CSC Volume 1 Chapter 7 PDF - Fixed-Income Securities Pricing & Trading

Fixed-Income Securities: Pricing and Trading 7 CHAPTER OVERVIEW In this chapter, you will learn how to calculate the price and yield of fixed-income securities. You will also learn about int...

Fixed-Income Securities: Pricing and Trading 7 CHAPTER OVERVIEW In this chapter, you will learn how to calculate the price and yield of fixed-income securities. You will also learn about interest rates on bonds, including the difference between the nominal and the real rate of return, how interest rates are depicted on a yield curve, and how they are determined according to three theoretical principles. You will then learn how and why bond prices go up or down according to certain fixed-income pricing properties. Next, you will learn about bond trading and the rules and regulations around the delivery of bonds and the settlement of transactions. Finally, you will learn how bond indexes are used by portfolio managers as performance measurement tools and to construct bond index funds. LEARNING OBJECTIVES CONTENT AREAS 1 | Perform calculations relating to bond pricing Calculating Price and Yield of a Bond and yield. 2 | Describe the factors that determine the term Term Structure of Interest Rates structure of interest rates and shape of the yield curve. 3 | Explain how bond prices react to changes in Fundamental Bond Pricing Properties interest rates, maturity, coupon, and yield. 4 | Describe how bond trading is conducted. Bond Market Trading 5 | Define bond indexes and how they are used Bond Indexes in the securities industry. © CANADIAN SECURITIES INSTITUTE 7 2 CANADIAN SECURITIES COURSE      VOLUME 1 KEY TERMS Key terms are defined in the Glossary and appear in bold text in the chapter. accrued interest market segmentation theory bearer bonds nominal rate buy side present value current yield real rate of return discount rate registered bonds duration reinvestment risk expectations theory sell side inter-dealer broker trade ticket liquidity preference theory yield curve © CANADIAN SECURITIES INSTITUTE  CHAPTER 7      FIXED-INCOME SECURITIES: PRICING AND TRADING 7 3 INTRODUCTION Before you recommend fixed-income securities to clients, you must understand the potential risks and rewards of bonds and other securities of this type. An important part of this process is knowing how bond yields and prices are determined and understanding the strong relationship between prices and prevailing interest rates. In the most common scenario, the investor buys a bond at one price, receives a regular stream of interest payments, holds the bond to maturity, and cashes it in at face value. However, fixed-income securities can also be bought in the secondary markets. The price that an investor pays for a particular security in the secondary market applies as much to bonds as it does to equities. Price is especially a concern for investors seeking capital gains in the bond market. Both bond prices and equity prices are affected by economic conditions and changes in interest rates, among other factors; however, they do not react in the same way. In this chapter, we focus on the methods used to determine the fair price for a fixed-income security, as well as fixed-income pricing properties. You will also learn about the impact that various events have on the markets and on the prices of fixed-income securities. CALCULATING PRICE AND YIELD OF A BOND 1 | Perform calculations relating to bond pricing and yield. The most accurate method used to determine the value of a bond is to calculate the present value. 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. EXAMPLE 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: Present Value ´ (1 + Interest or Discount Rate) = Future Value Present Value ´ 1.05 = 1,000 1,000 Present Value = = 952.38 1.05 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. You can verify the manual calculation on your calculator by entering: $952.38 + 5% or $952.38 × 1.05. The example is simplified in that it calculates a single future value at maturity. In reality, the cash flow from a typical bond is made up of regular coupon payments and the return of the principal at maturity. Because a bond represents a series of cash flows to be received in the future, the sum of the present values of all of these future cash flows is what the bond is worth today. © CANADIAN SECURITIES INSTITUTE 7 4 CANADIAN SECURITIES COURSE      VOLUME 1 The present value of a bond with coupon payments is calculated in four steps: 1. Choose the appropriate discount rate. 2. Calculate the present value of the income stream from the bond’s coupon payments. 3. Calculate the present value of the bond’s principal to be received at maturity. 4. Add these present values together to determine the bond’s worth today. The general formula used to factor in coupon payments in calculating present value is shown in Figure 7.1. Figure 7.1 | Formula for Calculating Present Value C1 C2 Cn + FV PV = 1 + 2 ++ n (1 + r ) (1 + r ) (1 + r ) Where: PV = Present value of the bond C = Coupon payment r = Discount rate per period n = Number of compounding periods to maturity FV = Principal received at maturity (i.e., the future value or FV) The math behind the calculation for present value is not intended to be cumbersome. In the next few sections, we explain how to carry out and interpret the results. Note: You will notice that throughout the examples in this chapter, we always use a four-year, semi-annual, 9% coupon bond with a discount rate of 10%. Bond prices are often quoted using a base value of $100. We therefore use $100 as the principal of our four-year, semi-annual, 9% bond. THE DISCOUNT RATE The discount rate is the rate at which you would discount a future value to determine the present value. The appropriate discount rate is chosen based on the risk of the particular bond. It can be estimated based on the yields currently applicable to bonds with similar coupon, term, and credit quality. Yields are determined by the marketplace and change as market conditions change. Yields are often quoted as being equal to a Government of Canada bond with a similar term, plus a spread in basis points that reflects credit risk, liquidity, and other factors. It is important to note that the terms discount rate and yield are often used to refer to the same thing. However, the discount rate should not be confused with the coupon rate on the bond, which determines the income to be paid to the bondholder. The coupon rate is set when the bond is issued and, unlike the yield, generally does not change. If the bond pays interest more than once a year, the coupon payments, the compounding periods, and the discount rate must be adjusted for the number of times interest is paid each year. Most bonds pay interest twice a year, and so the following adjustments are required: Coupon = (9% ¸ 2) ´ $100 = 4.5% ´ $100 = $4.50 per period Compounding periods = 4 years ´ 2 payments per year = 8 compounding periods Discount rate = 10% ¸ 2 payments per year = 5% per period © CANADIAN SECURITIES INSTITUTE  CHAPTER 7      FIXED-INCOME SECURITIES: PRICING AND TRADING 7 5 CALCULATING THE FAIR PRICE OF A BOND The fair price of a bond is the present value of the bond’s principal and the present value of all coupon payments to be received over the life of the bond. Table 7.1 shows the timing of the cash flows on the example four-year, semi-annual, 9% bond. Table 7.1 | Cash Flow Timeline on a Four-Year, Semi-Annual, 9% Bond Year 1 Year 2 Year 3 Year 4 C1 ($4.50) C2 ($4.50) C3 ($4.50) C4 ($4.50) C5 ($4.50) C6 ($4.50) C7 ($4.50) C8 ($4.50) + P ($100) PRESENT VALUE OF A BOND Table 7.1 shows that coupon payments are made twice a year and that, at maturity, the bondholder receives the final coupon payment and the return of the principal (or the par value of the bond). By discounting