Equity Transactions - CSC Volume 1 Section 3 PDF

Equity Securities: Equity Transactions 9 CHAPTER OVERVIEW In this chapter, you will learn about the characteristics of equity transactions. First, we will discuss the d...

Equity Securities: Equity Transactions 9 CHAPTER OVERVIEW In this chapter, you will learn about the characteristics of equity transactions. First, we will discuss the difference between a cash account and a margin account, and between long and short positions. We will then discuss in detail margin account transactions and short selling rules, techniques, and risks. You will also learn how trades are conducted and settled, and finally how securities are bought and sold through different types of orders. LEARNING OBJECTIVES CONTENT AREAS 1 | Define cash and margin accounts. Cash Accounts and Margin Accounts 2 | Describe the process for establishing long Margin Account Transactions margin and short margin positions. 3 | Interpret the impact price changes have on long and short margin requirements. 4 | Describe the trading and settlement Trading and Settlement Procedures procedures for equity transactions. 5 | Distinguish among the types of buy and How Securities Are Bought and Sold sell orders. © CANADIAN SECURITIES INSTITUTE 9 2 CANADIAN SECURITIES COURSE      VOLUME 1 KEY TERMS Key terms are defined in the Glossary and appear in bold text in the chapter. cash account market order confirmation on-stop buy order day order on-stop sell order good til order professional (PRO) order limit order settlement date long position short position margin short selling margin account stop buy order Margin Account Agreement Form stop loss order margin call © CANADIAN SECURITIES INSTITUTE  CHAPTER 9      EQUITY SECURITIES: EQUITY TRANSACTIONS 9 3 INTRODUCTION By now, you should have a good understanding of the different types of securities that trade in the market. In this chapter, we turn our attention to the mechanical process by which investments are acquired, held, and sold. On the surface, buying or selling a stock on an exchange seems fairly straightforward. However, there is more to trading than simply calling an investment dealer or self-directed broker and placing a buy or sell order. For example, an investor has the option of buying shares on margin or short selling the stock. The investor can also place a limit price on the trade, place the trade at the market, or add other conditions to the purchase. These considerations are important to the decision-making process and, ultimately, to the choice of investment strategy. Of course, there are risks, advantages, and disadvantages to the chosen trading strategy. This chapter focuses on equity transactions, including margin, short selling, and the various buy and sell orders investors use to trade stocks. CASH ACCOUNTS AND MARGIN ACCOUNTS 1 | Define cash and margin accounts. A securities transaction through a dealer member must be made in either a cash account or a margin account. Clients with regular cash accounts are expected to make full payment for purchases or full delivery for sales on or before the settlement date. The settlement date is specified in the contract, generally according to the following industry rules: Government of Canada Treasury bills—on the day that the transaction takes place All other securities—one business day after the transaction takes place In contrast, margin accounts are used by clients who wish to buy or sell securities on partial credit. In such cases, the client pays only a portion of the purchase price and the investment dealer lends the balance to the client, charging interest on the loan. The difference between cash accounts and margin accounts is important. When a client opens a cash account, the investment dealer does not grant credit. The explicit understanding is that the client will pay for the security in full on the settlement date. With a margin account, on the other hand, it is understood that the firm is granting credit based on the market value and quality of the securities held in the account. LONG POSITIONS AND SHORT POSITIONS Throughout this chapter, we refer to long and short positions. A long position represents actual ownership in a security. In contrast, a short position is created when an investor sells a security that the investor does not own. EXAMPLE An investor buys common shares to initiate a long position in a stock and must pay for the stock purchase by the settlement date. To close the long position, he sells the stock in the market. Another investor, with the dealer member’s permission, sells securities she does not own to initiate a short position. The borrowed shares are delivered to the purchaser. She must leave the proceeds of the sale in her margin account and make an additional margin deposit in case the value of the securities rises. To close the short position, she buys back the stock from the market. © CANADIAN SECURITIES INSTITUTE 9 4 CANADIAN SECURITIES COURSE      VOLUME 1 MARGIN ACCOUNT TRANSACTIONS 2 | Describe the process for establishing long margin and short margin positions. 