Fixed Income Securities: Pricing and Trading Flashcards
The most accurate method used to determine the value of a bond is to calculate the present value. What is the present value conceptually and how is it calculated?
- The present value is the amount an investor should pay today to invest in a security that offers a guaranteed sum of money on a specific date in the future
- Suppose you had the opportunity to invest money today to receive $1,000 one year from today. Suppose also that the average current interest rate is 5%. Considering that you could invest the money today and earn 5% interest over the course of a year, the present value must be less than its future value of $1,000.
- The question, then, is how much you must invest today at 5% to achieve that future value of $1,000. Here is a simplified way to determine this amount:
o Present value x (1 + Interest or Discount Rate) = Future Value
o Present value x 1.05 = 1,000
o Present value = 1,000/1.05 = 952.38 - We see, therefore, that $952.38 invested today for one year at a 5% rate of interest will grow to a future value of $1,000.
What is a discount rate and how is it determined?
- The discount rate is the interest rate used to determine how much future cash flows are worth today (the rate at which you discount a future value to determine the present value). It reflects the level of risk associated with the bond.
- Steps to determine the discount rate:
o Find the Risk-Free Rate (Baseline):
1. Investors often use a Government of Canada bond (which is considered risk-free) with the same maturity as a reference.
2. Example: If a 4-year Government of Canada bond has a yield of 3%, that is the starting point.
o Add a Credit Spread:
1. Since corporate bonds carry risk, investors demand extra compensation.
2. This extra yield (called the credit spread) is measured in basis points (1 basis point = 0.01%).
3. A company with high credit quality might have a spread of 100 basis points (1%).
4. A riskier company might have a spread of 300 basis points (3%).
5. Example: If the government bond yield is 3%, and the corporate bond has a 200-basis point spread, the discount rate is: 3%+2%=5%
o Adjust for Liquidity and Other Market Factors:
1. Some bonds are harder to sell (less liquid) and may have a higher discount rate to compensate.
2. Economic conditions, inflation, and investor demand can also affect the spread.
What are the steps to calculate the present value of a bond with coupon payments and what is the equation, explaining the key variables in it:
- Choose the appropriate discount rate.
- Calculate the present value of the income stream from the bond’s coupon payments.
a. If a bond has a 9% annual coupon rate and a $100 face value, it pays $9 per year in interest. If it pays interest twice a year, each payment is $4.50 (9% ÷ 2 × $100). - Calculate the present value of the bond’s principal to be received at maturity.
- Add these present values together to determine the bond’s worth today.
- PV= C/(1+r)^1 + C/(1+r)^2 + C/(1+r)^3 … + FV/(1+r)^n
Where: - PV = Present value of the bond
- C = Coupon payment per period
- r = Discount rate per period
- n = Number of periods until maturity
- FV = Face value (principal) of the bond
Example:
Coupon payment:
C = (9%/2) x 100 = 4.5
- The bondholder receives 4.50 every six months
Number of periods:
n = 4 years x 2 = 8 periods
Discount rate per period r
r = 10%/2 = 5% = 0.05
Calculate present value of coupon payments
PV = 4.50/(1.05)^1 …. All the way up to 8 periods
Period Coupon Payment Discount Factor Present Value
1 4.50 1.0500 4.2857
2 4.50 1.1025 4.0816
3 4.50 1.1576 3.8873
4 4.50 1.2155 3.7022
5 4.50 1.2763 3.5260
6 4.50 1.3401 3.3581
7 4.50 1.4071 3.1982
8 4.50 1.4774 3.0460
PV coupons = present value of all 8 periods added
$29.09
Calculate present value of principal
$100 face value in 8 periods
PV principal = 100/1.05^8
PV principal = 67.64
Add the present values
PV bond = PV coupons + PV principal
PV bond = 29.09 + 67.64 = 96.73
The value of $96.77 indicates the price at which the bond will be quoted for trading in the secondary market. In other words, this is the bond’s fair value, given current market conditions. Thus, the value of a bond is the sum of what its coupons are worth today, plus what its principal is worth today, based on an appropriate discount rate that reflects the risks of that particular bond. The appropriate discount rate changes with changing economic conditions and reflects the yield that investors expect
What is a yield, a current yield, and a yield to maturity (just conceptually)?
- A yield is the return an investor earns from a bond, expressed as a percentage of its price. It measures how much income the bond generates relative to its cost.
- Current Yield = (Annual Coupon Payment / Market Price) × 100 → focuses on interest income
- Yield to Maturity (YTM) = Total return if held to maturity, including interest, price changes, and reinvestment.
What is the equation for calculating the current yield on a bond?
- Current yield = annual coupon payment / current market price x 100
o Current yield = 9.00 / 9.677 x 100 = 9.30% - This doesn’t factor in price changes over time – just the income you’re getting today
- This means, based on today’s price, the bond earns 9.3% per year in interest payments
What is the equation for calculating yield to maturity on a bond?