these cash flows back to the present, we can solve for the present value of a bond. The present value of a future amount to be received is calculated by dividing that future amount by (1 + interest rate) raised to the power of the number of compounding periods in the life of the bond. This method is called discounting the cash flows because the future cash flows are discounted to arrive at the present value. We can carry out the calculation either by hand or by using a financial calculator, but the calculator method is much quicker and more precise. For the four-year, semi-annual, 9% bond in our example, we can set up the formula as shown in Figure 7.2. Figure 7.2 | Calculating Present Value of a Four-Year, Semi-Annual, 9% Bond 4.50 4.50 4.50 + FV PV = 1 + 2 ++ 8 (1 + 0.05) (1 + 0.05) (1 + 0.05) Calculation Note You may be wondering how to approach calculations that involve (1 + r)n. The bracketed information is read as being to the power of n. Therefore, if we have (1.05)8, the 1.05 is raised to the power of 8. Most calculators are equipped with a yx or yexp key to simplify this calculation. Simply key in 1.05 and press the yx or yexp key, then enter 8 as the power and press the = button to find the answer: 1.4775. 1. Present value of the income stream The present value of a bond’s income stream is the sum of the present values of each coupon payment. On our four-year, semi-annual, 9% bond with a par value of $100, there are eight remaining semi-annual coupon payments of $4.50 each, for a total value of $36 in coupon payments over time. The present value of each of these $4.50 coupons, added together, is the present value of the bond’s income stream. Using a financial calculator, we can calculate the present value of the coupon payments as follows: 1. Type 8, then press N. 2. Type 5, then press I/Y. 3. Type 4.50, then press PMT. 4. Type 0, then press FV (to tell the calculator you are not interested in the principal). 5. Press COMP, then press PV (some financial calculator models use the COMP button while others may use CPT). Answer: −29.0845 © CANADIAN SECURITIES INSTITUTE 7 6 CANADIAN SECURITIES COURSE      VOLUME 1 DID YOU KNOW? When using the time value of money functions on your calculator, a negative value denotes an outflow of money, whereas a positive value denotes an inflow of money. In this case, −29.0845 denotes that the investor must pay $29.0845 (outflow) to purchase the series of eight coupon payments of $4.50 (inflow). Those positive and negative signs are how the calculator keeps track of money flowing into and out of the investor’s pocket. This calculation tells us that the value of the stream of eight coupon payments totalling $36 is worth $29.08 today. 2. Present value of the principal Because the bond’s principal represents a single cash flow to be received in the future, we can calculate the present value of the principal of our bond as follows: 1. Type 8, then press N. 2. Type 5, then press I/Y. 3. Type 0, then press PMT (to tell the calculator you are not interested in the coupons). 4. Type 100, then press FV. 5. Press COMP, then press PV. Answer: −67.6839 The present value of the principal is approximately $67.68. This tells us that if you were to invest $67.68 at a semi- annual rate of 5% today, you would receive $100 in four years. You can verify this on your calculator by entering $67.6839 + 5% + 5% + 5% + 5% + 5% + 5% + 5% + 5%. 3. Present value of the bond The fair price for a bond is the sum of its two sources of value: the present value of its coupons and the present value of its principal. In the example above, the coupons are worth $29.08 and the principal is worth $67.68. Therefore, at a discount rate of 10%, this bond has a present value of $96.77 (calculated as $29.0844 + $67.6839) today. We can also carry out the calculation for the present value of the bond in one easy step using a financial calculator: 1. Type 8, then press N. 2. Type 5, then press I/Y. 3. Type 4.50, then press PMT. 4. Type 100, then press FV. 5. Press COMP, then press PV. Answer: −96.7684 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. © CANADIAN SECURITIES INSTITUTE  CHAPTER 7      FIXED-INCOME SECURITIES: PRICING AND TRADING 7 7 The financial calculator simplifies the present value calculations, although knowing how to carry out the calculations manually is important. We include those step-by-step calculations in Figure 7.3 so that you can gain an appreciation of what is involved at each step. Figure 7.3 | Calculating the Present Value of a Bond Step 1: Present Value of the Principal Because the bond’s principal represents a single cash flow to be received in the future, we can calculate the present value of the principal of a four-year, semi-annual bond with a par value of $100 as follows: FV 100 100 PV = n = 8 = = 67.6839 (1 + r ) (1 + 0.05) 1.47746 Therefore, the present value of the principal is $67.68. Step 2—Method 1: Present Value of the Income Stream We can calculate the present value of the first coupon payment using the same formula: 4.50 4.50 PV = 1 = = 4.2857 (1 + 0.05) 1.05 Therefore, the present value of the first coupon to be received six months from now is approximately $4.29. You can verify this with your calculator by entering $4.2857 + 5% = $4.50. In the same example, the present value of the second coupon is calculated as follows: 4.50 4.50 PV = 2 = = 4.0816 (1 + 0.05) 1.1025 Therefore, the present value of the coupon to be received a year from now is approximately $4.08. You can verify this with your calculator by entering $4.0816 + 5% + 5% = $4.50. Repeat this process for each of the coupon payments to be received, and add the present values together to obtain the present value of the income stream. In this example, the result is $29.08 (calculated as $4.29 + $4.08 + $3.89 + $3.70 + $3.53 + $3.36 + $3.20 + $3.05). © CANADIAN SECURITIES INSTITUTE 7 8 CANADIAN SECURITIES COURSE      VOLUME 1 Figure 7.3 | Calculating the Present Value of a Bond Step 2—Method 2: Present Value of the Income Stream A faster way to calculate the present value of a series of time payments is by using the formula for the present value of an annuity. With this formula, the sum of the present value of all coupons is found all at once. é 1 ù ê1 - ú ê (1 + r ) n ú ê APV = C ê ú r ú ê ú ê ú êë úû Where: APV = Present value of the series of coupon payments C = Payment (the value of one coupon payment) r = Discount rate per period n = Number of compounding periods We can apply the formula to our previous bond calculation problem as follows: é 1 ù ê1 - ú ê (1 + 0.05) 8 ú ê APV = 4.50 ê ú = 4.50 éê 1 - 0.676839 úù = 4.50 êé 0.323161 úù = 4.50 ´ 6.4632 ú êë ê 0.05 ú 0.05 ûú ëê 0.05 ûú ê ú êë úû = 29.084 Therefore, the present value of the income stream using this method is $29.084. Step 3: Present Value of the Bond The fair price for a bond is the sum of its two sources of value: the present value of its principal and the present value of its coupons. Therefore, at a discount rate of 10%, this bond has a value today of $96.77 (calculated as $29.0844 + $67.6839). CALCULATING THE YIELD ON A TREASURY BILL A Treasury bill (T-bill) is a very short-term security that trades at a discount and matures at par. No interest is paid in the interim. Instead, the return is generated from the difference between the purchase price and the sale price (if sold before maturity) or maturity value (if held to maturity). For tax purposes, the investor’s earnings from the T-bill are treated as interest income. A simple formula for calculating this yield is shown in Figure 7.4. Figure 7.4 | Calculating the Yield on a Treasury Bill 100 - Price 365 Yield = ´ ´ 100 Price Term © CANADIAN SECURITIES INSTITUTE  CHAPTER 7      FIXED-INCOME SECURITIES: PRICING AND TRADING 7 9 EXAMPLE The yield on an 89-day T-bill purchased for a price of 99.5 is calculated as follows: 100 - 