ALM 2024 S2 C05 Debt Securities copy.pdf

Asset Liability Management Chapter 5: Debt securities 5. Debt securities This chapter covers the following learning objectives: Item Learning Object...

Asset Liability Management Chapter 5: Debt securities 5. Debt securities This chapter covers the following learning objectives: Item Learning Objectives 3 Discuss the characteristics of the three traditional asset classes including their long term returns Debt securities (C5), Equities (C6), and Property (C7) are the three principal asset classes and they are discussed in learning objectives 3.1., 3.2., and 3.3 3.1 Describe the characteristics of the three principal asset classes 3.2 Discuss the components and drivers of the three principal asset classes’ risk and return 3.3 Compare valuation methods including discussing assumptions and evaluating limitations 5.1. Overview 5.1.1. What this chapter covers Debt securities are debt instruments (i.e. contracts) that can be bought or sold between two parties. The securities will have agreed terms such as amount of interest and maturity date. In this chapter, the term ‘debt securities’ is used as a generic term capturing all forms of securities where there is a debt created when the security is issued, whereby the issuer (or borrower) owes an agreed set of payments to the investor in the debt security. The agreed set of payments is defined in the terms of the security issue and usually includes the definition of how interest payments are calculated and when they are paid as well as the time of the repayment of the amount borrowed—that is, the interest rate and the return of capital at maturity. The term debt security is used interchangeably with debt instruments, fixed interest securities, and sometimes bonds in the various texts and references you may use. © June 2024 The Institute of Actuaries of Australia Page 4 of 62  Asset Liability Management Chapter 5: Debt securities The return on a debt security is the rate of interest received on the amount borrowed. The risk of a debt security is mainly the possibility that the agreed payment terms are not fulfilled in practice—that is, the borrower defaults on some or all of the agreed interest payments or the repayment of the amount borrowed (often referred to as the principal of the loan). Debt arises when someone lends money to someone else, including the loan that effectively takes place when investors place money on deposit with a bank. Colloquially, we speak of money on deposit whereas when you make a deposit you are lending money to a bank. The bank does not repay you with the actual banknotes you may have deposited. Debt can take various forms: it can be defined in terms of a local currency, a foreign currency, or by reference to an index such as a consumer price index; it can have fixed or variable rate of interest; and it can be repayable at a fixed date or at the option of either the borrower or the lender, or in some cases may be a perpetual debt with no fixed term for repayment. it may be tradeable on an exchange or via some other organised market, so that the securities can be sold before the maturity date. This chapter recaps your prior learning about debt securities, particularly valuation techniques and yield curves. It will cover the different types of debt securities in some depth and investigates the risk and return characteristics of the class as a whole as well as each type of debt security. Together with the next two chapters, on equities and property, the goal of this chapter is to build the knowledge required to competently evaluate the asset classes and types of securities available in order to select the most appropriate investments for a portfolio of assets that will provide the means to meet a portfolio of liabilities. Section 5.2 of this chapter lists the types of security that will be analysed and introduces a mnemonic that assists in remembering the parameters that should be considered when comparing different types of assets. Sections 5.3, 5.4, and 5.5 describe cash, money markets, and bonds. The final section discusses theories about the term structure of interest rates. The mechanics of bonds will be familiar to you, but you should consider reading it critically and thinking about the paradigm concepts discussed in Chapter 2. © June 2024 The Institute of Actuaries of Australia Page 5 of 62  Asset Liability Management Chapter 5: Debt securities Debt securities introduce a good deal of algebra for the practitioner to master, and it is important to have a good grasp of the formulae because they also underlie most of the arithmetic pertaining to equities and property. You should already be familiar with the pricing formulae from your study of compound interest in Foundation subjects. If you have a shaky memory of bond pricing, then read the refresher on compound interest problems in the pdf file ‘Revision of compound interest.pdf’ located on the Learning Management System (‘LMS’). Figure 5.1 shows the components of the chapter and their interrelationships. You will note as you progress through the reading that key concepts arise several times, reflecting the relationships between the topics. Figure 5.1 – Mind map SYSTEM T Types Risk & return Debt securities Pricing Yield curves Term structure Whilst you may find many parts of this chapter straightforward, we would like to emphasise that you need to think though the material critically. Examinations are open-book, but few marks involve quoting from a chapter. Rather, exam questions will focus on demonstrating you can appraise the material. For example, a relatively simple application question may ask you to compare two contracts described in this chapter. You do not have to memorise the definition of each contract but should have a good awareness of the form of each contract. © June 2024 The Institute of Actuaries of Australia Page 6 of 62  Asset Liability Management Chapter 5: Debt securities A short course cannot provide you with investment market experience. As a proxy for experience, it is useful to examine past outcomes of investment returns and, for this chapter specifically, bond returns. Exemplars in your Foundation studies usually posed cash and bonds returns as constant items. This is partly an outworking of using expected returns rather than actual returns. Whilst you should not memorise past returns, we have included detail on the Australian market in Chapter 10 (Long-term returns) which shows that actual returns can depart far from expectations. 5.1.2. Setting the scene The global bond (debt) markets far outweigh global equity markets in both market value and annual issuance. According to the (US) Securities Industry and Financial Markets Association 1 in their 2021 report: Global bond markets outstanding value increased by 16.5% to $123.5 trillion in 2020, while global long-term bond issuance increased by 19.9% to $27.3 trillion. Global equity market capitalization increased by 18.2% year-over-year to $105.8 trillion in 2020, while global equity issuance decreased by 52.9% to $826.8 billion. Figure 5.2 shows the relative values of the two asset sectors for issuance in each year. 1 SIFMA 2021, Capital Markets Fact Book, 2021, https://www.sifma.org/resources/research/fact-book/ © June 2024 The Institute of Actuaries of Australia Page 7 of 62  Asset Liability Management Chapter 5: Debt securities Figure 5.2 – Global fixed income and equity issuance It is apparent that the bond market is a key source of capital for businesses and governments and therefore represents a significant investing opportunity for institutions as well as individuals. Investors are attracted to investment in debt securities because, compared with equity or property, debt securities offer (near) certainty of the agreed payments, which usually include interest payments and the return of capital at a set point or points in time. This enables them to arrange their own financial affairs to meet their liabilities with more certainty than other assets can usually offer. The trade-off required to achieve the lesser degree of uncertainty of payments is usually that of accepting a lower long-term return on debt securities compared with the returns on equity or property securities. © June 2024 The Institute of Actuaries of Australia Page 8 of 62  Asset Liability Management Chapter 5: Debt securities 5.2. Main types 5.2.1. Overview It is no surprise that, given the sheer size of the debt market, there is a security for every situation. This means a very diverse range of characteristics when considering structure, coupon, term, conditions, currency, and so forth. In Table 5.1 we list well-known types of debt securities. Table 5.1 – Well-known types of debt securities Type Examples Deposit Cash Term deposit Money market security Certificate of deposit Bill of exchange (including bank bill) Promissory note Treasury note Repurchase agreement Debt market security Government bond Corporate bond Floating rate note Inflation-linked bond There is a common distinction between cash instruments in the money market (with terms to maturity up to one year) and the debt capital market (with terms greater than one year). Of course, this is just an arbitrary distinction, dictated by convention. For example, there is no fundamental difference, in terms of risk, between a security with a duration of one year less one day and a security with a duration of one year plus one day. © June 2024 The Institute of Actuaries of Australia Page 9 of 62  Asset Liability Management Chapter 5: Debt securities Debt securities are also used to build a wide range of investment products such as: mortgage-backed security (MBS); collateralised debt obligation (CDO); and credit default swap (CDS). Some of these are considered by some market practitioners to be derivatives. Chapter 8 (Derivatives) will discuss these and other derivatives in detail. Sections 5.3 (Deposits), 5.4 (Money markets), and 5.5 (Bonds) discuss the various types of debt in detail. The descriptions are sufficient for this subject, but there are references in Section 5.8 that contain a comprehensive discussion for the Australian market. Note that each market will have its own peculiarities and you should check technical definitions in your local market. 