3 | Interpret the impact price changes have on long and short margin requirements. Margin accounts require only partial payment for a purchase of securities. The investment dealer lends the client the unpaid portion of the market value of the securities at prevailing interest rates. The client must make an initial deposit of a specified portion of the value of the securities. Interest on a margin loan is calculated daily on the debit balance (i.e., the outstanding balance) in the account and charged monthly. Investment dealers usually charge interest based on the rates the clients are charged on their chartered bank loans. The word margin refers to the amount of funds the investor must personally provide. The margin plus the loan provided by the dealer member together make up the total amount required to complete the transaction. Two types of margin positions are possible: A long margin position allows investors to partially finance the purchase of securities by borrowing money from the dealer. Investors buy on margin with the expectation that the price of the security will rise. A short margin position allows investors to sell borrowed securities in the expectation that the price will fall, allowing the investor to buy back the shares at a lower price for a profit. Not every dealer member allows margin accounts, and those that do must obtain an authorized Margin Account Agreement Form from the client before any business is transacted. LONG MARGIN ACCOUNTS The amount of credit that a dealer member may extend to its clients for the purchase of securities (both listed and unlisted) is strictly regulated and enforced by the Canadian Investment Regulatory Organization (CIRO). Examiners conduct spot checks, in addition to regular field examinations, to ensure that the firms keep clients’ accounts properly margined. Table 9.1 shows the minimum margin requirements that dealer members require from clients for long positions in equity securities listed on a recognized exchange in Canada. Table 9.1 | Margin Required for Long Positions (For information only) On Listed Equities Selling Minimum Margin Required At $2.00 and over 50% of market value At $1.75 to $1.99 60% of market value At $1.50 to $1.74 80% of market value Under $1.50 100% of market value (i.e., no loan value) Securities Eligible for Reduced Margin* 30% of market value * Note that these margin amounts are determined by CIRO. Dealer members may choose to set more stringent requirements. For example, many firms do not allow clients to take margin positions on stocks that trade under $3. © CANADIAN SECURITIES INSTITUTE  CHAPTER 9      EQUITY SECURITIES: EQUITY TRANSACTIONS 9 5 EXAMPLE To purchase shares on credit from a dealer when the shares trade at $1.85 per share, the dealer may loan a maximum of 40% of the market value of the shares. Therefore, the investor’s margin would be 60% of the market value. If, instead, the purchase was for shares that trade at $1.55 per share, the dealer may loan a maximum of 20% of the market value of the shares. Therefore, the investor’s margin would be 80% of the market value. CIRO produces a quarterly list of “securities eligible for reduced margin”. Inclusion in the list is restricted to those securities that demonstrate both sufficiently high liquidity and sufficiently low price volatility, based on specific price risk and liquidity risk measures. MARGINING LONG POSITIONS When a long position is established on margin, sufficient funds (or securities with excess loan value) must be in the account to cover the purchase. The dealer member lends some of these funds to the client, and the client is responsible for the balance. Therefore, margin refers to the amount put up by the client. The minimum margin required equals the initial cost of the transaction minus the loan amount. The sum of the margin and the loan must always be equal to the original purchase price, at a minimum. If the price of the security falls, the value of the loan drops accordingly. The client must then immediately provide additional funds in the account to cover the shortfall up to the original purchase price. This requirement to deposit additional money is known as a margin call. If, on the other hand, the security price rises, the loan amount rises accordingly, and the client has access to additional funds in the account immediately. This additional amount is called excess margin. The margin requirement is always the difference between the original purchase price and the loan, as illustrated in the following examples. (Note that, in these examples, commissions are excluded from the calculations.) Note: The margin calculations in the examples that follow are for information only. However, by working through these examples, you will strengthen your understanding of how long margin accounts in general are affected by changing stock prices. (Note that commissions are excluded from the calculations.) EXAMPLE (For information only) Assume that a client buys 1,000 shares of listed ABC Company on margin at a loan rate of 50%. The security sells for $25 per share. In other words, the client puts up $12,500 to buy $25,000 of ABC shares. The firm lends the remaining half of the money to the client. Total cost to buy ABC shares $25,000 (A) Less: Maximum loan put up by the firm (50% of $25 × 1,000) $12,500 Equals: Margin put up by the client $12,500 (B) Now let’s consider two scenarios: In Scenario 1, the price of ABC stock declines to $22. In Scenario 2, the price of ABC stock increases to $29. © CANADIAN SECURITIES INSTITUTE 9 6 CANADIAN SECURITIES COURSE      VOLUME 1 EXAMPLE (cont'd) Scenario 1: Margin Call Original cost of ABC shares (A above) $25,000 Less: Member’s revised maximum loan (50% of $22 × 1,000) $11,000 Equals: New margin requirement $14,000 Less: Client’s original margin deposit (B above) $12,500 Equals: Net margin deficiency (for which a margin call is issued to the client) $1,500 In this scenario, with the price of the security falling to $22, the amount of money the dealer is willing to lend drops