99.5 365 0.5 365 Yield = ´ ´ 100 = ´ ´ 100 = 2.061% 99.5 89 99.5 89 CALCULATING THE CURRENT YIELD ON A BOND Current yield looks only at cash flows and the current market price of an investment, not at the amount that was originally invested. We can calculate the current yield of any investment, whether it is a bond or a stock, using the formula shown in Figure 7.5. Figure 7.5 | Calculating the Current Yield on a Bond Annual Cash Flow Current Yield = ´ 100 Current Market Price EXAMPLE The current yield on a four-year, semi-annual, 9% bond, trading at a price of 96.77 is calculated as follows: 9.00 Yield = ´ 100 = 9.30% 96.77 CALCULATING THE YIELD TO MATURITY ON A BOND The most popular measure of yield in the bond market is yield to maturity (YTM). This measure shows the total return you would expect to earn over the life of a bond starting today, assuming you are able to reinvest each coupon payment you receive at the same YTM that existed at the time you purchased the bond. The YTM takes into account the current market price, its term to maturity, the par value to be received at maturity, and the coupon rate. This calculation involves finding the implied interest rate (r) in the present value formula (shown in Figure 7.1), but where PV, rather than r, is known. The YTM calculation makes the assumption that the investor will be repaid the par value of the investment at maturity. (In contrast, current yield is calculated as the coupon income divided by current price.) Therefore, YTM not only reflects the investor’s return in the form of coupon income; it also includes any capital gain from purchasing the bond at a discount and receiving par at maturity, or any capital loss from purchasing the bond at a premium and receiving par at maturity. © CANADIAN SECURITIES INSTITUTE 7 10 CANADIAN SECURITIES COURSE      VOLUME 1 FOR INFORMATION ONLY Why Would an Investor Buy a Bond at a Premium if It Guarantees a Capital Loss? If you are new to investing in bonds, you may wonder why anyone would buy a bond at a premium that will produce a capital loss if held to maturity. In fact, there is more to a bond than the purchase price. Although the capital loss is guaranteed, you should not overlook the stream of coupon payments and their reinvestment potential. For example, consider a bond that costs $103 and matures in four years. The bond has a 7% coupon rate. If you pay $103 and hold the bond to maturity, you will end up with a $3 capital loss. However, over the course of four years, you will also receive the following payments from the issuer: $3.50 + $3.50 + $3.50 + $3.50 + $3.50 + $3.50 + $3.50 + $3.50 + $100 = $128 Also, each time you receive a regular coupon payment of $3.50, you have the opportunity to invest that money in the market and earn a return on it. Manually calculating YTM is difficult; the task is made easier with a financial calculator. EXAMPLE With a four-year, semi-annual, 9% bond trading at a price of 96.77, we can find the semi-annual YTM as follows: 1. Type 8, then press N. 2. Type 4.50, press PMT. 3. Type 96.77, then press +/−, then press PV. (The +/− sign in front of 96.77 denotes an inflow or outflow of funds from the investor.) 4. Type 100, then press FV. 5. Press COMP, then press I/Y. Answer: 4.9997 (rounded to 5) Therefore, the semi-annual YTM on this bond is 5.0%. The annual YTM is 10% (calculated as 5% × 2), which makes sense because the bond is trading at a discount to par. If you buy this bond today at the price of $96.77 and hold it to maturity, you will receive eight payments of $4.50 plus $100 at maturity. The YTM calculation factors in the $3.23 gain on the bond ($100 − $96.77), the coupon income, plus the reinvestment of the coupon income at this YTM. Figure 7.6 shows how to manually calculate the approximate YTM. (A financial calculator produces slightly more accurate results.) DID YOU KNOW? The manual method of calculating YTM produces only an approximate yield. However, the results from a manual calculation are usually very similar to the results you would get with a financial calculator. Figure 7.6 | Approximate Yield to Maturity—Manual Calculation Interest Income ± Price Change per Compounding Period AYTM = ´ 100 (Purchase Price + Par Value) ¸ 2 © CANADIAN SECURITIES INSTITUTE  CHAPTER 7      FIXED-INCOME SECURITIES: PRICING AND TRADING 7 11 We use +/− in the formula to show that you can buy a bond at a price above or below par. Let’s assume that you buy a bond at a discount to par—at a price of 92, for example—and hold it to maturity. At maturity, the bond matures at par and you realize a gain on the investment. In the formula, you would add this price appreciation to the interest income. The opposite holds if you buy a bond at a premium—at a price of 105, for example—and hold it to maturity. In our formula, you would subtract the price decrease from the interest income. EXAMPLE On the four-year, semi-annual, 9% bond, trading at a price of 96.77 that matures at 100, the semi-annual interest or coupon income is $4.50. What is the annual price change on this bond (based on $100 par)? The present value of the bond is 96.77 and will mature at 100. Therefore, it will increase in value over the remaining life of the bond by $3.23. Because there are eight compounding periods remaining in this bond’s term, the bond generates a gain in price of $0.4038 per period over the remaining eight periods ($3.23 ÷ 8). What is the average price on this bond (based on $100 par)? The purchase price is $96.77. The redemption or maturity value is $100. The average price is therefore $98.385, calculated as (96.77 + 100) ÷ 2. The semi-annual approximate YTM on this bond is calculated as follows: $4.50 + $0.4038 $4.9038 ´ 100 = ´ 100 = 4.9842% (96.77 + 100) ¸ 2 98.35 The annual approximate YTM is 9.9684% (calculated as 4.9842% × 2). Notice that this result is very close to the YTM found using a financial calculator, although the calculator produces a more precise figure. When you buy a bond, the bond quote includes the price, the maturity date, the coupon rate (which tells how much income you will receive each year), and the YTM. EXAMPLE Issue Coupon Maturity Bid Ask Last Price Yield to Maturity XYZ Corp. 7% 5 years 79.75 80.25 80.00 12.50% Note: Yield to maturity is calculated as 10 N, −80 PV, 3.5 PMT, 100 FV, COMP I/Y × 2. All of this information is important; however, the YTM is the most important measure. In general, the YTM is an estimate of the average rate of return earned on a bond if it is bought today and held to maturity. To earn this rate of return, however, it is assumed that all coupon payments are reinvested in securities at a rate equal to the prevailing YTM at the time of purchase. In our example above, the bondholder will realize a return of 12.50% over the term of the bond if it is held to maturity and if the coupon payments are reinvested at this YTM. From this example, you can see that it is not just coupon income that contributes to the yield of the investment. The difference between the purchase price of $80 and the maturity price of $100 in five years also contributes to the overall YTM, as does the reinvestment of coupon payments. DID YOU KNOW? In most cases, the current yield, approximate YTM and the YTM will differ because they apply different formulas based on different assumptions. However, there is one instance in which the three measures will be equal: when the bond trades at par, the current yield, approximate YTM, and the YTM will be the same. © CANADIAN SECURITIES INSTITUTE 7 12 CANADIAN SECURITIES COURSE      VOLUME 1 REINVESTMENT RISK The YTM provides us with a good estimate of the return on a bond. However, you should keep in mind that the future trend in market rates could affect the true return on the bond, so it may differ from the YTM calculation. Because interest rates fluctuate, the interest rate prevailing at