5.2.2. System T There is a useful mnemonic, SYSTEM T, which provides students with a framework to consider the risk and return characteristics of any asset class and security type. SYSTEM T represents the following characteristics, which will influence the risk and return expectations of the asset class or security under consideration: Security (i.e. default risk where agreed payments of interest or capital are not made); Yield (i.e. real/nominal, expected return/running yield relative to other assets); Spread (i.e. expressed as a required margin of yield over government securities of the same term to compensate for increased risk of default); Term (i.e. short, medium, or long, expressed in remaining years to maturity); Expenses (i.e. dealing and management) or Exchange rate (i.e. currency risk); Marketability (i.e. tradeable on an exchange or market, liquidity related to volume traded, or non-tradeable, or illiquid; and Tax. Applying SYSTEM T to debt securities provides a guide to analyse, and comment on, risk and return expectations. © June 2024 The Institute of Actuaries of Australia Page 10 of 62  Asset Liability Management Chapter 5: Debt securities 5.3. Deposit securities Deposit securities are debt that arises by an investor placing (depositing) their money with a bank (or equivalent institution such as a building society or credit union) and receiving interest on the amount deposited. Remember that this is a debt instrument so that the depositor is lending money to the bank. The bank makes a promise that the loan will be repaid and may be subject to various conditions, such as written notice or that an agreed date has been reached. For ease of reading we will use the term ‘banks’ to include all the deposit-taker institutions in a jurisdiction. It is common for the deposit taker to be licensed by, or registered with, the government. For example, the deposit taker in Australia must be an authorised deposit-taking institution (ADI). An ADI is a bank, credit union, or building society that is under the supervision of the regulator—Australian Prudential Regulatory Authority in Australia. Generally, there are at-call deposits, where the investor can have access to the amount deposited at any time and term deposits, where the investor cannot access their account for an agreed period. These two types are discussed in detail in the next two sections. 5.3.1. At-call deposits Cash on deposit would typically include: where the depositor (investor) has instant access to withdraw the capital deposited (at-call bank account, transaction account); or where the depositor is required to provide a very short notice period (e.g. 24 hours) before being allowed to withdraw their capital. There may be fees charged on the deposit (e.g. explicit fee per transaction or service) and/or the issuer may adjust the interest rate payable to ensure a suitable expense recovery and profit margin. Cash deposits are often called sight deposits or call deposits as the investor may receive repayment ‘on sight’ or ‘on call’. © June 2024 The Institute of Actuaries of Australia Page 11 of 62  Asset Liability Management Chapter 5: Debt securities Return There is no capital gain and investment returns are the rate of interest paid by the issuer of the security (i.e. the deposit taker). The interest rate is set by the issuer and arrangements can vary, such as: fixed for the duration of the deposit; fixed for an initial period and then varied; variable day on day; or higher or bonus rate paid if certain conditions are met, such as no withdrawal. Cash rates paid are usually linked to the central bank’s cash rate. Where a central bank is using interest rates to achieve an inflation target, the cash rate may follow the inflation rate but not always and not consistently. Chapter 3 (Money) discussed the operation of the money market and the mechanisms that drive cash rates. As an example of how cash rates move over time, we consider what has occurred in Australia. Over the very long term in Australia, cash rates have been higher than price inflation, and have generated a real return for the investor. However, from time to time the relationship is inverted and a negative real return arises. For example, in March 2020, the Reserve Bank of Australia’s (RBA’s) cash rate was 0.25% per annum and the inflation rate was 1.8% per annum, generating a real return of -1.55% per annum. Real returns on cash can vary widely depending on economic circumstances—back in 1974 the real return on cash was -6% per annum; in 1991 it peaked at +10% per annum. Risk In a well-regulated economy, the likelihood of failure of a cash deposit taker is very low. However, extreme events, such as the Global Financial Crisis (GFC) or major fraud, the deposit taker may fail with partial or complete loss of investors’ capital. Notably, in 2008, and as a direct consequence of what Australians refer to as the GFC, many governments introduced a guarantee to reassure investors that their cash was ‘safe’ in local banks. This was an attempt (which proved successful) to prevent a run on the banks’ capital that might have led to the collapse of one or more banks. © June 2024 The Institute of Actuaries of Australia Page 12 of 62  Asset Liability Management Chapter 5: Debt securities The operation of the guarantee varies in each country that introduced such protection measures. For example, the Australian Government introduced the Financial Claims Scheme (FCS). The FCS is a scheme that provides protection to deposits in ADIs (banks, building societies, and credit unions) and to policies with general insurers in the unlikely event that one of these financial institutions fails. The FCS provides protection to depositors of up to $250,000 per account holder per ADI in the event of the ADI failing. Note that the protection amount was $1m in 2008 until 2012. The FCS does not apply to branches of foreign banks in Australia, nor to branches of Australian banks in foreign countries, or any entity not licensed by APRA, which administers the scheme. 5.3.2. Term deposits Deposits can be made with varying terms and conditions. Where cash is deposited with an agreement that the investor has no access to the capital before the end of an agreed period of time (the term), this is known as a term deposit. The term can range from overnight to beyond a year. It is possible under certain conditions for the investor to gain access to the funds earlier than the original term. However, this comes at a cost and the investor may be penalised, usually through the loss of interest or the payment of exit fees. The period for which the investor has given up access to the capital will affect the expected return the investor will receive in order to compensate for the ‘loss of access’ for that period. The issuer is likely to price their deposits to balance their need for capital now with their expectations of future cash rates falling/rising (making it cheaper/more expensive to raise capital in the future). Investors generally use term deposits to hold capital until it is required for a future planned cash flow and/or to ensure no capital losses during the term of investment. This suits investors with known liabilities that require funding at a known future date, as well as those with no specific liability but a strong aversion to loss. © June 2024 The Institute of Actuaries of Australia Page 13 of 62  Asset Liability Management Chapter 5: Debt securities Return As with at-call deposits, there is no capital gain and the investment return is the rate of interest paid by the issuer of the security (i.e. the deposit taker). The term deposit rates are quoted daily by banks, reflecting the bank’s need to secure deposits and the rate the bank expects to be earning on the money when it is used by the bank to fund assets such as loans to customers (e.g. home loans). Three major external factors affect how term deposit interest rates are set by banks: the cash rate set by the central bank (in Australia, the RBA); market competition between banks for deposits (i.e. the deposit rates set by other banks and the need for deposits of the particular bank); and banking regulations. Exercise 5.1 Research the relationships between cash rates set by the RBA and the inflation rate. What are your observations on the cash rate and inflation rate? By what theoretical mechanism does the cash rate influence the inflation rate? Is there evidence of this relationship? Banks also set different interest rates for their different term deposit products based on each of the following features: term; amount invested; interest payment frequency; and early exit fees/penalties. The investor benefits if the market rates decline during the term of the deposit, as they continue to be paid at the higher rate. However, expectations about the future will drive the behaviour of both the investors and the deposit takers when establishing a new term deposit. © June 2024 The Institute of Actuaries of Australia Page 14 of 62  Asset Liability Management Chapter 5: Debt securities Investors expecting a fall in cash rates may seek a longer term to lock in the current higher cash rate for a longer period; however, the bank may have the same expectations and offer a lower rate for longer-term deposits. Exercise 5.2 Select one Australian ADI and obtain their term sheet. Figure 5.3 – ANZ Term Sheet is an example of the ANZ Bank term deposit rates on 17 April 2020. What factors were influencing the rates being offered? © June 2024 The Institute of Actuaries of Australia Page 15 of 62  Asset Liability Management Chapter 5: Debt securities Figure 5.3 – ANZ Term Sheet as at April 2020 © June 2024 The Institute of Actuaries of Australia Page 16 of 62  Asset Liability Management Chapter 5: Debt securities Risk Similar to cash on deposit, the likelihood of failure of a term deposit taker is very low in markets where the banking sector is regulated and supervised. Nonetheless, it does remain possible, however unlikely, that a deposit taker can fail, with partial or complete loss of investors’ capital. The guarantee schemes described in the previous section (including the Australian FCS) will also apply to term deposits. The investor also accepts the risk that market interest rates increase during the term of the deposit, as such increases will not be passed onto existing term deposits. The investor may be able to break the term deposit to reset the interest rate, although an investor exercising this option would need to consider penalties incurred on early release. Exercise 5.3 How do the cash flows differ, in terms of timing and amount, between a fixed rate term deposit at a fixed interest rate and an instant access cash account with a variable interest rate? 5.4. Money market securities 5.4.1. General background The basic structure of a money market security (or instrument) is that an investor lends capital to a borrower for a short period, usually less than one year, at an agreed rate of interest, which is usually expressed as a margin above an agreed reference rate. The investor then expects to receive the capital invested, together with any interest earned at the end of the period. Money market securities are issued at a discount to the maturity value (par), to reflect the interest rate, and then redeemed at par. They are referred to as discount securities because the return is earned as a result of the amortisation of the discount between the time of issue (or subsequent purchase) and the maturity date (or date of subsequent sale). The return is