measure of the average rate of return that will be earned on a bond if it is bought now and held until maturity
Gilt
Is a UK gov liability denominated in sterling issued by HM Treasury and listed on the LSE
Bond yields and prices move in opposite directions
- Higher yields => lower bond price
- Lower yields => higher bond price
- Since the YTM is the discount rate used in the bond price calculation bond prices and yields must move in opposite direction:
- Higher yields: present value of future coupon payments and of final payment reduces
- So when bond prices fall, YTM must rise
- Lower yields: present value of future coupon payments and of final payment increases
- So when bond prices rise, YTM must fall
Spot market rates
- Refer to the current interest rates for lending or borrowing money for a specific period of time starting immediately (or on the spot)
- These rates are determined by market supply and demand dynamics for financial instruments with immediate settlement (2-3 days)
Why do bond yields and prices move in opposite directions? - 1st reason
- A bond’s coupon interest payments (coupons) and principal repayment are not affected by changes in the spot market rates
- They are determined at the time of issuance based on the current market conditions
- That is, market interest rates, the issuer’s creditworthiness and other economic factors when the bond is issued
- Coupon rate needs to reflect prevailing market interest rates otherwise it would not be attractive to potential investors and competitive with other investment options
- Once the coupon rate is fixed, the issuer is obligated to pay that amount regardless of how interest rates in the market change after issuance
Why do bond yields and prices move in opposite directions? - 2nd reason
- When spot market interest rates rise, bond prices fall in the secondary market
- Investors do not want to pay full price for bonds with lower fixed coupon payments when new bonds offer higher rates
- They would instead prefer investing in other new instruments that offer
higher interest rates (higher coupon payments) due to the current market conditions - So the price of the old bond will drop due to decreased demand
- And its YTM will increase
- They will only buy the lower-coupon bond if its price drops enough to make its return competitive
Coupon Payment
Regular interest payment from the bond
Starting price
The price at which the bond was purchased
Ending pirce
The price at which the bond is sold (or its value at maturity)
Discount Bond
- A bond that is priced below its face value is said to sell at a discount and is known as discount bond
- Investors who buy a discount bond receive a capital gain over the life of the product
- Discount bonds: YTM > Coupon rate
Premium Bond
- A bond that is priced above face value sells at a premium and is known as a premium bond
- Investors in premium bonds face a capital loss over the life of the bond
- Premium bonds: YTM < Coupon rate
Why long term bonds react more to interest rates?
- LT bond prices are more sensitive to changes in interest rates compared to short term bonds
- The cash flows from long term bonds are spread out over a longer period of time making their present value more impacted by changes in interest rates
- Duration risk is a primary factor contributing to interest rate risk: the longer the maturity, the higher the sensitivity to rate changes
Interest rates vs returns
- A rise in the interest rate means that the price of the bond falls and we experience a capital loss, if time to maturity is longer than the holding period
- The more distant a bond’s maturity, the lower the rate of return that occurs as a result of an increase in the interest rate
Maturity and the volatility of bond returns: interest rate risk
- Prices and returns for LT bonds are more volatile than those for shorter term bonds
- There is no interest rate risk for any bond whose time to maturity matches the holding period
- The key to understanding why there is no interest rate tisk for any bond whose time to maturity matches the holding period is to recognise that (in this case) the price at the end of the holding period is already fixed at the face value
Negative yields on bonds
- Which occur when bond prices climb so high that buyers holding them to maturity are guaranteed to lose money
- If interest rate are negative you still use the same procedure for calculating the bond price but now (1 + r) is less than 1
Term structure of interest rates
Depicts the relationship between short and long term interest rates
Yield curve
The yield curve is used to describe the term structure of interest rates for bonds with differing terms to maturity but identical risk, liquidity and tax considerations such as gov bonds
Slope of the yield curve
The difference between long term and short term rates is called the slope of the yield curve
Expectations theory of term structure
- Because both strategies must have the same expected return, the interest rate on the 2 year bond must equal the average of the two 1 year interest rates
- Only if that is the case would investors be prepared to hold both short and long maturity bonds
- Key assumption: bond holders consider bonds with different maturities to be perfect substitutes
- Buyers of bonds don’t prefer bonds of one maturity over another
- They will not hold any quantity of a bond if its expected return is less than that of another bond with a different maturity
Law of one price
- The law of one price asserts that identical assets in a competitive market should have the same selling price
- Therefore if two assets make a safe payment on the same future date, these payments must be worth the same today and should be discounted at the same spot interest rate
Expectations theory of term structure: pt 2
- The interest rate on a long term bond will equal the average of the short term interest rates that people expect to occur over the life of the long term bond
- The expectations theory predicts that interest rates on bonds of diff maturities differ beacuase short term interest rates are expected to have different values at future dates
The expectation theory predicts that:
- The only reason for upward sloping term structure is that investors expect short term investment rates to rise
- The only reason for a declining term structure is that they expect short term rates in the future to fall
- If the term structure is flat: short and long term rates are the same
Limitations of the expectations theory of term structure
- It does not consider risk: bonds with shorter maturities have less interest rate risk as within a shorter investing horizons changes interest rates will not change the value of the bond a lot
- The price of longer-term bonds will be affected more since a change in the interest rates will affect the value of distant cash flows more than that of shorter-term ones
- Also, investing in longer-term instruments means that although you know exactly the amount of money that you will receive at maturity, you do not know its purchasing power due to inflation
Nominal interest rate
- Makes no allowance for inflation
- It is the growth rate of your money
Real interest rate
- Is adjusted for changes in general price level so it more accuratley reflects the cost of borrowing
- Is the growth rate of your purchasing power
Ex ante real interest rate
Is adjusted for expected changes in the price level
Ex post real interest rate
Is adjusted for actual changes in the price level
Real interest rates are determined by:
- Propensity of households to save (supply)
- Expected profitability of real investment (demand)
- Gov actions (fiscal and monetary policy)
Fisher equation
- Predicts the nominal rate of interest should track the inflation rate leaving the real rate somewhat stable
- Appears to work far better when inflation is more predictable + investors can more accurately gauge
the nominal interest rate they require to provide an acceptable real rate of return
Fisher Hypothesis
- We expect higher nominal interest rates when inflation is higher, leaving the real rate somewhat stable
- The validity of the Fisher hypothesis depends on the ability of investors to predict expected inflation
- High real interest rates can be a cause for alarm and celebration
- Coming out of recession real rates typically rise (due to expected profitability of real investment
- But, if real interest rates rise because the supply of capital is contracting, then high real rates would be a bad sign