to $11,000 (50% of the market price). Because the original purchase price must be in the account at all times, the margin requirement has increased to $14,000. The client had originally put up an initial margin of $12,500, which means that there is now a $1,500 shortfall. The firm issues a $1,500 margin call, which means that the client must deposit this amount immediately into the account. Scenario 2: Excess Margin Original cost of ABC shares (A above) $25,000 Less: Member’s revised maximum loan (50% of $29 × 1,000) $14,500 Equals: New margin requirement $10,500 Less: Client’s original margin deposit (B above) $12,500 Equals: Excess margin in account $2,000 In this scenario, with the price of the security rising to $29, the amount of money the firm is willing to lend rises to $14,500 (50% of the market price). This increase reduces the margin requirement to $10,500 ($25,000 − $14,500 = $10,500). Because the client put up an initial margin of $12,500, there is now an excess margin of $2,000 in the account for the client to use as desired. The excess $2,000 can be used as margin toward the purchase of another security, or it can be withdrawn from the account. However, it is not an idle amount of cash that can be removed without consequence. The client is still borrowing money from the dealer member, on which interest is charged. If the excess margin is left in the account, the borrowed amount is still $12,500 (calculated as $25,000 − $12,500), which was loaned initially by the dealer. What has changed is the amount of money that the dealer is willing to lend. Because the collateral value of the shares has increased, the member is willing to lend $14,500, instead of the initial $12,500. By withdrawing the $2,000 margin surplus, the client is choosing to borrow (and thus pay interest on) this additional amount. MARGIN RISKS It is important to recognize that borrowing funds to invest involves more risk than simply buying and paying for a security in full from a cash account. Here are some of the risks associated with using a margin account: Margin increases Borrowing to buy securities magnifies the outcome, either in a positive or negative way. market risk © CANADIAN SECURITIES INSTITUTE  CHAPTER 9      EQUITY SECURITIES: EQUITY TRANSACTIONS 9 7 Loan and interest must The client must pay interest during the period that the security is margined and must be repaid repay the loan at the end, regardless of the value of the security. Margin calls must be If the security has fallen in price and the client fails to meet the margin call, the dealer paid without delay can sell the security without notice or consent, and the client will suffer a loss. Clients with margin accounts should avoid the practice of margining close to prevailing price limits (i.e., keeping a minimum amount of margin on deposit in the account). Additional funds or securities with excess loan value on deposit protect against the risk of a margin call after a minor adverse price fluctuation. The cushion of protection also reduces the possibility that the dealer will be forced to sell out the margin account in the event of a drastically adverse price fluctuation. SHORT MARGIN ACCOUNTS Short selling is defined as the sale of securities that the seller does not own and can only be done in a margin account. Profits are made whenever the initial sale price exceeds the subsequent purchase cost. This is unlike a long position, where the investor purchases a security and then holds it in the hope of eventually selling it at a higher price. With short selling, the order of the transactions is reversed: the investor sells the security first, and then waits in the hope of eventually buying it back at a lower price. Because the seller does not own the securities sold, the seller in effect creates a short position, during which the seller still owes the securities. The subsequent purchase eventually compensates for this deficit. Short selling is generally carried out in the belief that the price of a stock is going to fall, and the investor who sells it short will be able to buy it back later at a lower price. If that subsequent purchase is lower than the investor’s original sale price, the investor has made a profit. EXAMPLE A client contacts you, his investment advisor, wishing to short a security. Your client declares his intention to sell short at $10 per share. Your firm proceeds to lend the securities to be shorted to your client, which the client then sells into the market. The process is similar to the way a long position is sold. The only difference is that the short sale must be declared at the time of the trade. The proceeds of the short sale are then deposited in your client’s account. The client then deposits enough margin into the account ($5 per share), in addition to the sale proceeds, to bring the account balance up to the required minimum. After the short position is established, your client then waits for an opportune moment to cover the sale of the securities with a purchase when the price is lower. Of course, the price can also rise, which could lead to incurring a loss. Therefore, both the firm and your client keep regular monitoring of the position. Your client eventually purchases the stock originally sold short, and the stock is returned to your firm. In some circumstances, your firm could require the client to return the security. If another lender is not available, the client is forced to buy back the security at the current price. If the current price is higher than the original sale, your client will be forced