considered to be interest and not capital gains. These securities are usually very short term, often overnight. For example, the Australian money market is limited to securities that have terms of 1 to 365 days. © June 2024 The Institute of Actuaries of Australia Page 17 of 62  Asset Liability Management Chapter 5: Debt securities Money market securities are issued by a variety of borrowers, and actively traded—traders and transactions are referred to as ‘money markets’. The money markets are generally dominated by banks, which manage their own liquidity by issuing securities when they need short-term capital or purchasing securities when they have excess short-term liquid funds. The money markets are also used by other financial institutions and non-financial companies to lend and borrow short-term capital. Central banks act as the lenders of last resort by being able to provide liquidity to the financial system via the money markets, as and when required to do so. Central banks can also use the money markets to establish the level of short-term interest rates. Central banks do this through the sale or purchase of certain money market securities and the subsequent repurchase or sale, respectively, at an agreed price (see repurchase agreements in Section 5.4.6). Return According to the Organisation for Economic Cooperation and Development (2020): Short-term interest rates are the rates at which short-term borrowings are effected between financial institutions or the rate at which short-term government paper is issued or traded in the market. Short-term interest rates are generally averages of daily rates, measured as a percentage. Short-term interest rates are based on three-month money market rates where available. Typical standardised names are ‘money market rate’ and ‘treasury bill rate.2 Investors can look to interest rate benchmarks to assess current pricing for short-term money market securities and observe historical experience. Importantly, interest rate benchmarks are widely referenced for corporate borrowing rates (i.e. quoted as a spread over the benchmark) and in financial contracts, including derivatives and asset-based securities. Interbank rates have been the most common benchmark for short-term interest rates—notably, the London Inter-Bank Offered Rate (LIBOR), which was used for money markets in several major currencies including the US dollar and UK pound. However, the LIBOR scandal in 2012 3 brought this under a cloud, with alternative benchmarks being developed and it is expected LIBOR will be phased out by 2021. 2 OECD 2020, Short-term interest rates (indicator). doi: 10.1787/2cc37d77-en (Accessed 17 April 2020). 3 In the LIBOR scandal, bankers reported false interest rates to manipulate the markets and boost their own profits. The scandal, which went undetected for years, involved many major financial institutions. After 2021, the LIBOR may be phased out in favour of alternative rate-setting systems. © June 2024 The Institute of Actuaries of Australia Page 18 of 62  Asset Liability Management Chapter 5: Debt securities In 2017, the RBA flagged that Australian financial institutions had around $5 trillion in contracts referencing LIBOR and that the market needed to begin transition to other suitable benchmarks. Some of the findings presented in a speech by the Deputy Governor4 are summarised in Table 5.2 – RBA findings on the LIBOR scandal. Table 5.2 – RBA findings on the LIBOR scandal LIBOR cannot be assumed to continue as a benchmark. Actions are being taken to strengthen the Australian equivalent, the bank bill swap rate (BBSW). The BBSW will be calculated by the ASX as the weighted average price of bank bill transactions. The RBA concluded there are enough transactions in the local bank bill market each day relative to the size of the financial system for it to remain a robust benchmark. Risk-free benchmarks may be more appropriate than credit-based benchmarks. “For instance, floating rate notes (FRNs) issued by governments, non-financial corporations, and securitisation trusts, which are currently priced at a spread to BBSW, could instead tie their coupon payments to the cash rate.” The cash rate (as determined by the RBA) is not a perfect substitute for BBSW. It is an overnight rate rather than a term rate and doesn't incorporate a significant bank credit risk premium. “For other products, it makes sense to continue referencing a credit-based benchmark that measures banks' short-term wholesale funding costs. This is particularly the case for products issued by banks5, such as FRNs and corporate loans.” The RBA cash rate and BBSW continue as Australia’s key short-term interest rate benchmarks, and internationally, central banks have begun (Euro) or completed (US) their transition to LIBOR alternatives, using both credit-based and risk-free rate benchmarks. It is worth noting that BBSW is a market-determined rate and that ASIC has taken enforcement action against some Australian banks that have sought to manipulate the BBSW rate to their advantage. 4 G Debelle, Deputy Governor RBA, Interest Rate Benchmarks, Speech 8 September 2017. 5 In this quote, the Deputy Governor is referring to commercial banks, that is products with credit risk. © June 2024 The Institute of Actuaries of Australia Page 19 of 62  Asset Liability Management Chapter 5: Debt securities Risk Money market securities can be attractive to risk-averse investors, especially from high-quality issuers, due to the stability of capital values. This effect is amplified during times of economic uncertainty. However, over the long-term money market, securities are expected to provide a lower return than riskier or less liquid investments. All securities in this market are short term, do not pay interest during the term, and have a fixed maturity date. The key distinguishing characteristic between the types is the credit risk. Types Five types of money market instruments that we will look at in detail are: certificate of deposit; promissory note; bills of exchange; treasury notes (also known as treasury bills); and repurchase agreements. These are discussed in turn in the following sections. 5.4.2. Certificate of deposit A certificate of deposit (CD) is a term deposit that is freely traded between investors. Note that the term deposits described in the section on cash are not tradeable. The term of the deposit ranges from seven days to one year. Features of these deposits are: the ‘certificate’ acts as an acknowledgement for money that has been deposited with a bank— therefore, it is issued by a bank; CDs are freely negotiable—the initial investor can sell their certificate to another investor, who then has the right to receive the interest and capital from the bank; CDs are only issued if the amount is sizeable; and CDs are issued at a discount to par, where the investor deposits say $0.95m and receives back $1m a year later, where the $0.05m difference is the interest payment. © June 2024 The Institute of Actuaries of Australia Page 20 of 62  Asset Liability Management Chapter 5: Debt securities 5.4.3. Promissory note A promissory note is a written promise for the amount owed to a specified counterparty at a specified time or on demand. It is one of the earliest types of fixed income security. It is settled through the payment of the amount owed by the borrower (maker of the note) to the lender (the payee, or the bearer of the note). Whilst banks may issue promissory notes, these debt instruments allow funding from non-bank sources. At a practical level, promissory notes are usually: issued for relatively short terms, say 185 days or less; must be signed by the party making the promise; must be for a specific sum of money; must specify the time for repayment; must be in bearer form; are transferable by delivery without endorsement; are issued and traded at a discount; and are redeemable at maturity. If the promissory note is unconditional and readily saleable, it is called a negotiable instrument. The difference between an unsecured and a secured promissory note is that a secured note is guaranteed by a certain asset, such as a property or vehicle, whereas an unsecured note does not have any collateral associated with it. The credit, or default, risk reflects the credit risk of the issuer as well as the value of the secured asset (if any). Generally, only financially sound corporations issue promissory notes, although their credit risk may not be assessed as low as that of a bank or a government. Commercial paper, in the global financial market, is an unsecured promissory note with a fixed maturity of often no more than 270 days. Commercial paper is issued by companies for the purpose of raising capital directly from the market. However, returns are usually compared to treasury bills when assessing the attractiveness, compensating for the lower level of security offered. There is an active secondary market for commercial paper. © June 2024 The Institute of Actuaries of Australia Page 21 of 62  Asset Liability Management Chapter 5: Debt securities 5.4.4. Bills of exchange A bill of exchange is an unconditional order in writing, addressed by one person to another, signed by the person giving it (the maker or borrower), requiring the person to whom it is addressed (the acceptor) to pay on demand or at a fixed or determinable future time, a sum certain in money or to the order of a specified person (the bearer). At a practical level, a bill of exchange is generally described as a negotiable instrument maturing within six months (at which time it will be redeemed for its face value). It is sold at a discount to face value. Bills of exchange are similar to promissory notes, but they are settled by the bearer drawing on the funds available from the nominated acceptor, usually a bank. Bills of exchange can also be redeemed at another bank or broker, usually at a discount. See Figure 5.4 for the process. Where a bank is the acceptor, the bill is referred to as a bank accepted bill of exchange, or bank bill. Where the bank has endorsed the bill on the back, either through buying the bill in the market or for a fee to raise the bill’s status, it is referred to as a bank endorsed bill. © June 2024 The Institute of Actuaries of Australia Page 22 of 62  Asset Liability Management Chapter 5: Debt securities Figure 5.4 – Bank accepted bill of exchange Bank accepted bills are as sound as the accepting bank and are usually assumed to carry negligible risk of default, making them highly marketable. The bank will, of course, charge a fee for accepting the bill, and this fee will reduce the return to the investor—a trade off for the reduced risk of default. © June 2024 The Institute of Actuaries of Australia Page 23 of 62  Asset Liability Management Chapter 5: Debt securities 5.4.5. Treasury notes Many central governments offer short-term debt securities that are guaranteed by that government