the time of purchase is unlikely to be the same as the interest rate prevailing at the time the investor reinvests cash flows from each coupon payment. The longer the term to maturity, the less likely it is that interest rates will remain constant over the term. The risk that the coupons will earn a return at a lower overall rate than the rate that prevailed at the time that the bond was purchased is called reinvestment risk. If all coupon payments are reinvested at a rate that is higher on average than the bond’s YTM at the time of purchase, the overall return on the bond will be higher than the YTM quoted at the time that the bond was purchased. In this case, the YTM at the time of purchase would be understated. If, on the other hand, coupon payments are reinvested at a rate that is lower on average than the bond’s YTM at the time of purchase, the overall return on the bond will be lower than the YTM quoted at the time that the bond was purchased. In this case, the YTM at the time of purchase would be overstated. Only a zero-coupon bond has no reinvestment risk because there are no coupon cash flows to reinvest before maturity. Instead, these bonds are purchased at a discount from their face value. The price paid takes into account the compounded rate of return that would have been received had there been coupons. CALCULATING BOND YIELD AND PRICE Can you calculate the yield on a bond? How well do you understand bond pricing? Complete the online learning activity to assess your knowledge. TERM STRUCTURE OF INTEREST RATES 2 | Describe the factors that determine the term structure of interest rates and shape of the yield curve. The market forces of supply and demand can affect the trading prices of bonds, and therefore their YTM. For example, if there is excess demand for a bond, the buying pressure will push the bond’s price higher, and therefore the YTM will fall. Another major driving force of a bond’s price is market interest rates. It is important, therefore, that you understand the factors that determine two things: The general level of interest rates at any particular time The level of interest rates at different terms to maturity Several theories have been proposed to explain why interest rates for different terms vary and how these variances create different results. In a general sense, interest rates are simply the result of the interaction between those who want to borrow funds and those who want to lend funds. The Fisher Effect is a well-known theory that explains how interest rates are determined. This theory, named after economist Irving Fisher, is based on the interaction between the inflation rate, the nominal interest rate, and the real interest rate. © CANADIAN SECURITIES INSTITUTE  CHAPTER 7      FIXED-INCOME SECURITIES: PRICING AND TRADING 7 13 THE REAL RATE OF RETURN The rate of return that a bond (or any investment) offers is made up of two components: The real rate of return The inflation rate 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. DID YOU KNOW? The real rate of return is determined by the level of funds supplied by investors and the demand for loans by businesses. The supply of funds tends to rise when real rates are high because investors are more likely to earn higher returns on the funds they lend. On the other hand, the demand for loans tends to rise when real rates are low because businesses that borrow to invest in their companies are more likely to earn returns that are higher than the costs of borrowing. The nominal rate for loans is made up of the real rate, as established by supply and demand, plus the expected inflation rate, as shown in Figure 7.7. Figure 7.7 | Calculating the Nominal Rate Nominal Rate = Real Rate + Inflation Rate Two factors affect forecasts for the real rate: The real interest rate rises and falls throughout the business cycle. During a recession, the real rate falls along with demand for funds. When rates fall far enough, however, the demand starts to rise again. As the economy expands, demand for funds continues to grow and the real rate rises in tandem. An unexpected change in the inflation rate also affects the real rate. Investors who lend money generally demand an interest rate that includes their expectations for inflation, thereby ensuring a satisfactory real rate. If the inflation rate is higher than expected, the investor’s real rate of return will be lower than expected. THE YIELD CURVE Just as bond prices and yields fluctuate, so does the relationship between short-term and long-term bond yields. This relationship between bonds of varying terms to maturity is referred to as the term structure of interest rates. The structure can be easily plotted on a graph for similar long-term and short-term bonds to show a continually changing line called the yield curve. A hypothetical yield curve for Government of Canada bonds is depicted in Figure 7.8. This upward-sloping curve is an example of a normal yield curve. © CANADIAN SECURITIES INSTITUTE 7 14 CANADIAN SECURITIES COURSE      VOLUME 1 Figure 7.8 | Short- and Long-term Government of Canada Security Yields 5 4 3 Yield % 2 1 0 1 month 3 months 6 months 12 months 2 years 3 years 5 years 7 years 10 years Long Time to Maturity The yield curve indicates the yield at a specific point in time for bonds of a similar type that have the same credit quality but different terms to maturity. In Figure 7.8, for example, very short-term Government of Canada bonds show a yield of 1%, whereas long-term bonds show yields around 4%. Three theories that attempt explain the shape of the yield curve are the expectations theory, the liquidity preference theory, and the market segmentation theory. EXPECTATIONS THEORY The expectations theory says that current long-term interest rates foreshadow future short-term rates. According to this theory, investors buying a single long-term bond should expect to earn the same amount of interest as they would buying two short-term bonds of equal combined duration. The theory implies that the shape of the yield curve indicates investor expectations about future interest rates. To illustrate, an investor who wants to invest money in the fixed-income market for two years has at least three choices: Buy a two-year bond. Buy a one-year bond, and then buy another one-year bond, when the first one matures. Buy a six-month bond, and then buy three more six-month bonds at intervals, as each bond matures. The expectations theory holds that, in an efficient market, each choice will be equally attractive. Accordingly, the two-year interest rate must be equal to two successive and consecutive one-year rates, and the one-year rate must be an average of two consecutive six-month rates. © CANADIAN SECURITIES INSTITUTE  CHAPTER 7      FIXED-INCOME SECURITIES: PRICING AND TRADING 7 15 EXAMPLE You are interested in a two-year bond that has a current rate of 5%. Your return on investment in the two-year bond at maturity would be 10.25%, which is calculated as 1.05 × 1.05 = 1.1025, or 1.052 = 1.1025. You are also interested in a one-year rate for the bond that is currently 4%. You plan to roll over (or reinvest) your investment into another one-year bond a year later. What will you need the second year’s one-year bond return to be so that the two consecutive one-year bonds produce the same return as the two-year bond? This statement is represented in the following balanced equation: 2 Year Return = 1 Year Return (Year 1) ´ 1 Year Return ( Year 2) The answer is found in the following calculation: 2 (1 + 0.05) = (1 + 0.04) ´ (1 + r ) 1.1025 (1 + r ) = = 1.06009 1.04 r = 0.06009 = 6% According to this calculation, with one-year rates at 4% and two-year rates at 5%, rates on one-year bonds are expected to increase from 4% to 6% a year from now. Assuming this expectation is correct, you will achieve the same result whether you buy a two-year