to suffer a loss. Short selling has an element of leverage because the investor borrows stock from the dealer and puts up less money than the minimum required balance. Therefore, short selling is considered riskier than purchasing an outright long position. Theoretically, short selling has unlimited risk because the security that the investor sold short could potentially rise to infinity. Because of the high risk, some basic precautions are available to the investment advisor for clients who wish to short a security. We will discuss in detail these precautions later in this chapter. © CANADIAN SECURITIES INSTITUTE 9 8 CANADIAN SECURITIES COURSE      VOLUME 1 Figure 9.1 illustrates a brief version of the short selling process. Figure 9.1 | Short Selling—Simplified Steps Step 1 Your client calls you and instructs you to sell 10,000 shares of ABC short. Step 2 Your firm lends the ABC shares to your client, who immediately instructs you to sell them into the market. Step 3 The proceeds from the short sale are deposited in the client’s account. Step 4 The client deposits the required margin into the account. Step 5 The share price of ABC falls, and your client wants to close the position. You buy ABC back on the client’s behalf at the lower price and return the stock to your firm. DID YOU KNOW? So, why does an investment dealer agree to lend securities to a new client for short selling? The investment dealer gains a specific benefit in the process. As security for the loaned securities, the investment dealer is free to use the money put up by the short seller in the firm’s business or in interest- earning activities. MARGINING SHORT POSITIONS In contrast to a long position, margin is always required for a short position because of the risks involved. In a short sale, the client borrows the stock from the dealer member, but no money is loaned to the client. Instead, the client deposits additional money into the account to cover potential losses from the short sale. Table 9.2 shows the minimum margin requirements for short sales. Table 9.2 | Minimum Margin Requirement for Short Sales (For information only) On Listed Equities Selling Margin Required At $2.00 and over 50% of market value At $1.75 to $1.99 60% of market value At $1.50 to $1.74 80% of market value At $0.25 to $1.49 100% of market value Under $0.25 $0.25 per share Securities eligible for reduced margin 30% of market value EXAMPLE To short common shares at a price of $5.00 per share, the investor must deposit a margin of 50% of the market value of the shares along with the proceeds of the short sale. In other words, the investor must have 150% of the market value of the shares in her account. If, instead, the investor shorted shares priced at $1.55 per share, she must deposit a margin of 80% of the market value of the shares along with the proceeds of the short sale. In other words, the investor must have 180% of the market value of the shares in her account. © CANADIAN SECURITIES INSTITUTE  CHAPTER 9      EQUITY SECURITIES: EQUITY TRANSACTIONS 9 9 Note: The margin calculations in the examples that follow are for information only. However, by working through these examples, you will strengthen your understanding of how long margin accounts in general are affected by changing stock prices. (Note that commissions are excluded from the calculations.) EXAMPLE (For information only) In this example, the margin required to sell short is illustrated in three different scenarios. Assume that a client wishes to sell short 100 shares of listed FED Company Ltd. at its current market price of $5.00. The minimum account balance required is the proceeds of the short sale plus 50% of the market value, or 150%. The client must put up a margin of $250.00, as shown below. Minimum account balance required: 150% of $5.00 × 100 shares $750.00 Less: Proceeds from short sale 100 × $5.00 $500.00 Equals: Minimum margin required (50% of the market value) $250.00 Scenario 1 Assume that, later on, the price of FED’s shares declines to $4.00. The client now has more margin in the account than the required minimum. Minimum account balance required: 150% of $4.00 × 100 shares $600.00 Less: Proceeds from short sale 100 × $5.00 $500.00 Equals: Margin required $100.00 Because the client has already deposited a margin of $250.00, the account now has excess margin of $150.00. This amount may be withdrawn, used to purchase more securities, or left in the account to cover possible margin calls (should FED’s price begin to rise). Scenario 2 Assume that FED’s shares continue to decline to $1.60. The account balance required is now governed by a different category. Minimum account balance required: 180% of the market value (consisting of 80% margin $288.00 plus 100% of the proceeds of the sale) Less: Current account balance: Proceeds from short sale ($500) plus margin $750.00 already deposited ($250) Equals: Minimum margin required ($1.60 × 100 shares × 180%) nil Because the account balance required is less than the short sale proceeds, no additional margin is required. Scenario 3 If the price of FED’s shares advanced to $6.00 instead of declining, the client would receive a margin call, as shown below. Minimum account balance required (based on current price of shorted security): 150% of $900.00 $6.00 × 100 shares Less: Proceeds from the short sale (excluding commission), based on the original $500.00 price of the shorted security: 100 × $5.00 Equals: Minimum margin required $400.00 Less: Amount already deposited $250.00 Equals: Margin deficiency (for which a margin call is