and usually assumed by investors to be free of default risk. Chapter 2 discussed one major financial incident where this proved to be a false assumption. For example, Australian Treasury notes are a short-term discount security redeemable at face value on maturity. Terms are less than 12 months. Treasury notes are issued to assist with the Australian Government's within-year financing task. A US Treasury bill (T-Bill) is a short-term US Government debt obligation issued by the US Treasury Department with a maturity of one year or less. Treasury bills are usually sold in denominations of $1,000. However, some can reach a maximum denomination of $5 million in non-competitive bids. These securities are widely regarded as low-risk and secure investments. The US Treasury Department sells T-Bills during auctions using both competitive and non- competitive bidding processes. Non-competitive bids have a price based on the average of all the competitive bids received. Exercise 5.4 In Australia, the most important types of discount securities are Treasury notes and bank accepted bills of exchange (bank bills). Determine the current value of these securities on the Australian short-term money market. Two useful resource sites that will help are: https://www.aofm.gov.au/securities/treasury-notes and https://afma.com.au/ © June 2024 The Institute of Actuaries of Australia Page 24 of 62  Asset Liability Management Chapter 5: Debt securities 5.4.6. Repurchase agreements A repurchase agreement is where the party willing to buy the underlying security provides the party selling the asset with temporary capital in exchange for the underlying security as collateral. These transactions tend to have a very short term, often overnight, after which the party selling the asset has an obligation to repurchase the asset at an agreed price (hence the term ‘repo’). Repurchase agreements, commonly called repos, are a form of short-term borrowing or lending. Given the important role these securities play in maintaining liquidity in the secondary market, it is worth noting them separately as another specific debt security type distinct from the money market securities covered so far. In Australia, each bank holds an exchange settlement (ES) balance with the RBA. The ES balance is an at-call cash deposit, which must be positive at all times. As a bank cannot predict if their balance will be positive at the end of any particular day, after all customer transactions are settled, they may need to borrow temporarily from another bank to provide cash for the ES balance to the RBA. There are transactions between the government (RBA is the banker) and the commercial world (commercial banks) daily that change the ES balances. The RBA acts daily to stabilise the aggregate level of ES balances (and thereby the cash rate for the overnight borrowings). The RBA’s main tool is a repurchase agreement. To inject ES balances, the RBA provides cash to a bank and the bank provides eligible debt securities as collateral to the RBA. This protects the RBA from counterparty default losses by the bank. At an agreed future date (chosen to manage liquidity and could be the next day) the bank returns the ES balance and the RBA returns the securities to the bank. This approach means the underlying debt securities do not have to be sold to any other market participant to obtain the required cash. Exercise 5.5 Provide an example of when a reverse repo is likely to occur. © June 2024 The Institute of Actuaries of Australia Page 25 of 62  Asset Liability Management Chapter 5: Debt securities 5.5. Bonds 5.5.1. General background An entity requiring longer-term capital can raise it via equity or via debt. Equity is discussed in Chapter 6 and the rest of this chapter discusses debt. To raise debt, the entity creates and sells (issues) a debt security. This commits the entity to paying interest to the purchaser as per the agreement and repaying the principal at the end of the term of the security. We will use the term bonds to distinguish longer-term debt securities (over 365 days) from the short-term money market and deposit securities already discussed. A coupon or coupon payment is the annual interest rate paid on a bond, expressed as a percentage of the face value, and paid from issue date until maturity. Coupons are usually referred to in terms of the coupon rate, which is the sum of coupons paid in a year divided by the face value of the bond in question. The bond investor has an initial negative cash outflow, followed by a possible series of smaller known positive cash flows at specified future dates and the potential to receive a final positive cash flow with the amount known in advance at a specified future date. Note that the bond investor may sell the bond before the specified contractual end-date to maturity and thus the actual yield obtained may be different from the expected yield when the bond is purchased. When holding long-term securities, day-to-day pricing fluctuations can mean the value of the security moves significantly in the short term. The short-term returns can be higher or lower than the prevailing cash rate or the inflation rate and may even be negative. This point is often missed by actuarial students. Always be conscious of the difference between the return on a single security or portfolio of debt securities and the current yield to maturity6 (gross redemption yield) on a single security or a portfolio of securities. 6 Yield to maturity is the total return anticipated on a bond if the bond is held until it matures, determined by applying the current price of the bond (not the original purchase price or the principal value). © June 2024 The Institute of Actuaries of Australia Page 26 of 62  Asset Liability Management Chapter 5: Debt securities The exact details regarding the amount of cash flows from the bond will be determinable in advance either in absolute terms or by reference to some benchmark or event, in which case they are unknown in monetary terms at the point of entering the agreement. Sections 5.5.3 and 5.5.4 detail conventional bonds, where payments are fixed in monetary terms. Section 5.5.5 discusses bond where payments are linked to inflation and section 5.5.6 discusses bonds where payments are linked to short-term cash rates. Even though the basis for amounts and timing of cash flows is agreed in advance, there is still uncertainty regarding the actual receipt of these amounts due to the credit risk of the issuer, which relates to the probability that the issuer will default on some or all of the agreed interest payments and the capital repayment at maturity. A key point to note is that the bond investor has provided leverage to the bond seller. The borrowing will increase the leverage of the borrower and may itself contribute to a greater risk of default. The bond investor receives, at most, what has been contractually agreed. If the bond seller successfully invests the loan in a business venture, then the bond seller does not share any additional profit with the bond purchaser. When you read Chapter 6 (Equities), you should consider who has leverage. This is important when considering the relative performance between equities and bonds. Following issuance of a bond on the primary market, it may be traded in the secondary market. For corporations, governments, and institutions, these types of securities are predominantly issued and traded through bond markets (including stock exchanges) but can also be transacted via private placements. Quoted bond prices in the secondary market may or may not allow for the next coupon payment. The convention in the USA, Australia, and the UK is to quote prices net of the next coupon payment. This is known as the flat price, or clean price. The purchaser pays the flat price plus accrued interest at the settlement date. In continental European markets, the price is the sum of the clean price and accrued interest and is called the dirty price. Each market has its own convention and you need to check which convention applies in your local market. © June 2024 The Institute of Actuaries of Australia Page 27 of 62  Asset Liability Management Chapter 5: Debt securities The bonds we discuss in this chapter do not contain options to the buyer or seller. Pricing issues with optionality are covered in the Fellowship Investment subject, although the techniques are simple applications of the mathematics you have learned during your Foundation studies. A key actuarial skill is recognising optionality in contracts and understanding their implications. Think about the implications of the following three option types as you work through the rest of this chapter: callable bonds puttable bonds; and convertible bonds. A callable bond, also known as a redeemable bond, is a bond that the issuer may redeem before it reaches the stated maturity date. A callable bond allows the issuing company to pay off their debt early. A business may choose to call their bond if market interest rates move lower, which will allow them to re-borrow at a more beneficial rate. Callable bonds typically offer a more attractive interest rate or coupon rate due to their callable nature. The higher interest rate is usually needed to compensate investors for the risk of the bond being redeemed at a time unfavourable to them— for example, when the prevailing level of interest rates at which they can re-invest the redemption proceeds is low and the borrower has the incentive to redeem and refinance the loan. A puttable bond is a debt instrument with an embedded option that gives bondholders the right to demand early repayment of the principal from the issuer. The embedded put option acts as an incentive for investors to buy a bond that has a lower return. The put option on the bond can be exercised upon the occurrence of specified events or conditions or at a certain time or times. A convertible bond is a corporate debt security that yields interest payments but can be converted into a predetermined number of common stock or equity shares. The conversion from the bond to stock can be done at certain times during the bond's life and is usually at the discretion of the bondholder. As a hybrid security, the price of a convertible bond is especially sensitive to changes in interest rates, the price of the underlying equity stock, and the issuer's credit rating. © June 2024 The Institute of Actuaries of Australia Page 28 of 62  Asset Liability Management Chapter 5: Debt securities 5.5.2. Bond returns In general: returns to the investor come from the contracted cash flows or the sale of the securities 7; if the issuer (borrower) gets into financial difficulties and cannot pay the contracted cash flows, the investor (lender) may be left with nothing, even though their investment ranks ahead of equity investors; there is no upside for the investor in terms of bonus payments or profit