bond today or two one-year bonds consecutively. The expectations theory holds that an upward sloping yield curve indicates an expectation of higher rates in the future, whereas a downward sloping curve indicates that rates are expected to fall. A humped curve indicates that rates are expected to first rise and then fall. The yield curve is thus said to reflect a market consensus of expected future interest rates. The yield curve in Figure 7.8, for example, which slopes upward from left to right, indicates a market consensus that investors expect interest rates to rise. LIQUIDITY PREFERENCE THEORY According to the liquidity preference theory, investors prefer short-term bonds because they are more liquid and less volatile in price. An investor who prefers liquidity will venture into longer-term bonds only if there is sufficient additional compensation for assuming the additional risks of lower liquidity and increased price volatility. According to this theory, the upward sloping yield curve in Figure 7.8 reflects additional return for assuming additional risk. The simplicity of this theory may be appealing, but it does not explain a downward sloping yield curve. MARKET SEGMENTATION THEORY The various institutional players in the fixed-income arena each concentrate their efforts in a specific term sector. For example, the major chartered banks tend to invest in the short-term market, whereas life insurance companies operate mainly in the long-term bond sector because of their long investment horizon. The market segmentation theory postulates that the yield curve represents the supply of and demand for bonds of various terms, which are primarily influenced by the bigger players in each sector. This theory can explain all types of yield curves, including a normal, upward-sloping curve, an inverted (downward sloping) curve, and a humped curve. © CANADIAN SECURITIES INSTITUTE 7 16 CANADIAN SECURITIES COURSE      VOLUME 1 YIELD CURVE Three popular theories explain the structure of interest rates on the yield curve: the expectations theory, the liquidity preference theory, and the market segmentation theory. Can you explain the concept behind each theory? Complete the online learning activity to assess your knowledge. FUNDAMENTAL BOND PRICING PROPERTIES 3 | Explain how bond prices react to changes in interest rates, maturity, coupon, and yield. Earlier, in our discussion of present value, we explained how to determine the appropriate price to pay for a bond or other fixed-income security. Another important thing to know is where that price is headed. Current interest rate levels and your understanding of term structure may help you forecast the general direction of bond prices. However, you should also understand the specific features of an individual bond that determine how that particular bond will react to interest rate changes. We now turn our attention to several tables showing calculations. The yields in these tables are calculated using precise present value techniques, including semi-annual compounding and full reinvestment of all coupons at the prevailing yield. You can duplicate the price information with a financial calculator. THE RELATIONSHIP BETWEEN BOND PRICES AND INTEREST RATES 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. Table 7.2 shows the inverse relationship of bond prices and interest rates (and therefore bond yields). Table 7.2 | Effect of an Interest Rate Change on the Price of a 3% Five-Year Bond % Yield % Change Yield Price Price Change % Price Change 3% 0 100.00 0 0 1% Increase (to 4%) +33.33* 95.51 −4.49 −4.49 1% Decrease (to 2%) −33.33 104.74 +4.74 +4.74 * This number is calculated as follows: (Ending Value − Beginning Value) ÷ Beginning Value × 100, or (0.04 − 0.03) ÷ 0.03 × 100 = 33.33%. Remember that the coupon rate doesn’t change over the life of the bond; the bondholder continues to receive the established coupon rate regardless of whether the bond price goes up or down. When interest rates rise and the bond yield rises to keep pace, the only way to create additional yield beyond what the coupon rate already provides is to lower the price of the bond. For example, Table 7.2 shows that when the yield of a 3% bond rises to 4%, the price of the bond must drop from 100 to 95.51 to achieve a yield of 4%. New buyers paying 95.51 would receive a combination of interest income ($3 per $100 of par value) and a gain on the price of the bond (based on the difference between the purchase price and eventual maturity price of par). The overall yield thereby increases to 4%. © CANADIAN SECURITIES INSTITUTE  CHAPTER 7      FIXED-INCOME SECURITIES: PRICING AND TRADING 7 17 Conversely, when interest rates fall and the bond yield falls to 2% to keep pace, the only way to reduce the yield to 2% is to increase the price of the bond from 100 to 104.74. New buyers paying 104.74 would receive a combination of 3% interest income and a loss on the price of the bond, thereby reducing the overall yield to 2%. THE IMPACT OF MATURITY The next important relationship to recognize is that longer-term bonds are more volatile in price than shorter-term bonds. For example, Table 7.3 compares a 3%, five-year, semi-annual coupon bond with a 3%, 10-year, semi-annual coupon bond. Note that when interest rates are 3%, both bonds are priced at par to yield 3%. Table 7.3 | The Effect of Interest Rate Changes on Bonds of Different Terms 3% FIVE-YEAR BOND % Yield % Change Yield Price Price Change % Price Change 3% 0 100.00 0 0 1% Increase (to 4%) +33.33 95.51 −4.49 −4.49 1% Decrease (to 2%) −33.33 104.74 +4.74 +4.74 3% 10-YEAR BOND Interest Rate (Yield) % Change Yield Price Price Change % Price Change 3% 0 100.00 0 0 1% Increase (to 4%) +33.33 91.82 −8.18* −8.18 1% Decrease (to 2%) −33.33 109.02 +9.02 +9.02 * This number is calculated as follows: (Ending Value − Beginning Value) ÷ Beginning Value × 100, or (91.82 − 100) ÷ 100 × 100 = −8.18. If interest rates rise to the point at which each bond yields 4%, both the five-year and the 10-year bond will drop in price to different degrees: the five-year bond drops 4.49%, and the 10-year bond drops 8.18%. A similar pattern occurs when interest rates, and therefore yields, drop. 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. The longer-term bond will rise more sharply (9.02% if yields drop to 2%) than the shorter-term bond (which rises only 4.74%). As bonds approach maturity over the years, they become less volatile. For example, a bond is originally issued with a 10-year maturity; seven years later, it has only a three-year term. As such, it will be priced as, and will trade as, a three-year bond at that time. THE IMPACT OF THE COUPON Our next pricing relationship states that lower-coupon bonds are more volatile in price percentage change than high-coupon bonds. Table 7.4 compares a 3%, five-year, semi-annual coupon bond with a 2%, five-year, semi- annual coupon bond. All other factors are assumed to be constant, such as credit quality and liquidity. Therefore, the only difference between the two bonds is the coupon rate. Market rates start at 3%. © CANADIAN SECURITIES INSTITUTE 7 18 CANADIAN SECURITIES COURSE      VOLUME 1 Table 7.4 | The Effect of Interest Rate Changes on Bonds with Different Coupons 3% FIVE-YEAR BOND % Yield % Change Yield Price Price Change % Price Change 3% 0 100.00 0 0 1% Increase (to 4%) +33.33 95.51 −4.49 −4.49 1% Decrease (to 2%) −33.33 104.74 +4.74 +4.74 2% FIVE-YEAR BOND % Yield % Change Yield Price Price Change % Price Change 3% 0 95.39 0 0 1% Increase (to 4%) +33.33 91.02 −4.37 −4.58 1% Decrease (to 2%) −33.33 100.00 +4.61 +4.83 When yields rise, both bonds drop in price; however, the lower coupon bond drops more (4.58%) than the higher- coupon bond (4.49%). This difference is significant when there is a considerable difference between coupons or when large sums of money are