Bond Prices

• Bonds offer relatively known and certain returns.
• So where do our returns on bonds come from? They come from two main sources.
• Primary source of returns for a bond is the coupons we are paid over the course of the bond.
• Unlike dividends, these represent a legal obligation, which means that failing to pay a coupon on time can result in the company’s bankruptcy. As such, companies will do their best to ensure that they pay their coupons on time.
• Second source of returns is either capital gains or losses driven by changes in the price of the bond.
• Bond prices are often quoted as a percentage of the par value. For instance, 128.7 is 128.7% of the par. If par was $1 then you would pay $1.287 per bond.
• However conventions differ country to country. The US still use fractional quotes, and London Bond market uses decimal.
• Just like stocks, bonds have bids and asks.
• The big question then becomes the price of the bond at the time that we sell.
• The price of a bond is the present value of its future cashflows, and given we have a lot of clarity about the future cashflows, we can determine the price relatively accurately at any point in time.
• Bond Price = PV of Coupon Payments + PV of Par Value

• If we purchased a bond at a premium, above the bond’s par value, then overtime the price will decrease until at maturity the price of the bond equals the par value of the bond.

• If we buy a bond for a discount then the price of the bond will increase overtime until it reaches the par value at the time of maturity. This however only holds if the yield to maturity stays constant.
• What happens if the yield is not constant, and why does the yield change.
• The yield to maturity is the compensation we require based on the risk of the bond, and by extension the underlying company.
• In effect, the yield is the prevailing risk-free rate for that investment period plus a risk premium that accounts for the risk of the company and the bond (different bond features can mean two bonds issued at the same time by the same company with slightly different characteristics might have different yields).
• So immediately, we can see two reasons why the yield might change – the Prevailing Interest Rates change or the Riskiness of the Company changes.
• Let’s explore these further.
  • Prevailing interest rates. Most market interest rates are inherently linked to the interest rate set by the central bank. This goes by different terms including the Fed Funds Rate (US), the Official Cash Rate (NZ and Australia), Official Bank Rate (UK), and Key Interest Rate (Euro), Key Policy Rate.
  • As most other interest rates within a country are based on the central bank rate, an increase in the rate tends to increase interest rates across the board increasing the required yield on a bond.
  • Company Risk. A change in the risk of the company can also change the yield. We will explore this more later.
  • It is worth noting that if the credit rating of a bond decreases, then we would expect the yield to increase. Recognising that the bond has become riskier and requires a higher return as compensation.
• So how does prevailing interest rates and company risk impact the price of a bond, and therefore the capital gain or loss we make?
• Remember that the price of a bond is the present value of future cashflows. A higher discount rate (in this case the yield) makes future cashflows worth less in the present, the price of a bond will drop if the yield increases and vice versa.
• As a result, increasing yields will cause capital losses. Although these are somewhat offset by being able to reinvest our coupons at a higher rate. Decreasing yields will cause capital gains, although there is an offset based on what we can reinvest our coupons at.

OVER TO YOU

• The price of a bond is calculated at the present value of all the future cashflows which include the coupons paid and the principle returned at the end.
• Using the present value formula from week 1 calculate the price you would expect to pay for a bond with the following features:
  • Coupon rate: 4.5% per annum paid annually
  • Yield to Maturity: 3.75%
  • Time to maturity: 3 years
  • Par Value: $1,000
• If the current market price for this bond was $1,024 would you buy the bond? Why?

ANSWER

$1020.91 is the present value of the future cashflows, or what we should pay for this bond. If we were offered the bond for 1,024 then we should not buy it as we would be paying more then it is actually worth.