share if the issuer does well financially, only the contracted payments; and therefore, the certainty of receiving the payments (i.e. the quality of the credit) is the most crucial factor in assessing the risk of a debt security. Note that the purchaser of a bond may be in the same country as the issuer, the same country as the listing, or neither. This will influence the capacity of investors to take legal action to enforce payment. For a specific bond: return is determined by the value and timing of the future cash flows over the remaining life of the security to maturity; and risk is predominantly measured as the expected loss in the event of cash flows not being received as promised or anticipated at the time of the investment. It is important to remember that an investor can buy a debt security and either: hold the security to maturity receiving all coupons and the principal; or sell the security prior to maturity receiving none or some coupons and the sale price. The return may be quite different between these options, as the market price of the security may change over time (unlike the principal). The yield to maturity, or gross redemption yield, is the internal rate of return that results in the sum of the present values of the cash flows, discounted at this rate, equaling the current market price of the bond. This uniform interest rate is the implied market rate of return at that date for that bond if it is then held to maturity. Note that there is a clear mathematical relationship between the market price and market rate of return (or yield to maturity). In effect, the yield to maturity is an alternative way of expressing the market price of a bond. 7 With the exception of convertible bonds or other conversion rights. These are discussed later in the course. © June 2024 The Institute of Actuaries of Australia Page 29 of 62  Asset Liability Management Chapter 5: Debt securities The yield to maturity is based on the following three assumptions: 1. The bond is held to maturity. 2. The issuer does not default on any of the payments—that is, all of the coupon and principal payments are received as per the original agreed dates. 3. Coupon payments can be reinvested at the same rate. Chapter 2 discussed exemplars, and the Foundation compound interest subject often set examples that only considered returns if a contract was held until maturity. In practice, insurance companies will not hold bonds until maturity. For an investor holding a portfolio of bonds, the securities within the portfolio may be sold before maturity and the return obtained on the bonds held in the portfolio will differ from the original expected yield to maturity. Valuation of debt securities is capable of more exact mathematical treatment than the valuation of securities in other asset classes such as equities or property. It depends basically on three factors: the amounts of the cash flows and their timing, as prescribed in the contract; the probability of the cash flows occurring, which requires credit analysis; and the appropriate rate of interest to use to calculate the present value of the cash flows, as determined by market forces. It is important to realise that the market-determined yield to maturity can change at any time. Changes in the yield to maturity will change the then present value of the security, even though all the future cash flows are unchanged, and the credit risk may be unchanged. If the investor sells the security before maturity, depending on the yield to maturity that applied at the time of sale (i.e. the sale price), they will have a capital gain or loss on their original investment. If the investor holds the security through to maturity, all cash flows will have occurred as foreseen at the time of the initial purchase. © June 2024 The Institute of Actuaries of Australia Page 30 of 62  Asset Liability Management Chapter 5: Debt securities The factors that affect the yield to maturity on bonds include the: supply of bonds; demand for bonds; issuing organisation; expected inflation; uncertainty of inflation; exchange rate; taxation; and return on US bonds. The supply of government bonds is related to a government’s fiscal policy. If governments fund fiscal deficits through the issuance of bonds, then bond yields at those targeted durations will rise as prices will need to fall to tempt buyers. The picture can be very nuanced as, for example, a government may decide to switch to issuing inflation-linked bonds. The effect would be a relative decrease in supply of conventional bonds, which will cause their price to rise (i.e. yields to fall). Demand for bonds arises from private and institutional investors. Institutional demand may change depending on savings patterns, or as a result of government policy. An example is the 2020 Australian Government decision to allow early partial withdrawal from superannuation accounts, which led to the need for major superannuation funds to sell more liquid assets such as bonds, increasing supply to the secondary market. Another example is if a government relaxes the need for insurance companies to hold bonds, demand may fall. Alternatively, if a government imposed compulsory annuitisation on work-based pension savings, then that would increase the demand for both government-issued bonds and high-credit-rated bonds. Different issuing organisations have different credit ratings. The demand for these bonds will also differ by type of organisation and this affects the marketability, or liquidity, of an issue. It implies that the probability of payment—credit risk—and the difficulty of selling before maturity— liquidity risk—changes by organisation. Credit risk can be defined as the risk of the counterparty or issuer not meeting their commitments and failing to make payments. There is always a risk of default by the issuer as even sovereign governments have been known to default on government bonds from time to time (see Chapter 2). © June 2024 The Institute of Actuaries of Australia Page 31 of 62  Asset Liability Management Chapter 5: Debt securities Chapter 4 discussed credit rating agencies, which place a value on the risk of default. The potential for default is assessed as ‘credit quality’—the higher the quality, the lower the risk of default. As the circumstances of an issuer (government or corporation) change over time, the credit quality of the issuer may change. A reassessment to lower quality would imply more risk of default by the issuer, so more capital risk for the investor, hence the investor would expect a higher margin over the risk-free rate. This devalues the security. The credit spread is the difference in yield between two securities of the same maturity but different credit quality. Typically, the credit quality of securities is assessed against that of a flagship government security (e.g. a US Treasury Bond) that is considered risk free. The difference in yield is quoted in basis points (1% is 100 basis points). The credit spread indicates the additional return that the buyer is seeking in compensation for the credit risk assessment of the issuer. Conventional bonds are exposed to changes in expected inflation. There is no law of nature that fixes a margin between inflation and interest rates, even though the past data may show long periods where interest rates are consistently above inflation. Market commentators, forecasters, and modellers may well set an expected margin for risk-free interest rates above price inflation. When the outlook for inflation is uncertain, then investors may add a margin to reflect the uncertainty on future inflation. Bond markets are global markets and overseas demand for government bonds depend on expectations of changes in future exchange rates. This subject focuses on long-term expected returns and we assume that, in the long run, changes in the price level in one country will cause changes in nominal exchange rates, thus keeping the real exchange rate constant. This suggests a link between long-term bond yields across similarly rated countries. Because of the size of the US market, one argument is that all bonds are priced in relation to the return of US short-term bonds. One model of prices suggests that pricing bonds is a three-stage approach as shown below: 1. The risk-free real rate in the US Treasury market reflects the supply and demand of global capital. 2. The nominal risk-free government rate in other countries is priced off the US rate plus local factors of exchange rates, inflation expectations, economic factors, and political stability. 3. Credit assessment of the various issuers (both government and non-government) leads to various appropriate credit risk premiums, defined as a percentage per annum additional to the yield on the risk-free (US) government bond of a similar maturity. © June 2024 The Institute of Actuaries of Australia Page 32 of 62  Asset Liability Management Chapter 5: Debt securities You may question how can global markets determine local interest rates outside the US when the cash rate is set by the local central bank? The answer is that the global rate refers to a longer-term rate, over which the local central bank has little control. The other reason stems from the control of a floating exchange rate. If the local central bank sets the cash rate too high (in the eyes of the global market), then foreign investors will demand more local currency and the exchange rate will appreciate, reducing international competitiveness. The reverse applies for a cash rate that is too low. Inflationary and growth expectations are the key driver of nominal interest rates, at both the short and long ends of the yield curve. We will assume that observable government bond yields are a proxy for the unobservable risk-free rates. A possible relationship between nominal yields and real yields for government bonds is: 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑟𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑦𝑖𝑒𝑙𝑑 = 𝑟𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑟𝑒𝑎𝑙 𝑦𝑖𝑒𝑙𝑑 + 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑓𝑢𝑡𝑢𝑟𝑒 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 + 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 At the short end, the local central bank changes the cash rate in effecting its monetary policy. It will lift rates if the economy is expanding too rapidly, and lower rates if the economy is too sluggish. The main indicators of an over-stretched or stagnant economy are the level of inflation and the growth rate. At the long end, the erosion of purchasing power, which shows up as the inflation rate, is a major driver of yields. A fixed interest investor receiving fixed coupons and principal in the future has lower real cash flows if inflation should increase. Other investors considering buying these bonds push yields up in the market to compensate them for this erosion of purchasing power. Long-term