invested. THE IMPACT OF YIELD CHANGES Our last bond pricing relationship states that the relative yield change is more important than the absolute yield change. For example, a drop in yield from 12% to 10% will have a smaller impact on a bond’s price than a drop in yield from 4% to 2%. Although both represent a drop of 200 basis points, the former is a 17% change in yield, and the latter is a 50% change in yield. Therefore, bond prices are more volatile when interest rates are low. On another note, when the yield rises or falls by the same percentage, the price of a bond is impacted more by the fall in yield. For example, Table 7.5 demonstrates that a 1% drop in yield leads to a greater change in price than a 1% rise in yield. The price rises by 4.74% in the first scenario and falls by 4.49% in the second. Table 7.5 | Price Changes Relative to Changes in Yield 3% FIVE-YEAR BOND % Yield % Change Yield Price Price Change % Price Change 3% 0 100.00 0 0 1% Increase (to 4%) +33.33 95.51 −4.49 −4.49 1% Decrease (to 2%) −33.33 104.74 +4.74 +4.74 DURATION AS A MEASURE OF BOND PRICE VOLATILITY So far in this chapter, we discussed the following relationships: The value of a bond changes in the opposite direction to a change in interest rates: as interest rates rise, bond prices fall; as interest rates fall, bond prices rise. 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. © CANADIAN SECURITIES INSTITUTE  CHAPTER 7      FIXED-INCOME SECURITIES: PRICING AND TRADING 7 19 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. Given these relationships, it is fairly easy to compare bonds with the same term to maturity or the same coupon. But how do we compare bonds with different coupon rates and different terms to maturity? For example, how can we determine whether a bond with a high coupon and a long term will be more or less volatile than a bond with a lower coupon and a shorter term? A change in interest rates affects the price of different bonds differently, depending on features such as coupons, maturities, and protective covenants. In fact, a change in interest rates is one of the main risks faced by investors holding fixed-income securities. To make sound investment decisions, you must be able to determine the impact of interest rate changes on the prices of different types of bonds. The calculation that combines the impact of both the coupon rate and the term to maturity is called duration. Duration is a measure of the sensitivity of a bond’s price to changes in interest rates. It is defined as the approximate percentage change in the price or value of a bond for a 1% change in interest rates. The higher the duration of the bond, the more it will react to a change in interest rates. When duration is known, that value helps investors determine the bond’s, or the bond fund’s, volatility—the amount of change in price as interest rates change. In this way, a single duration figure for each bond can be compared directly with the duration of every other bond. EXAMPLE You are interested in buying a DEC Corp. bond priced at 105 with 12 years left to maturity, but you are concerned that interest rates are going to rise by 1% over the next year. The duration of the bond is 10, which means that its price will change by approximately 10% for each 1% change in interest rates. You determine that the price of the bond could drop from 105 to 94.50, if your expectations about the interest rate change are correct. This figure is calculated as follows: 105 − (10% × 105) = 94.50. A higher duration translates into a higher percentage price change for a given change in yield. To earn the greatest return, you should therefore invest in bonds with a higher duration when you expect interest rates to decline. Conversely, when interest rates are expected to rise, you should invest in bonds with low duration to protect a bond portfolio from a dramatic decline. Table 7.6 shows the impact that interest rate changes have on bonds with different durations and different rate changes. As the table shows, the same interest rate change has a greater impact on the price of Bond A compared with the price change on Bond B. Table 7.6 | Impact of an Interest Rate Change on Bonds with Different Durations Bond A: Duration = 10 Bond B: Duration = 5 Current price $1,000 $1,000 Price when interest rates rise by 1% $900 (−10%) $950 (−5%) Price when interest rates fall by 0.5% $1,050 (+5%) $1,025 (+2.5%)* * We are not constrained to 1% interest rate changes. As long as the duration of the bond is known, the effect of any range of interest rate changes can be determined. The change in price for Bond B with a duration of 5 and a 0.50% interest rate drop is 2.5% (calculated as 5 × 0.50%). © CANADIAN SECURITIES INSTITUTE 7 20 CANADIAN SECURITIES COURSE      VOLUME 1 DIVE DEEPER Calculating a bond’s duration is a complicated process, and the value can also change over longer holding periods and larger interest rate swings. Therefore, we do not show the formula for calculating duration in this course. The concept is explained more fully in three CSI courses: Investment Management Techniques (IMT), Portfolio Management Techniques (PMT), and Wealth Management Essentials (WME). BOND MARKET TRADING 4 | Describe how bond trading is conducted. Fixed-income trading activities in the investment banking business take place in two separate areas of operation: the sell side and the buy side. The two sides sometimes operate out of separate institutions, but some large investment banks encompass both a sell-side desk and a buy-side desk. THE SELL SIDE The sell side of fixed-income trading is the investment dealer side. Sell-side institutions (or divisions) are concerned with the trading (i.e., the buying and selling) of investment products for their own accounts. Sell-side services include everything related to creating, producing, distributing, researching, marketing, and trading fixed-income products. Most medium-to-large sell-side firms divide fixed-income duties into three primary occupational roles: Investment banker Investment bankers help their clients to structure new debt issues and bring these new issues to the primary market. Their clients are firms that need to raise funds for working capital and to fund asset acquisitions. Trader Traders trade securities that exist in the secondary market. They typically trade on a proprietary basis. Sales representative Sales representatives market new (primary) and existing (secondary) products, conduct research, and provide market analysis, credit analysis, and commentary. They also take client orders, which are then relayed to traders for pricing. THE BUY SIDE The buy side of fixed-income trading is the investment management side. Buy-side institutions (or divisions) are concerned with asset management and are typically engaged in the buying and holding of securities on behalf of their institutional clients. Their clients include entities such as mutual funds, insurance companies, and pension funds. Most buy-side firms divide fixed-income investment management duties into two primary occupational roles: Portfolio manager Trader We will discuss the subject of institutional clients more fully in the next volume of this course, the Canadian Securities Course (CSC) Volume II. © CANADIAN SECURITIES INSTITUTE  CHAPTER 7      FIXED-INCOME SECURITIES: PRICING AND TRADING 7 21 BUYING BONDS THROUGH AN INVESTMENT DEALER The bond-trading approach of investment advisors acting on behalf of their clients varies according to the bond- trading capacity of their firm. TRADING IN FIRMS WITH A LARGE INSTITUTIONAL DEALING DESK In firms with a large institutional dealing desk, investment advisors are typically served by a retail trading desk. The role of the retail desk is in many ways similar to that of the institutional sales desk. Its primary function is to help the advisors by sourcing