issued to the client) $150.00 © CANADIAN SECURITIES INSTITUTE 9 10 CANADIAN SECURITIES COURSE      VOLUME 1 EXAMPLE (cont'd) Because the price rises to $6, the new margin required is now $400. Since the initial deposit made by the client was $250, a margin call is issued to cover the margin deficiency. PROFIT OR LOSS ON SHORT SALES The profit or loss on a short sale transaction is calculated in the same way as on a long transaction. It is simply the difference between the purchase and sale prices, or between the sale proceeds and the purchase cost. EXAMPLE (For information only) In this example, the profit or loss on a short sale is illustrated in two different scenarios. Scenario 1 Assume that a client sells short 100 shares of FED Company Ltd. at its current market price of $5.00. The price of FED’s shares later declines to $1.60, and the client wishes to calculate the profit, on paper. Proceeds of the short sale $500.00 Less: Cost of buying 100 FED in the market at $1.60 per share, should the client $160.00 decide to cover the short sale Equals: The client’s pre-tax profit on the short sale $340.00 Because the price has dropped and the client is able to purchase the shares at a lower price than they were previously sold at, there is a profit, on paper. Scenario 2 Assume instead that the price of FED’s shares rises to $6.00, and the client wishes to calculate the loss, on paper. Proceeds of the short sale $500.00 Less: Cost of buying 100 FED in the market at $6.00 per share, should the client $600.00 decide to cover the short sale: $600.00 Equals: The client’s loss on the short sale $100.00 Because the price has risen, there is a loss rather than a profit, on paper. If the position were covered at the current price, the price of the purchase would be higher than the price of the sale. TIME LIMIT ON SHORT SALES There is no limit on the amount of time that a short sale position may be maintained, provided that the stock does not become delisted or worthless. As well, the position remains open as long as equivalent amounts of the shorted security can be borrowed by the short seller’s dealer, and as long as adequate margin is maintained in the short account. For short sales of listed securities, borrowing can be arranged between dealers to facilitate the delivery required by the short sale. COVERING A SHORT POSITION In some cases, the short seller may be unable to borrow enough stock from the investment dealer to maintain or carry a short position. In such cases, the client must buy the necessary shares to cover the short sale. This © CANADIAN SECURITIES INSTITUTE  CHAPTER 9      EQUITY SECURITIES: EQUITY TRANSACTIONS 9 11 transaction must be done regardless of the short seller’s intention to buy back the shorted security or market price of the shorted security. There is also an issue with short selling shares that are thinly traded. It can be difficult to borrow sufficient stock with low marketability to maintain a short position for a prolonged period. Short sellers generally look for shares of companies that have a large number of shares outstanding and that are widely held by many shareholders. DECLARING A SHORT SALE All of the exchanges require dealer members to confirm whether a sale is a short or a long sale, upon accepting an order for the sale of a security. Investment advisors entering an order for a short sale of a security for any client must clearly mark the sell-order ticket Short (or S), so that the trading department may process the order properly. The Toronto Stock Exchange (TSX) and the TSX Venture Exchange compile and publicly report total short positions in applicable securities twice a month. RISKS OF SHORT SELLING There are various risks associated with short selling. Some of these risks are summarized as follows: Borrowing shares It may be difficult to borrow a sufficient quantity of the security sold short to maintain the short sale. Adequate margin The short seller must maintain adequate margin in the short account as the price of the shorted security fluctuates. Liability The short seller is liable for any dividends or other benefits paid during the period that the account is short. Buy-in requirements If an adequate margin cannot be maintained by the client, the investment dealer must buy back the stock to close the short sale. Similarly, if the borrowed stock is called by its owner, the client may be unable to borrow other stock to replace it. Insufficient It is difficult to obtain up-to-date information on total short sales on a security. information (The exchanges do not report short positions on a daily basis, and no data is available on unlisted short sales.) Price action The price of a shorted security may become volatile when a number of short sellers try to cover their short sales at the same time, creating a buying rush. Unlimited risk There is a possibility of unlimited loss if a shorted stock starts a dramatic rise in price. Unlike a typical investor who can lose no more than the security’s purchase price, there is no maximum to the loss that a short seller can incur, because there is no limit to how high the price of a stock can advance. Regulatory risk The risk that the regulators may ban short selling for certain types of stocks. The most obvious example of this was during the credit crisis. The SEC, for example, banned short sales of banks and other financial institutions. When such a ban is put in place, short sellers may be forced to cover their positions (creating an upward spike in prices) at a loss. © CANADIAN SECURITIES INSTITUTE 9 12 CANADIAN