Week 2 Lecture Slides - ECN 241 Asset Pricing

ECN 241 Asset Pricing* Lecture 2 Bonds *Some slides contain material from Bodie, Kane & Marcus (2021). Investments, 12th Edition. McGraw-Hill....

ECN 241 Asset Pricing* Lecture 2 Bonds *Some slides contain material from Bodie, Kane & Marcus (2021). Investments, 12th Edition. McGraw-Hill. 1 Bonds – definition and terminology A bond is a security that is issued in connection with a borrowing arrangement: Borrower issues (sells) the bond to the lender for some cash; Issuer agrees to make specified payments (a series of coupons) to the bondholder. At maturity, the nominal value is repaid. Bonds – definition and terminology 2 Bonds – definition and terminology Par value (i.e., face or nominal value) is the payment to the bondholder on the bond’s maturity date (redemption date). Coupon rate is a bond’s interest payments relative to the bond’s par value (e.g., 2%). There are also zero-coupon bonds. Bond indenture is the contract between the issuer and the bondholder. Bonds – definition and terminology 3 Bond coupon A bond with par value of $1,000 and coupon rate of 8% may be sold for $1,000. Bondholder (lender) is entitled to 8% of par (face) value, or $80 per year, for the bond’s life. Typically, the $80 payment comes in two semi-annual instalments of $40 each. At maturity, the issuer pays the par value of $1,000 to the bondholder. Bonds – definition and terminology 4 Bonds – a form of debt Bonds are a form of debt. Interest payments are tax deductible for firms. The issuer of a bond is a borrower, and the buyer of the bond is a lender. How do they differ from bank loans? Bonds are typically issued by governments, large corporations, or municipalities to many lenders. Gives borrowers access to a larger pool of lenders -> better pricing. Bonds are tradeable and can be sold in secondary markets (loans are usually not). Easily convertible to cash, unlike loans. More standardized payment structure. Bonds – definition and terminology 5 Bond prices Bonds are often issued at par, i.e., at a price equal to par value. Zero-coupon bonds are issued at a discount (the discount is needed because there are no interest payments to compensate for the time value of money). After issuance, the price depends on the market conditions. Bonds – definition and terminology 6 Accrued interest Bonds purchased between coupon payments: the buyer must pay the seller for accrued interest, the prorated share of the upcoming semiannual coupon. e.g., 30 days have passed since last coupon payment → there are 182 in the semiannual coupon period. The seller is entitled to a payment of accrued interest of 30/182 of the semiannual coupon. The sale or invoice price of the bond would be: flat price + accrued interest. The practice is to quote bond prices net of accrued interest. 𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑜𝑢𝑝𝑜𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 𝐷𝑎𝑦𝑠 𝑠𝑖𝑛𝑐𝑒 𝑙𝑎𝑠𝑡 𝑐𝑜𝑢𝑝𝑜𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 𝐴𝑐𝑐𝑟𝑢𝑒𝑑 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = ∗ 2 𝐷𝑎𝑦𝑠 𝑠𝑒𝑝𝑎𝑟𝑎𝑡𝑖𝑛𝑔 𝑐𝑜𝑢𝑝𝑜𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠 Bonds – definition and terminology 7 Accrued interest - example Suppose the coupon rate is 8%. Then the annual coupon payment is $80, which means $40 semiannual coupon payment. Because 30 days have passed since the last coupon payment, the accrued interest on the bond is: 30 $40 ∗ = $6.59 182 If the quoted price of the bond is $990, then the invoice price will be: $990 + $6.59 = $996.59 Bonds – definition and terminology 8 How are bonds traded? Primary Market Issuance Bonds are issued by governments or corporations to raise capital. Investors purchase bonds directly from them. Secondary Market Trading After issuance, bonds are typically traded among investors in the Over-the-Counter (OTC) Market. Majority of bond trading occurs OTC, not on formal exchanges. Role of Dealers and Brokers (e.g., Barclays Capital) Dealers buy and sell bonds from their own inventory, providing liquidity. Brokers connect buyers and sellers without holding inventory themselves. Bonds – definition and terminology 9 Bond types by issuer Bond types by issuer 10 Government bonds The main way for governments to raise funding. In the U.S., Treasury notes (maturity: 1 to 10 years) or Treasury bonds (10 to 30 years). Both bonds and notes may be purchased directly from the Treasury. Often seen as very safe investments (since backed by the government; this depends a bit on which government it is). Bond types by issuer 11 Agency and municipal bonds Some government agencies issue their own bonds to finance themselves. In the U.S., there are two main types of such bonds: Federal agency bonds: e.g., issued by mortgage-related agencies: Freddie Mae, Freddie Mac, Fannie May. Municipal bonds “munis”: issued by local government institutions. Semi-formally backed by the government. For “munis” interest payments tax-free! Bond types by issuer 12 Corporate bonds Time of maturity usually 7-30 years, but also there are longer-term bonds: Walt Disney ‘Sleeping Beauties’ 100-years (redeemable in 30 years) Canadian Pacific Corporation and Orsted 1,000 years! Many investors buy and hold until maturity. Companies issue several bonds with different characteristics (maturity, coupon rate, seniority etc.). Secondary markets can be thin; so, most of trading takes place between investors and bond dealers: over-the-counter markets (OTC). Bond types by issuer 13 Bond types by issuer 14 Bond types by characteristics Bond types by characteristics 15 Callable bonds Allows the issuer to repurchase the bond at a specified call price before the maturity date. ⇒ If a company issues a bond with a high coupon rate when market interest rates high and interest rates later fall, the firm might want to retire the high coupon-paying instrument and replace with a lower coupon-paying issue to reduce its cost of capital (refunding). Callable bonds typically come with a period of call protection (an initial time during which a bond is call-protected until a deferral date). Firms’ benefit is bondholders’ burden: when bonds are called investors must forfeit them for the call price. So, callable bonds are issued with higher coupons and yields to maturity. Suppose