yields are very sensitive to inflationary expectations. Contrast this to an ordinary share, where the dividend income can grow with inflation—in which case, while inflation is important, economic growth takes on a more prominent role in driving the return. In addition, long-term bonds compete with other asset classes such as property and equities to attract investors. The relative merits of other asset classes, including perceived riskiness and the return offered, will influence the long-term yield. The taxation of bonds will affect demand. For example, in some markets, coupons may be taxed as income and proceeds taxed as capital gains or loses. If there is a differential in tax rates between income tax and capital gains tax, then that will affect demand for high- or low-coupon bonds. As well as the main factors described above, you should be aware of how changes in interest rates affect bond prices. © June 2024 The Institute of Actuaries of Australia Page 33 of 62  Asset Liability Management Chapter 5: Debt securities Interest rate risk There are quantitative measures of interest rate risk, which you should be familiar with from your Foundation studies. Duration measures the weighted average time to receipt of cash flows, the weights being the present value of cash flows. A closely related concept is modified duration, which is the proportional first derivative of price with respect to yield. In symbols, the duration, D, say, of a cash flow sequence {Ct}, using a constant rate of interest i, say, is: ∑ 𝑡 𝐶𝑡 𝑣 𝑡 ∑ 𝑡 𝐶𝑡 𝑣 𝑡 𝐷= = , ∑ 𝐶𝑡 𝑣𝑡 𝑃 where v = 1/(1+i), and P (= represents the price of the cash flows. The modified duration, D*, say, is: 1 𝜕𝑃 𝐷∗ = − = 𝑣𝐷 𝑃 𝜕𝑖 The equation for modified duration demonstrates that the concept is a measure of the sensitivity of the price of the security to a change in interest rates. Convexity is the proportional second derivative of price with respect to yield. Combining convexity with duration gives a much more accurate approximation of the price–yield relationship than duration alone, particularly for large-yield changes. Convexity is a measure of the curvature, or the degree of the curve, in the relationship between bond prices and bond yields. Convexity demonstrates how the duration of a bond changes as the interest rate changes. Portfolio managers use convexity to measure and manage the portfolio's exposure to interest rate risk. We can use Taylor’s theorem to show how convexity aids the concept of duration. Let P(i) denote the price of a bond at rate i. Then: 𝜕𝑃 1 𝜕2 𝑃 1 𝑃(𝑖 + ∆𝑖) − 𝑃(𝑖) ≈ ∆𝑖 + (∆𝑖)2 = - 𝐷 ∗ ∗ 𝑃(𝑖) ∗ ∆𝑖 + ∗ 𝑐𝑜𝑛𝑣𝑒𝑥𝑖𝑡𝑦 ∗ (∆𝑖)2 𝜕𝑖 2 𝜕𝑖 2 2 For small, or sudden, changes in interest rates, duration will indicate how bond prices will change. However, as we will see when we study the yield curve in Section 5.6, the relationship between bond prices and yields is typically more convex. Therefore, convexity is a better measure for assessing the impact on bond prices when there are large fluctuations in interest rates. © June 2024 The Institute of Actuaries of Australia Page 34 of 62  Asset Liability Management Chapter 5: Debt securities Further discussion of how convexity helps manage bond portfolios is discussed in the Fellowship Investment subject. The concept is required in Chapter 11 when we discuss asset liability matching. Be aware that duration and convexity have their limitations as risk measures, due to: the inherent assumptions about the yield curve shape and yield changes; and the features of particular debt securities, including embedded options and interest-sensitive cash flows. In effect, duration and convexity are measures of sensitivity of bond prices to shifts in yield, rather than measures of the probability of loss. Relationships between characteristics and price The price of a fixed rate bond will change whenever the assumed yield changes. The following four relationships between the price of an instrument and the yield should have been discussed during your Foundation studies: price is inversely related to the yield. As the yield increases, the price will decrease and vice versa; given the same coupon rate and time to maturity, the absolute change in price is greater when the yield decreases compared to when it increases—the convexity effect or convexity bias; given the same time to maturity, the absolute value of the percentage change in price is greater for a bond with a lower coupon than a bond with a higher coupon when the yields change by the same amount -— the coupon effect; and for bonds with the same coupon rate, a longer-term bond has a greater absolute change in price than a shorter-term bond for the same change in yield—also known as the duration or maturity effect). Figure 5.5 and Figure 5.6 visually demonstrate the above four points by examining the relative change in price to the relative change in yield. © June 2024 The Institute of Actuaries of Australia Page 35 of 62  Asset Liability Management Chapter 5: Debt securities Table 5.3 – Coupon effect For a 1 year $10,000 face value bond (face value paid at maturity) Yield at issue 4%pa Yield at issue 8% Purchase price $10,000/ 1.04 = $9,615 Purchase for $10,000/ 1.08 = $9,259 Next day market yields fall by 2% Required yield now 2% Require yield now 6% Present value now $10,000/1.02 = $9,804 Present value now $10,000/1.06 = $9,434 Change in value +1.96% Change in value +1.89% Figure 5.5 – Constant coupon 8% Coupon paid monthly - 5, 15 and 25 year terms 100% 90% 80% 70% 60% Change in price 50% 40% 30% 20% 10% 0% -10% -3.5% -3.0% -2.5% -2.0% -1.5% -1.0% -0.5% 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% -20% -30% -40% -50% Change in yield from 8% 5 15 25 © June 2024 The Institute of Actuaries of Australia Page 36 of 62  Asset Liability Management Chapter 5: Debt securities Figure 5.6 – Fixed term 25 year term - 4% and 8% coupon paid monthly 100% 90% 80% 70% 60% 50% Change in price 40% 30% 20% 10% 0% -10% -3.5% -3.0% -2.5% -2.0% -1.5% -1.0% -0.5% 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% -20% -30% -40% -50% Change in yield from 8% 8.00% 4.00% 5.5.3. Conventional government bonds Sovereign governments issue a variety of conventional bonds that have different redemption dates (i.e. when the loan is repaid at par) and different coupon rates. The word ‘conventional’ refers to payments being made in nominal terms (i.e. in monetary terms). You would have studied the pricing of these bonds in your Foundation studies. The following text uses SYSTEM T (explained earlier) to determine the risk and return characteristics. It is often claimed that there is a very small or negligible risk of default for bonds issued by major sovereign governments, and the risk is virtually nil where the sovereign entity controls fiat money. Thus, security in monetary terms is usually high. However, sovereign governments can and do default. Chapter 2 outlined the shock that occurred when Russia defaulted on its bonds. Further, countries in currency unions (e.g. the Euro) have different credit ratings that lead to non-negligible risks of default, which are then usually reflected in differences in yields on bonds of the same maturity issued by different governments within the currency union. © June 2024 The Institute of Actuaries of Australia Page 37 of 62  Asset Liability Management Chapter 5: Debt securities The yield is known at outset in monetary terms, but this will equate to the rate of return on the bond only if the bond is held to redemption and coupons received are all reinvested at the expected rate. The inflation-adjusted return (i.e. the real return) is unknown at outset because the rate of inflation is unknown. The expected income over one year divided by the current price—also known as the running yield—is more difficult to compare against equities in recent years because of the significant market swings. Further, governments may launch bonds with relatively high-, medium-, or low- coupon rates, which invalidates potential comparisons with other asset classes. The total return is secure in nominal returns and this may lead to the conclusion that it should be lower than more risky investments. However, an alternative argument is that the nominal return should price in the risk of inflation and consequent erosion of real return. This is considered in more detail in Chapter 10 (Long-term returns). Exercise 5.6 Describe two scenarios where conventional bonds perform well in terms of the return achieved for the risk that is borne. Supply and demand factors will affect daily market values but the spread, which is compensation for credit risk, should be relatively small for government bonds. The term of government bonds varies from one year to undated bonds, which are sometimes called perpetual bonds. This will vary by market. Expenses of dealing are very low. There is an exchange-rate risk if the loan is not in the investor’s domestic currency. Government bonds typically have excellent marketability and liquidity. The low dealing cost assists marketability, but more important are the large volumes of bonds held and traded by institutional investors. In some markets, liquidity is further assisted by an active market in derivatives based on bonds (see Chapter 8) and also in some cases by a market that decomposes a bond into its components—often called the STRIPS market. © June 2024 The Institute of Actuaries of Australia Page 38 of 62  Asset Liability Management Chapter 5: Debt securities STRIPS is an acronym for Separate Trading of Registered Interest and Principal of Securities. These types of bonds are generally known as zero-coupon bonds since they pay no interest, or coupon. As the acronym implies, STRIPS are created when a bond's coupons are separated from the bond. The bond, minus its coupons, is then sold to an investor at a discount price. An investor buying the bond stripped of its coupons does not have to worry about not being able to reinvest coupons at a lower rate that will detract from the expected return, if the stripped- down bond is held to maturity. Each coupon payment can also become a separate zero-coupon bond that can be sold separately. 