SECURITIES COURSE      VOLUME 1 TRADING ON MARGIN What are the key differences between buying long on margin and selling short? How well do you understand margin strategies from an investment perspective? Complete the online learning activity to assess your knowledge. TRADING AND SETTLEMENT PROCEDURES 4 | Describe the trading and settlement procedures for equity transactions. Stock exchange trades may involve the investment dealer acting as agent or as principal. Our description of the roles that investment dealers may play focuses on a traditional trade involving two customers and two investment dealers acting as agents. TRADING PROCEDURES Figure 9.2 shows a simplified securities transaction in a retail setting. Figure 9.2 | A Retail Securities Transaction 5 Stock Exchange (Listed Securities) Common Shares Preferred Shares Exchange Traded Fund 3 Income Trusts 4 Options & Futures 1 2 Investment Advisor Investment Advisor Buyer Alternative Trading Seller Dealer Member A Dealer Member B systems or Over the Counter (Unlisted Securities) Bonds Money Market instruments Unlisted common and Preferred Shares Referring to the diagram in Figure 9.2, assume that XYZ’s common shares are listed for trading on a stock exchange. No matter which exchange the trade takes place on, the major steps are the same. All trades involve both a buyer and a seller (positions 1 and 2 in the diagram) who may live next door to, or across the country from, each other. Perhaps after consultation with their respective investment advisors (positions 3 and 4), the buyer has decided to acquire 100 XYZ shares and the seller wishes to sell 100 XYZ shares in his possession. Both phone their investment advisors for a current price quotation. Their advisors learn, through communication links with the exchange, that XYZ common is currently $10.50 bid and $10.75 asked. Both advisors report this quotation to their clients. © CANADIAN SECURITIES INSTITUTE  CHAPTER 9      EQUITY SECURITIES: EQUITY TRANSACTIONS 9 13 The prospective buyer now knows that the lowest price at which anyone is currently willing to sell one standard trading unit (100 shares) of XYZ stock is $10.75 a share. The seller now knows that the highest per share price anyone is currently willing to pay for a standard trading unit is $10.50. A sale is possible if the buyer is willing to pay the seller’s price or if the seller is willing to accept the buyer’s price. The two clients then instruct their investment advisors to get the best possible current price for XYZ stock (a market order). The orders are relayed to the stock trading departments at each dealer member. The exchange’s data transmission system reports the trade over the exchange’s ticker. It also provides the buying and selling dealers with specific details of the trade, such as the time of the trade and the identity of the other firm. Details are relayed to the investment advisors who originated the transactions, and the advisors phone their clients to confirm the transaction. Each dealer mails a written confirmation to its client that day or the next business day at the latest. SETTLEMENT PROCEDURES Once a transaction has occurred, the buyer and seller each receive a confirmation and must settle the transaction. The buyer’s confirmation shows details of the purchase and the amount payable, including commission. The amount will be withdrawn from the client’s account, if the buyer has sufficient funds on deposit with the firm (either for payment in full, with a cash account, or for initial margin requirements, in a margin account). Otherwise, the buyer must provide sufficient funds by the settlement date (i.e., one business day after the trade date). The buyer’s firm then makes payment for the purchase to the seller’s firm. The seller’s confirmation also shows details of the sale, as well as the amount to be received by the seller after commission is deducted. DID YOU KNOW? In Canada, stock and bond certificates are not in the form of paper; they are mainly held electronically by a clearing corporation. At the end of each trading day, the clearing corporation settles all purchases and sales of stock and bonds among dealers. The entries are made in the dealer’s book of record showing who owns the stocks and bonds, and who owes money to pay for them. HOW SECURITIES ARE BOUGHT AND SOLD 5 | Distinguish among the types of buy and sell orders. As an investment advisor, you may be called on to execute many types of buy and sell orders that are common to both listed and unlisted trading. Order types are generally categorized according to the following characteristics: Duration How long is the order valid for? Price restrictions Have any limits been set on the price? Special instructions Are there any special conditions attached to the order? Other For example, are there any changes to the original order? © CANADIAN SECURITIES INSTITUTE 9 14 CANADIAN SECURITIES COURSE      VOLUME 1 When trading securities on the market, buyers always want to pay the lowest price possible for the stocks they want, and sellers always try to get the highest price possible for the stocks they own. This dichotomy creates two prices for a single security: a bid and an ask price. In Chapter 2 of this course, we discussed that the bid price is the highest price that a buyer is ready to pay for a stock, whereas the ask price is the lowest price that a seller will accept for the same stock. The difference between the two prices is the bid-ask spread. This principle is illustrated in the following formula: Ask Price - Bid Price = Bid - Ask