products and providing market commentary. The advantage of dealing within a larger firm is the access it provides to the wide range of securities in its inventory. Typically, each firm has a proprietary trading system linked directly to its inventory, which allows for automatic execution of trades once the advisor enters them into the system. Most trades take place using the system, with no need for the advisor to contact the retail trading desk by phone. For large trades and some illiquid securities, however, auto-execution is not normally available, and trades must be executed over the phone. TRADING IN FIRMS WITHOUT A LARGE INSTITUTIONAL DEALING DESK In firms without a large institutional dealing desk, investment advisors are served by a trading desk as the source of product. Without a large internal institutional inventory to draw on, the trading desk must build its own inventory of products. It also sources products that it does not own from other dealers. ROLE OF INTER-DEALER BROKERS Inter-dealer brokers are participants in the wholesale bond market (i.e., the bond market between the institutional buy side and sell side). These brokers act solely as agents, bringing together institutional buyers and sellers in matching trades (rather than the institutions dealing directly with one another). In the process of doing so, they perform price discovery, which refers to determining the correct price of a security by studying the demand and supply in the market. They also perform trade execution, clearing, and settlement. In some cases, they also provide public transparency of prices. In some respects, inter-dealer brokers perform a similar function to that of a market exchange. In Canada, a significant amount of fixed-income trading volumes flow through these brokers. In some cases, a key advantage the inter-dealer broker provides for institutional clients is anonymity. For example, assume that you are holding a large fixed-income position at a loss that you want to sell. An inter-dealer broker might be able to help you gradually sell your position to other institutions, thus helping to prevent other market participants from discovering your position and trading against it. MECHANICS OF THE TRADE All non-electronic trades carried out between the investment advisor and the trader are consummated over the phone. As such, they carry the legal responsibility of a full commercial agreement or commitment. The calls are recorded, and all parties use key words and clear language to communicate. When a trader and the advisor commit to a trade, one party agrees to deliver the full amount of the bonds that were sold on the settlement date, either from the trading book or from the client’s account. The other side agrees to make payment in full on the settlement date, again either within the trading book or from the client’s account. © CANADIAN SECURITIES INSTITUTE 7 22 CANADIAN SECURITIES COURSE      VOLUME 1 THE TRADE TICKET The trade ticket is an electronic confirmation sent through secure, proprietary systems. It contains the following information: Specific details of the counterparties to the trade, including the name and address of the investment advisor’s employer (the investment dealer holding the client’s account on its books) and the name and account number of the client (Note: Retail trade tickets are usually written from the perspective of the client; therefore, a buy ticket means that the trading desk is selling to the client.) Full identification of the bond, including the issuer’s name, the maturity date, and the coupon The bond’s Committee on Uniform Security Identification Procedure (CUSIP), or other electronic settlement identification number (Note: The CUSIP number is an alphanumeric code used to identify all securities in North America. This system has been used since 1964 to facilitate the clearing and settlement of trades.) The nominal, par, or face amount of the transaction The price, and often the yield The settlement date The name of the custodian where the trade will settle The total settlement amount, sometimes with the amount of accrued interest shown separately CLEARING AND SETTLEMENT When a securities transaction has been confirmed, the change in legal ownership is effective immediately; however, payment for purchased securities does not have to be made until sometime later. The securities do not have to be delivered until the end of what is called the settlement period, when payment is made. The length of the settlement period varies depending on the type of security. T-bills settle on the day of the transaction. Other securities, such as bonds, debentures, certificates of indebtedness, preferred shares, and common shares settle on the first clearing day after the transaction takes place. Over time, the recognition of ownership of debt securities has taken on different forms. Table 7.7 describes the different methods in which debt securities have been issued. Table 7.7 | Fixed-Income Securities Ownership Ownership Characteristics History Bearer bonds A certificate is produced, and detachable The risk of losing certificates was a coupons are attached to the residual concern because they could be sold by principal payment. Investors detach the anyone who had physical possession, coupon and submit it to a bank or other whether or not the seller was considered financial institution to receive payment from the rightful owner. As an added protection the issuer on each coupon payment date. from theft, other methods of registration The same process is followed for the residual were sought. Some (though not many) principal, when due. Ownership is signified bearer bonds still exist today. by physical possession. © CANADIAN SECURITIES INSTITUTE  CHAPTER 7      FIXED-INCOME SECURITIES: PRICING AND TRADING 7 23 Table 7.7 | Fixed-Income Securities Ownership Ownership Characteristics History Registered bonds Registered bonds bear the name of the The added layer of protection through rightful owner and can be sold or transferred registration solved the issue of theft only when the owner signs the back of the and loss of certificates. However, the certificate. Coupon payments are mailed to evolution of the bond market led to the registered owner. demand for greater liquidity, as well as cheaper and faster ways to bring issues to the market. Bonds registered Rather than physical certificates, a book- Most bond issues around the globe are in book-based based format is an electronic record keeping now issued in a book-based format, with format system used by depositories that keeps track depository, trade clearing, and settlement of ownership and settlement of securities services provided by participating clearing transactions. In Canada, the national providers. provider of these services is the CDS Clearing and Depository Services Inc. CALCULATING ACCRUED INTEREST Most bonds pay interest twice a year, on the same month and day as the maturity date, and again exactly six months later. For example, if a bond’s maturity date is February 15, 2030, interest will be paid every February 15 and every August 15 until maturity. Some Eurobonds pay annually, and some provincial and corporate bonds pay monthly. It is possible, however, to purchase bonds on almost any day. Theoretically, you could purchase the above bond on August 1 of any year, hold it for two weeks, and receive a full six months’ interest. The previous bondholder, on the other hand, may have held the bond for five and a half months and received no interest. To ensure that the transaction between buyer and seller is equitable, the buyer pays accrued interest to the seller at the time of the purchase. Accrued interest is the amount of interest built up during the previous holding period. Interest accrues from the day after the previous interest payment date up to and including the day of settlement. The