- This is the most important bond yield. It tells you your total return if you hold the bond to maturity, including:
o Coupon payments (interest)
o Any capital gain or loss (if you bought it below or above par)
o Reinvestment of interest at the same YTM - YTM = coupon payment + price change per period/2 = # / average bond price
Look at the screenshot examples
What are factors to consider when interpreting YTM and whether it’s suitable for investment or not?
- Similar Bonds for a Fair Comparison
a. Government Bonds: Compare with bonds of the same maturity from the Government of Canada or the U.S. Treasury (low risk, lower yields).
b. Corporate Bonds: If your bond is from a company, compare it to bonds from companies with similar credit ratings and maturities. - Credit Ratings Matter
a. Higher YTM often means higher risk.
b. Compare with bonds that have the same credit rating (AAA, AA, BBB, etc.).
c. Example: A BBB-rated corporate bond with 7.5% YTM might not be better than a AAA-rated bond with 5% YTM if the risk of default is higher. - Yield Spreads (How Your Bond Compares to Risk-Free Bonds)
a. Compare your bond’s YTM to risk-free bonds (like the Government of Canada bonds).
b. Example: A 5-year Government of Canada bond yields 4%
c. A 5-year corporate bond from a bank yields 5.5% The spread is 1.5%, meaning the corporate bond compensates you for taking on extra risk. - Inflation and Interest Rates
a. If YTM is below expected inflation, your real return is negative. If interest rates rise, new bonds may offer higher YTMs, making older bonds less attractive.
b. This is called the real rate of return: Because inflation reduces the value of a dollar, the return that is received, called the nominal rate, must be reduced by the inflation rate to arrive at the real rate of return. - Example: Is 7.37% YTM a Good Deal?
a. If similar corporate bonds are offering 8% YTM, then your bond is underperforming.
b. If the Government of Canada bond is at 5% YTM, your 7.37% bond might be attractive (but check the credit risk).
c. If inflation is 6%, your real return on a 4.76% YTM bond would be negative.
Fundamental bond pricing properties, 1) interests rates, bond yields, and bond prices; 2) short-term vs long-term price volatility; 3) higher versus lower coupon rates
- Interest rate, bond yields, and bond prices: The most important bond pricing relationship to understand is the inverse relationship between bond prices and bond yields, which rise or fall in tandem with interest rates. In fact, the terms interest rate and bond yield are often used interchangeably, with both meaning a rate of return on an investment. Therefore, as interest rates rise, bond yields also rise but bond prices fall; when interest rates fall, bond yields also fall but bond prices rise.
o Example pasted below: - Given two bonds with the same coupon rate and same yield, the bond with the longer term to maturity is usually more volatile in price than the bond with the shorter term to maturity. Uncertainty about the markets and interest rates increases as we forecast farther into the future. Therefore, the longer the term of the bond, the more volatile its price will be.
- Given two bonds with the same term to maturity and the same yield, the bond with the higher coupon is usually less volatile in price than the bond with the lower coupon.
Look at the three screenshots in the document
What is duration, provide an example of one that has a duration of 10%, and what to keep in mind when investing?
- To measure how much a bond’s price will change when interest rates change, we use duration. What is Duration? Duration measures how sensitive a bond’s price is to interest rate changes. It tells us approximately how much a bond’s price will change for a 1% change in interest rates.
o Higher duration = More price movement (higher risk).
o Lower duration = Less price movement (lower risk). - Let’s say you are thinking about buying a bond from DEC Corp. The bond: Is priced at $105 (per $100 face value). Has 12 years to maturity. Has a duration of 10. If interest rates go up by 1%, the bond price will drop by 10%: New price = $105 - (10% × $105) = $94.50 This shows that bonds with higher duration lose more value when interest rates rise.
- How to Use Duration in Investing: If you think interest rates will drop, buy bonds with higher duration to maximize gains. If you think interest rates will rise, buy bonds with lower duration to minimize losses.
What is a bond index, what are two main reasons why it is used?
- A bond index measures the value and performance of a group of bonds over time. It is similar to a stock market index (e.g., S&P 500) but focuses on bonds instead of stocks.
- Bond indexes serve key purposes in the securities industry: Market Performance Indicator – Measures the overall bond market or specific bond categories (e.g., government or corporate bonds). Benchmark for Fund Managers – Allows investors and portfolio managers to compare their bond fund’s performance against the index.
- The FTSE Canada Universe Bond Index is the most widely used bond index in Canada. It tracks a diverse range of bonds.
- Several organizations track bonds in different global markets. Some key indexes include: Global Bond Indexes FTSE World Government Bond Index – Tracks government bonds worldwide. U.S. Bond Indexes Bloomberg U.S. Aggregate Bond Index – Tracks U.S. government and corporate bonds.