Spread You can see how this formula is applied in our examples of the different types of orders. TYPES OF ORDERS There are various types of orders that may be involved in a stock transaction, including market, limit, day, good til, on-stop sell, on-stop buy, and professional. All of these types are discussed in detail below: MARKET ORDER A market order is an order to buy or sell a specified number of securities at the prevailing market price. All orders not bearing a specific price are considered market orders. Generally, the buyer can expect to pay the ask price, and the seller can expect to accept the bid price. In any case, the trader tries to obtain a lower ask (also known as offer) or a higher bid than the prevailing level. The benefit of a market order is that the investor is certain that it will be executed. However, the price is not certain, particularly in shares (or units) that are less liquid. Market orders are often best used in a liquid market, where the bid/ask spread is tight. EXAMPLE Market Order: Bid Ask ABC $19.90 $20.10 “Buy 1,000 shares of ABC at market.” This order will be filled at the current ask price and the buyer will pay $20.10 for each ABC share purchased. “Sell 1,000 shares of ABC at market.” This order will be filled at the current bid price and the seller will receive $19.90 for each ABC share sold. LIMIT ORDER A limit order is an order to buy or sell securities at a specific price or better. The advantage to a limit order is that the order will be executed only if the market reaches that price or better. The downside to a limit order is that there is no certainty that the order will be filled. Limit orders are generally used by a buyer, or seller, with a specific price point. In particular, the limit order is used in a market that is less than liquid (i.e., a market with a wide bid/ask spread). © CANADIAN SECURITIES INSTITUTE  CHAPTER 9      EQUITY SECURITIES: EQUITY TRANSACTIONS 9 15 EXAMPLE Limit Order: Bid Ask ABC $19.90 $20.00 “Buy 1,000 shares of ABC at $20 or less.” This order will be filled only if it can be executed at $20 or less. In this case, the order will be executed because at least one seller is ready to sell ABC shares at $20. If no time limit is specified, and if the shares remain above $20, the order will be cancelled at the end of the trading day. “Sell 1,000 shares of ABC at $20 or more.” This order will be filled only if it can be executed at $20 or more. In this case, the order cannot currently be executed because buyers are willing to pay only $19.90. DAY ORDER A day order is an order to buy or sell that expires at the end of the day, if it is not executed on the day it is entered. All orders are considered to be day orders unless otherwise specified. EXAMPLE Day Order: “Buy 1,000 shares of ABC at $20 or less.” Because this order does not specify a time limit, the order is valid until it is filled or until the close of business on that day, whichever is sooner. GOOD TIL ORDER There are two good til order types that an investor can place: a good til date (GTD) order or a good til cancelled (GTC) order. A GTD order expires on a date specified by the investor. A GTC order expires 90 calendar days from entry on the TSX, unless the investor decides to cancel the trade sooner than the expiry date. EXAMPLE GTD Order: “Sell 1,000 shares of ABC if the price reaches $20 or more on or before March 30.” This order remains open until it is filled at $20 or more, or until the close of business on March 30, whichever is first. GTC Order: “Sell 1,000 shares of ABC if the price reaches $20 or more, good til cancelled.” This order remains open until it is filled at $20 or more, the client cancels the order, or the order expires after 90 days, whichever is first. © CANADIAN SECURITIES INSTITUTE 9 16 CANADIAN SECURITIES COURSE      VOLUME 1 ON-STOP SELL ORDER An on-stop sell order, also known as a stop loss order, is an order that is specifically used in connection with a sell order where the limit price is below the existing market price. The order is triggered when the stock drops to the specified level. The purpose is to reduce the amount of loss that might be incurred or to protect at least part of a paper profit when a stock’s price declines. Note: On the Toronto Stock Exchange and TSX Venture Exchange all on-stop sell orders must be entered with a limit attached. Once an on-stop sell order is triggered, it enters as an order at its on-stop (limit) price. EXAMPLE On-Stop Sell Order: “Sell 200 shares of ABC if the price drops to $24.50 or below.” Assume that ABC shares trade at $30 and your client has purchased the shares at this price. Your client decides that, should the price of ABC shares decline unexpectedly, he would prefer to limit his loss to $5.50 per share (ignoring commission). Therefore, your client places an on-stop sell order on 200 shares of ABC at $24.50. If the price of ABC declines to the point that it trades at $24.50 or below, the order would be triggered. In a different scenario, if your client had paid $20 per share for ABC shares (prior to the stock’s price advancing to $30), she could have put in an on-stop sell order at $24.50. This would allow her to protect at least part of her profit, on paper, should the stock’s price decline unexpectedly before she could act. ON-STOP BUY ORDER An on-stop buy order, also known as a stop buy order, is the opposite of an on-stop sell order – that is, an order to buy a stock at or above a certain price. On-stop buy orders are used for two reasons: To protect a short position when the stock’s