client who buys a bond pays the purchase price plus the interest that has accumulated since the last interest date. This interest is regained if the bond is held until the next interest payment date. If it is sold in the meantime, the new buyer pays accrued interest to the current seller. The accrued interest amount is found by using the following formula: Coupon Rate Time Period Par Amount ´ ´ = Accrued Interest 100 365 The amount is based on the par amount purchased or sold. The bond may have been purchased at a premium or a discount, but interest is always based on par value. The rate at which interest accrues is the coupon rate of the bond, not its yield. © CANADIAN SECURITIES INSTITUTE 7 24 CANADIAN SECURITIES COURSE      VOLUME 1 EXAMPLE You purchase an 8% Government of Canada bond, due to mature on March 15, 2033, with a principal amount of $200,000. You purchase the bond on Thursday, May 8 of this year, and the last coupon was paid on March 15 of this year. March 16 is therefore the first day of accrued interest. The settlement date for this transaction is May 9 (the first clearing day after the transaction took place). The number of days of accrued interest for this transaction falls between March 15 and May 9, as follows: March 16–31 16 days April 30 days May 9 days Total 55 days Notes: a. Include March 16 and May 9, but not March 15. b. If the year is a leap year, the seller is entitled to an extra day’s accrued interest in February. Nevertheless, the practice is to base the interest calculation on a 365-day year. Accrued interest on this bond is calculated as follows: 8.00 55 200,000 ´ ´ = 2,410.96 100 365 Because of the variation in the number of days in a calendar month, the calculation of accrued interest can result in an amount greater than half a year’s interest payment. In such cases, accrued interest is calculated on the basis of the full amount of the coupon, less one or two days, as the case may be. The amount of accrued interest owed to a seller or payable by a purchaser is shown on the confirmation contract that each party receives. ACCRUED INTEREST When a bond is bought or sold on the secondary market, part of the purchase price of the bond is any accrued interest that has accumulated. Can you calculate this accrued amount that must be paid to the seller? Complete the online learning activity to assess your knowledge. BOND INDEXES 5 | Define bond indexes and how they are used in the securities industry. An index measures the relative value and performance of a group of securities over time. Most people are familiar with stock indexes, such as the S&P/TSX Composite Index, which have been around for well over 100 years. Bond indexes, on the other hand, have been around only since the early 1970s. Bond indexes are generally used in three ways: As a guide to the performance of the overall bond market or a segment of that market As a performance measurement tool, to assess the performance of bond portfolio managers To construct bond index funds © CANADIAN SECURITIES INSTITUTE  CHAPTER 7      FIXED-INCOME SECURITIES: PRICING AND TRADING 7 25 CANADIAN BOND MARKET INDEXES FTSE Global Debt Capital Markets offers a comprehensive set of Canadian bond indexes. The best known of these indexes is the FTSE Canada Universe Bond Index, which tracks the broad Canadian bond market. The index consists of bonds representing a full cross-section of government and corporate bonds. All Canadian dollar-denominated investment-grade bonds with a term to maturity of one year or more are eligible for inclusion in the index. The bonds in the index are grouped into sub-indexes in different combinations according to whether they are government or corporate bonds, their time to maturity, and the bond rating (for corporate bonds only). The FTSE Canada Universe Bond Index measures the total return on bonds in Canada, including realized and unrealized capital gains, and the reinvestment of coupon cash flows. It is a capitalization-weighted index, with each bond held in proportion to its market value. GLOBAL INDEXES A number of securities firms and other organizations have created bond indexes, including those detailed below, that track the many global markets: Global bond indexes FTSE World Government Bond Index U.S. bonds Bloomberg U.S. Aggregate Bond Index FTSE US Broad Investment-Grade Bond Index Government bonds FTSE Actuaries UK Conventional Gilts 5-15 Years S&P France Sovereign Inflation-Linked Bond Index Emerging market J.P. Morgan Emerging Markets Bond Index Global bonds High-yield bonds Credit Suisse High Yield Index ICE Bank of America US High Yield Master II Total Return Index CASE SCENARIO Your nephew joined your financial firm but has some questions about the discount rate. Can you answer your nephew’s questions? Complete the online learning activity to assess your knowledge. KEY TERMS & DEFINITIONS Can you read some definitions and identify the key terms from this chapter that match? Complete the online learning activity to assess your knowledge. © CANADIAN SECURITIES INSTITUTE 7 26 CANADIAN SECURITIES COURSE      VOLUME 1 SUMMARY In this chapter we discussed the following aspects of fixed-income securities: Present value is the value today of an amount of money to be received in the future. The discount rate is the interest rate used to calculate present value. The fair price for a bond is the sum of the present value of its coupons and the present value of its principal. The current yield of any investment is the income yield on the security relative to its current market price. The YTM is calculated based on the assumption that all interest received from coupon bonds is reinvested at the YTM prevailing at the time the bond was purchased. The real rate of return is the return on an investment adjusted for the effects of inflation. The expectations theory states that the shape of the yield curve reflects expectations for future interest rates. The liquidity preference theory states that investors must be compensated for assuming the risk of holding longer-term debt securities. The market segmentation theory holds that investors concentrate their debt holdings in a particular term to maturity. When interest rates rise, bond yields rise and prices fall; when interest rates fall, bond yields fall and prices rise. Longer-term bonds are more volatile in price percentage change, compared to shorter-term bonds. Lower coupon rate bonds are more volatile in price percentage change than higher coupon rate bonds. And relative yield change is more important than absolute yield change. The sell side of fixed-income trading is the investment dealer side. The buy-side focuses on asset management on behalf of institutional clients. Trading in firms with a large institutional dealing desk allows for automatic execution in most cases. All non-electronic trades carried out between the investment advisor and the trader take place over the phone. Government of Canada T-bills settle on the day of the trade, whereas all other bonds, debentures, and certificates of indebtedness settle on the first clearing day after the transaction takes place. Interest on a bond accrues from the day after the previous interest payment date up to and including the day of settlement. An index measures the relative value and performance of a group of securities over time. Bond indexes are generally used as a guide to the performance of the overall bond market or a segment of that market, and as a performance measurement tool to assess bond portfolio managers. Bond indexes are also used to construct bond index funds. REVIEW QUESTIONS Now that you have completed this chapter, you should be ready to answer the Chapter 7 Review Questions. FREQUENTLY ASKED QUESTIONS If you have any questions about this chapter, you may find answers in the online Chapter 7 FAQs. © CANADIAN SECURITIES INSTITUTE