5.5.4. Corporate bonds Any corporation can issue a debt security to raise capital. However, to be tradable on the secondary market a debt security may need to meet a minimum capital amount and/or minimum credit assessment. Corporate bonds may be secured (historically known as debentures because the security was provided by a debenture trust deed) against assets of the corporation or unsecured. The ‘seniority’ of the debt indicates where it ranks in terms of order of repayment if the company is wound up. Debt securities normally rank ahead of equity securities—but be aware there are debt securities with options that allow the borrower to convert the debt to shareholder equity rather than repay the principal. Investors will seek a higher yield from corporate bonds compared with government bonds to compensate for the additional credit risk (i.e. the greater risk of default) as well as the lower liquidity (also referred to as marketability). The yield to maturity for corporate bonds can be calculated as: 𝑌𝑖𝑒𝑙𝑑 = 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑟𝑒𝑎𝑙 𝑦𝑖𝑒𝑙𝑑 + 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 + 𝑏𝑜𝑛𝑑 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 where the bond risk premium has the following three main components: inflation risk premium; credit default premium; and marketability premium. © June 2024 The Institute of Actuaries of Australia Page 39 of 62  Asset Liability Management Chapter 5: Debt securities The inflation risk premium represents an additional compensation to investors for taking on the risk that future inflation will be uncertain and is likely to differ from the expected future inflation estimate. Similarly, the credit default premium is to address risks that the bond issuer will default on payments and the marketability premium is to address the risk the bond can’t be resold before maturity. Corporate bonds are often issued with a floating rate, that is, the coupon is a fixed amount above a market benchmark rate. That market benchmark may be the central bank overnight rate. The fixed amount is set taking into account the relevant risk premia and credit spreads at the time of issuance. For all corporate debt, there is also the risk of the credit spread widening. In general, bonds are subject to short term market price risks due to potential changes of in the level and shape of the credit risk-free yield curve and in the credit spreads above this yield curve. Floating rates notes are also subject to this risk, as the credit spread may change but the coupon’s fixed amount above benchmark does not. Regulators often impose capital charges on insurers for credit spread risk as well as default risk for bonds or other debt instruments. Exercise 5.7 Use SYSTEM T to detail the investment and risk characteristics of: 1. money market instruments 2. corporate bonds. 5.5.5. Inflation-linked securities Inflation-linked (or index-linked) bonds have the coupon set as a margin over a specific index, typically a consumer price index (CPI). This margin may be referred to as the real return, or real yield. © June 2024 The Institute of Actuaries of Australia Page 40 of 62  Asset Liability Management Chapter 5: Debt securities The mechanics will be specified in the contract. For example, the Australian Government has issued inflation-linked bonds where the nominal amount of the security is adjusted for changes in the CPI each quarter. This adjustment is ‘lagged’ by one quarter and based on the average movement of the two previous quarters. Thus, for an interest payment in November, the nominal amount of the security is adjusted from the previous level by the average quarterly change in the CPI for the two quarters ending in June (March and June CPI changes). The amount of interest is based on the adjusted nominal face value (the indexed value) multiplied by the fixed coupon (margin) and is normally paid quarterly. On redemption, the adjusted capital value (i.e. the indexed value) is payable. Whilst the calculations are quite complex, in practice investors assume that both the income payments and the maturity payment are adjusted for inflation, as measured by the index, even though this is not strictly correct. Indexed bonds are traded on the basis of a ‘real’ yield, convertible quarterly, using a formula that is similar to a fixed coupon bond. The real yield is the return above inflation. This real return is known, provided the bonds are held to maturity, even though the inflation index returns are not known in advance. The real return is evaluated based on the assumptions that the reinvestment rate has the same margin as the coupon rate, the bonds are held to maturity, and no lags exist between the bond coupon payments and the underlying inflation index. In practice, a lag exists, which limits an index-linked security’s ability to hedge inflation risk as the cash flows do not relate to the inflation index at the time of payment. This is potentially due to delays in calculating the relevant value of the index. Quite often, there is also demand from the issuer (or even the investors), who may need to know the amounts of the payments in advance. This may lead to the requirement to use an index value from an earlier period in order to know the amount to be paid in advance of the actual payment date. Considering that the purchasing power of a fixed amount of capital diminishes over time (in an inflationary environment), investors are often attracted to a security for which the interest payments and the final capital redemption are not fixed but are rather linked to an ‘index’ to mitigate the effects of inflation. Note that the real yield on bonds is often used, as the benchmark required real yield for equities. © June 2024 The Institute of Actuaries of Australia Page 41 of 62  Asset Liability Management Chapter 5: Debt securities 5.5.6. Floating rate notes A floating rate note (FRN) is a non-conventional bond, also known as a floating rate bond or adjustable rate bond. These securities pay a coupon that is determined as a reference rate plus a specified margin. For example, ‘will pay the bank bill rate plus 1.5% pa’. Interest is usually paid quarterly. In Australia, most FRNs pay income at a margin over the bank bill swap rate (BBSW), which is the market benchmark cash or bank bill rate. The margin over the benchmark is set at the time of issue and not changed. Set by the issuer (in response to market appetite), it reflects the credit risk. A lower margin implies a lower risk (i.e. stronger credit assessment). As the interest rate payable is automatically adjusted in accordance with market movements of the reference rate (usually a cash rate), the capital value is not as sensitive to overall movements in interest rates as a fixed coupon bond. However, an adjustable rate bond with a longer term to maturity may be sensitive to movements in the market’s expectation of an appropriate margin over the reference rate. Such changes in expectation might be brought about by demand for funds or changes in credit quality assessment. Other factors affecting pricing: short term rate movements—due to the reset mechanism on the payment dates, FRNs will pay a fixed rate until the next coupon reset date. Therefore, an investor is locked in at the current rate until it resets at the next reset date; and accrued interest—as a note gets closer to the interest payment date, it builds up more accrued interest and its price, all other things being equal, will rise. When the interest is paid, the price will fall by the amount of the payment and will again start to accrue interest on a daily basis until it is paid on the next payment date. The same is true of fixed rate bonds. Because of the way they are structured, FRNs typically protect a portfolio when interest rates are rising. That is, as a central bank increases the cash rate to try to slow growth in an economy, FRN income will also increase with the cash rate. As the FRN income addresses the market’s expectations of higher interest rates, it is less exposed to a decline in price than fixed rate bonds under those economic conditions. © June 2024 The Institute of Actuaries of Australia Page 42 of 62  Asset Liability Management Chapter 5: Debt securities 5.6. Term structure of interest rates 5.6.1. Debt valuation methods and yields When pricing debt securities we generally use a present value. The method is fairly straightforward and accepted. However, we also need to make assumptions to determine the present value of future cash flows. That is, what is the probability of receiving each payment (income or capital) and what is an appropriate discount rate for the investor. These two assumptions combine to form the investor's required yield to maturity, which is then applied to determine the price they will set on the debt security. Thus, in the debt sector the focus is on the assumed yield to maturity as this will then lead to the price an investor is willing to trade the debt security. Alternatively, the price paid leads to the yield accepted. We concluded earlier that the yield to maturity is an alternative way of expressing the market price. Hence, the valuation discussion is about how to model or predict yield curves into the future, which will also predict future debt security prices. A key part of the discussion involves understanding the limitations on the modelling. This is where yield curve theories come in as the selected theory and associated yield curve generates the assumptions required to value the debt security. 5.6.2. Spot and forward rates Bonds often appear to be more straightforward than equites because of the relative ease of valuing the securities. However, we should not confuse the mechanics with the need to derive assumptions for every single possible maturity date. The yield to maturity for a bond represents a single statistic that belies the underlying complexity of yields to different points in time. The phrase “term structure” is reference to any summary of this complexity that conveys how interest rates vary by term. A key tool when discussing bonds is the concept of the term structure, that is, the various yields that are currently being offered on bonds of different maturities. This enables investors to understand the impact of accepting a longer term to maturity. © June 2024 The Institute of Actuaries of Australia Page 43 of 62  Asset Liability Management Chapter 5: Debt securities Yield Curve The first approach is the yield curve. This is a curve fitted to plot yield to maturity against term to maturity for similar credit rated securities. For example, one may construct a yield curve from yield to maturity for the various government bonds in issue in a country. The methods for fitting the curve are outside the syllabus but note that the curve is smoothed so that an individual bond’s yield to maturity is unlikely to lie exactly on the yield curve. The yield curve is not static and changes in response to market conditions. The shape of the yield curve is one representation of term structure of interest rates. Theoretically, the yield curve should be analysed for bonds that have the same properties other than time to maturity. The bonds should have the same currency and have the same credit risk, liquidity, and tax status. Their annual rates should also be quoted for the same periodicity (i.e. frequency of coupon payment). They should have the same coupon rate so that they each have the same degree of coupon reinvestment risk. Then, the two bonds only differ on time to maturity and this is the only reason for difference in yield. In practice, the yield curve is analysed and compared for bonds for which these strong assumptions rarely hold. Another way to use yields, that reflects the inherent risk and uncertainty associated with each cash flow, is to calculate the price of a bond based on a sequence of yields that corresponds to the cash flow dates. Each cash flow is treated separately. These yields are referred to as spot rates.8 A spot rate today for a specified period is the yield to maturity expected to be earned when holding a zero-coupon bond of the specified period. These spot rates reflect the term structure of interest rates. Using this approach for calculating the price of a bond is also known as the bond’s ‘no-arbitrage value’ as the spot rates are the rates currently observed in the market. If the price at which the bond is trading is different from this no-arbitrage value, then a trading opportunity exists as it is (theoretically) possible to construct the same cash flows using zero- coupon bonds, which will have a different price (this ignores the impact of transaction costs). 