price is rising. To ensure that a stock is purchased while its price is rising. A short seller who protects the short position with an on-stop buy order is following the same logic as a person owning a stock who uses an on-stop sell order. In the second case, a client may wish to buy a stock only after it has demonstrated a certain upward price move, which is usually associated with a technical analysis buy signal. Note: On the Toronto Stock Exchange and TSX Venture Exchange all on-stop buy orders must be entered with a limit attached. Once an on-stop buy order is triggered, it enters as an order at its on-stop (limit) price. EXAMPLE On-Stop Buy Order (Example 1): ABC stock is currently trading at $30 per share. Your client decides that she would like to buy it, but only if it moves up to $35. By entering the order as an on-stop buy at $35, the order is not triggered until the stock trades at $35 or above. On-Stop Buy Order (Example 2): ABC stock is currently trading at $30 per share. Your client decides to short it at that price. However, he would like to limit his loss to $5 per share, so he enters an on-stop buy order at $35. The on-stop buy order is triggered only if the price of ABC stock trades at $35 or above. The on-stop buy order offers the client insurance in one respect. If the share price rises instead of falls, the client’s position in ABC will be closed out, limiting the potential loss. © CANADIAN SECURITIES INSTITUTE  CHAPTER 9      EQUITY SECURITIES: EQUITY TRANSACTIONS 9 17 PROFESSIONAL (PRO) ORDER A fundamental trading regulation to protect the public relates to the priority given to client orders. If the order of a client competes with a non-client order at the same price, the client’s order is given priority of execution over the non-client order. A non-client order is an order for an account in which a partner, director, officer, advisor, or other employee of a dealer member holds a direct or indirect interest or an arbitrage order. This rule is applied within dealer members in its dealings with clients to ensure that a client’s order has priority over a professional (PRO) order. Tickets for orders for the accounts of partners, directors, officers, investment advisors, and specified employees (in some cases) must be clearly labelled PRO, N-C (non-client), or EMP (employee). Under the preferential trading rule, this type of order is executed after a client’s order if both orders compete at the same price for the same security. EXAMPLE PRO Order: An order is placed to sell 100 shares of ABC at $20. In this case, the account holder is an employee of the dealer member. Therefore, the order must be marked PRO (or EMP/N-C). If any client orders to sell ABC at $20 are outstanding, those orders will be filled before the employee’s order. BUY AND SELL ORDERS How do you determine the most appropriate type of order to place for a client, given the significant effect your decision can have on the share price? 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 9 18 CANADIAN SECURITIES COURSE      VOLUME 1 SUMMARY In this chapter, we discussed the following aspects of equity transactions: Unlike clients with cash accounts, clients with margin accounts can buy or sell securities on credit. Margin accounts can also hold long or short positions, whereas cash accounts can hold only long positions. A long margin position allows investors to partially finance the purchase of securities by borrowing money from the dealer. The margin is the amount put up by the client. The minimum margin required equals the initial cost of the transaction minus the loan. The investor earns a profit when the underlying stock price rises. A short margin position allows investors to sell securities they do not own. The short seller’s dealer lends the securities to be shorted to the investor, and the investor sells the securities in the market, declaring the trade to be a short sale. The investor earns a profit when the initial sale price exceeds the subsequent repurchase cost, once the short position is closed out. Among other risks, unlimited loss is a risk for short sellers if the price of the security rises rather than falls. When a trade is completed on an exchange, the exchange’s data transmission system reports the trade and provides the buying firm with trade details. Confirmation is sent to the buyer and seller. The buyer provides payment and the seller delivers the security by the settlement date. The mechanism and time frame for settlement depend on the type of securities traded. Buy and sell orders include the following types: Market order (an order to buy or sell at the prevailing market price) Limit order (an order to buy or sell at a specific price or better) Day order (an order that expires if it is not executed on the day it is entered) Good Til order (an order that is automatically cancelled on a date specified by the client or the market) On-stop sell order (an order to sell a security when the price of a standard trading unit falls to a specified point) On-stop buy order (an order to buy a security only after it has reached a specified price) PRO order (an order for the accounts of partners, directors, officers, investment advisors, and specified employees) REVIEW QUESTIONS Now that you have completed this chapter, you should be ready to answer the Chapter 9 Review Questions. FREQUENTLY ASKED QUESTIONS If you have any questions about this chapter, you may find answers in the online Chapter 9 FAQs. © CANADIAN SECURITIES INSTITUTE  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) ÷ 0.0