8 Also known as zero rates. © June 2024 The Institute of Actuaries of Australia Page 44 of 62  Asset Liability Management Chapter 5: Debt securities Spot yield curve The yields to maturity for a series of zero-coupon government bonds, with a range of maturities, can also be used to demonstrate the term structure. This dataset is the spot yield curve.9 This curve (also known as zero or strip curve) is a sequence of yields to maturity on zero- coupon bonds. Often, these government bond spot rates are interpreted as the risk-free yields and in this context, ‘risk free’ refers only to default risk. There remains a significant amount of inflation risk to the investor, as well as liquidity risk. Suppose we label the observed spot rate yield from today (t=0) for a period of n years from now (t=n) as yn. The corresponding price Pn, say, is: 𝑃𝑛 = 1⁄(1 + 𝑦𝑛 )𝑛 If such instruments exist, then we can observe a set of spot rates today. What we cannot observe are the spot rates that apply in future times. For example, measuring from today, we know the one-year spot rate is y1. We do not know today what the one-year spot rate will be in one year’s time. Label the future (unknown) one-year spot rate from time t= s-1 to time t = s as rs. Apart from r1, which equals y1, rs is unknown today as future interest rates are uncertain. Thus, it is not true that we can compound these one-year spot rates and equate them with the known spot rates. For example, (1+r1) * (1+E(r2)) is unlikely to equal (1+y2)2, where E(r2) is today’s expectation of r2. We revisit forward contracts in Chapter 8 (Derivatives), but the following will be familiar to you from your Foundation studies. Implied forward rates10 are derived from spot rates as the break-even reinvestment rate. The forward rates bridge the return on an investment in a shorter-term zero-coupon bond to the return on an investment in a longer-term zero-coupon bond. The forward rates are inferred or implied from the spot market. If we denote the forward rate in the period from time t = n-1 to time t = n as fn, then: 9 Also known as the zero or strip curve (the reason being that the coupon payments are ‘stripped’ off the bonds). 10 Also referred to as forward yields. © June 2024 The Institute of Actuaries of Australia Page 45 of 62  Asset Liability Management Chapter 5: Debt securities (1 + 𝑦𝑛 )𝑛 1 + 𝑓𝑛 = (1 + 𝑦𝑛−1 )𝑛−1 Let us compare f2 with r2 by considering an investor who has a one-year time horizon. The investor can obtain a guaranteed one-year yield of y1. Alternatively, they could buy a two-year guaranteed yield of y2 and sell at the end of year 1. If the one-year spot rate at the end of the year coincides with the expected value of r 2, then the return over the first year must be y1. However, there is a non-zero chance that the actual value of r2 is greater or less than its expected value. The one-year horizon investor would need to be tempted into the strategy of buying the two- year bond and selling it at the end of the first year. This would force up y 2. A consequence is that the forward rate, f2, would then exceed the expected future spot rate, r2. Mathematically, the increase in yield for y2 to tempt the short term investor means that: (1 + 𝑟1 )(1 + 𝐸(𝑟2 )) < (1 + 𝑦2 )2 Since the forward rate, f2, is defined by: (1 + 𝑦2 )2 1 + 𝑓2 = (1 + 𝑦1 ) And r1= y1 it follows that: 𝑓2 > 𝐸(𝑟2 ). However, if the market is dominated by long-term investors, then the opposite conclusion would be drawn. These investors need to be tempted into buying a 1 year contract at r 1 and then another next year at E(r2), rather than a 2 year contract at y2 now. This requires (1 + 𝑟1 )(1 + 𝐸(𝑟2 )) > (1 + 𝑦2 )2 So it follows that to attract these investors: 𝑓2 < 𝐸(𝑟2 ). In general, we conclude that there is a relationship between forward rates and expected future spot rates: © June 2024 The Institute of Actuaries of Australia Page 46 of 62  Asset Liability Management Chapter 5: Debt securities 𝑓𝑛 = 𝐸(𝑟𝑛 ) + 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 where the liquidity premium may be positive or negative. We do not have enough information to decide whether the premium is positive or negative. This is discussed in Section 5.6.3. Note that the market is basing forward rates on what it knows today. You can only infer the future spot rates from the current forward rates when there is no uncertainty about the future interest rates. When there is interest rate uncertainty, the forward rates do not inform you of likely future spot rates. 5.6.3. Yield curve shapes The most commonly observed yield curve shape in practice has the following features: upward slope; and a concave shape—that is, steeply upwardly sloping, then levelling out to become almost flat at longer durations. Short rates are more volatile than longer-term interest rates. This is a logical result, as the longer- term spot rates are averages of the one-year spot and forwards. As shown in Figure 5.7 – Yield curve shapes, the shapes that the yield curve can take include: upward sloping, or normal; flat; downward sloping, or inverted; and humped. Note that flat is a descriptive term, meaning that it does not have a large slope. The curve does not have to be absolutely flat. © June 2024 The Institute of Actuaries of Australia Page 47 of 62  Asset Liability Management Chapter 5: Debt securities Figure 5.7 – Yield curve shapes 7 6 5 4 % 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Term to maturity Normal Flat Inverse Humped It has been observed that longer-dated government bonds tend to have higher yield compared to shorter-dated government bonds under normal market conditions. 11 Theories to explain this observation are discussed in the next section. It is possible for shorter-dated government bonds to have yields that are higher than longer-dated government bonds. This situation is referred to as an inverted yield curve and occurs when the spot curve is downward sloping. Market conditions, changing expectations, or supply and demand for particular terms to maturity can all affect the shape of the curve. For example: if prudential oversight requires insurers to hold long-term bonds and there is not sufficient supply, this increased demand will drive yields down for long-term bonds but have no impact on shorter-term yields, leading to a humped curve; and there is some evidence that an inverted yield curve is a reliable indicator of recessions in the USA. 11 Normal market conditions would refer to conditions such as positive inflation and economic growth. © June 2024 The Institute of Actuaries of Australia Page 48 of 62  Asset Liability Management Chapter 5: Debt securities 5.6.4. Theories explaining yield curves Outlined here in Table 5.4 – Yield curve theories are four useful theories in relation to the factors affecting the shape of the yield curve. These theories assist when developing interest rate risk management strategies for debt security portfolios and when developing pricing models for interest rate sensitive derivatives. These topics will be covered in more detail in the Fellowship Investment subject. Table 5.4 – Yield curve theories Expectations theory Expectations theory aims to predict what short-term interest rates will be based on long-term interest rates, which in turn are driven by expectations of future economic factors. Pure expectations theory states that expectations alone drive interest rates. There is no bond liquidity risk premium. Thus, forward rates equal the future spot rates—that is: 𝑓𝑛 = 𝐸(𝑟𝑛 ). Market segmentation theory Economic theory generally states that prices and yields are determined by supply and demand. Remember that this is a theory and not a law of nature. Market segmentation theory asserts that certain types of investors restrict their purchases to certain maturity ranges (segments), commonly divided into short-term, medium-term, and long- term. An example of a short-term investor is a bank and an example of a long-term investor is a life insurer that sells annuity contracts. The bank is focused on protecting the principal and maintaining liquidity over the short term. The insurer is aiming to match long-term annuity payments with guaranteed income streams. The theory says that bonds of different maturities effectively trade in different markets, each with its own supply-and-demand forces that produce bond yields. Because of this, the yields from one group of bonds with a certain maturity length cannot be used to predict the yields of another group with a different maturity. The supply and demand in different segments lead to time-varying risk premia, which may be positive or negative. The yields for each segment are therefore driven by the demand and supply in that segment and each segment can have a different shape—so the overall yield curve may be quite different from what the other theories suggest would be observed. Liquidity preference theory © June 2024 The Institute of Actuaries of Australia Page 49 of 62  Asset Liability Management Chapter 5: Debt securities Liquidity preference theory is based on the notion that investors prefer access to their capital through liquid investments rather than having no or restricted access, all else being equal. Thus, investors expect to be compensated for locking in their capital by receiving a higher expected return than on liquid investments (such as cash). The theory claims that a positive bond liquidity risk premium exists, so that investors in longer duration bonds require a higher expected return as compensation for the extra risk borne. Thus, we have: 𝑓𝑛 > 𝐸(𝑟𝑛 ). Theoretically, this liquidity risk premium increases with duration, which is proportional to the volatility of bond prices with respect to yield. This is consistent with modern financial economic theory, although Chapter 9 notes that there is no universal consensus. There is some empirical evidence that this bond risk premium varies over time, par