a company issues two bonds with identical coupon rates and maturity dates. One bond is callable, however, the other is not. Which bond will sell at a lower price? Bond types by characteristics 16 Convertible bonds Give bondholders the option to exchange each bond for a specified number of shares of the firm. Conversion ratio is the number of shares for which each bond may be exchanged: 𝑃𝑎𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑏𝑜𝑛𝑑 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 = 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑝𝑟𝑖𝑐𝑒 If par value is £1,000 and the conversion price is £25, then each bond offers the right to convert to 40 ordinary shares. Convertible bonds offer lower coupon rates and yields to maturity as compared to nonconvertible ones ⇒ options always have non-negative value to the holder. Bond types by characteristics 17 Convertible bonds To convert or not? If at the time of the conversion the stock price is £20, then it is not profitable for bondholders to convert. If, for example, they collected the par value of £1,000 they can buy at the current price of £20, 50 shares. If at the time of the conversion the stock price is £30, then they would convert. They would get 40 x £30 =£1,200 worth of stock for a bond worth £1,000. The market conversion value is the value of the convertible bond if it were converted into ordinary shares at the current share price. At £20 the market conversion value would be £20 x 40 = £800. Bond types by characteristics 18 Puttable bonds Give holders the option to exchange for par value at some date or to extend for a given number of years. If the bond’s coupon rate exceeds current market yields, the bondholder can choose to extend the bond’s life. If the bond’s coupon rate is lower than prevailing current market yields, the bondholder will not extend. Instead, bondholders reclaim the principal and invest at current yields. Bond types by characteristics 19 Floating-rate bonds Floating-rate bond has interest rate that is reset periodically according to some market rate. For example, the rate might adjust annually to the current T-bill rate plus 2%. So, the bond pays approx. current market rates. Major risk with floaters is that the rate does not adjust to the changes in firm’s financial conditions (only to general market conditions). Interest follows the market rates but investors might want to be compensated more for risk if the firm’s situation deteriorates. Bond types by characteristics 20 Preferred Stock Considered to be equity, but often included in the fixed-income universe Promises to pay fixed a specified cash flow stream Unlike bonds, failure to pay the promised dividend does not result in corporate bankruptcy Dividends owed simply cumulate and preferred stockholders rank higher than common stockholders (and below bondholders). Preferred stock commonly pays a fixed dividend (unless floating rate) Rarely gives holders full voting privileges in firm Unlike interest payments on bonds, dividends on preferred stock are not considered tax deductible expenses. Reduces their attractiveness as a source of capital to issuing firms. Most preferred stock is held by corporations; corporations pay half the tax on received preferred dividends. Bond types by characteristics 21 International bonds Bond types by characteristics 22 Innovation in the Bond Market Just to get a sense of potential: Inverse floaters: like floating-rate bonds, except coupon rate falls (/increases) when the general level of interest rates rises (/falls). Asset-backed Bonds: use income from a specified group of assets to service the debt. Catastrophe (CAT) Bonds: a form of insurance securitization. Investors in these bonds receive compensation in the form of higher coupon rates for taking on the risk. But in the event of a catastrophe, the bondholder will lose all or part of their investments. Bond types by characteristics 23 Indexed Bonds Indexed bonds make payments that are tied to a general price index or the price of a commodity Treasury Inflation Protected Securities (TIPS), e.g., 4% coupon rate. Par value adjusts so that the interest is always 4% in real terms. The interest on these bonds is a risk-free real rate. Bond types by characteristics 24 Credit Risk Credit risk 25 Credit risk Credit risk, or default risk, is the risk the bond will not make all promised payments. Rating companies Moody’s Investor Service, Standard & Poor’s, and Fitch Investor Service Rating categories Highest rating is AAA (or Aaa) o Investment grade bonds are rated BBB/Baa or above Speculative-grade/junk bonds are rated below BBB/Baa Junk bonds (high-yield bonds). Credit risk 26 Determinants of bond safety Coverage ratios Company earnings to fixed costs. Leverage ratios e.g., debt-to-equity Liquidity ratios Firm’s ability to pay bills coming due with its most liquid assets (current ratio and quick ratio) Profitability ratios Return on assets or capital employed Cash flow-to-debt ratio Credit risk 27 Bond indentures Contract between issuer and bondholder. Includes a set of restrictions protecting the bondholder (protective covenants). →Sinking funds: calls for the issuer to periodically repurchase some proportion of the outstanding bonds prior to maturity. →Subordination clauses: restrict the amount of additional borrowing by the firm. →Dividend restrictions: limit the payment of dividends by firms. →Collateral: a particular asset that the bondholders receive if the firm defaults. Credit risk 28 Credit spread To compensate for the possibility of default, corporate bods must offer a default premium (credit spread). Credit spread is the difference between the promised Yield-to- maturity (YTM) and the yield of an otherwise identical risk-free government bond. Credit risk 29 Bond Pricing Credit risk 30 Bond value The price an investor is willing to pay for a bond depends on the present value of the cash flows expected to be received by holding the bond. Cash flows from bonds: coupon payments + par value. So, Bond value = Present value of coupons + Present value of par value The discount rate r used to compute present value comprises of the: ✓ Risk-free rate ✓ Expected inflation premium ✓ Risk-premium Bond pricing 31 Bond pricing T – maturity date 𝑇 𝐶𝑜𝑢𝑝𝑜𝑛𝑡 𝑃𝑎𝑟 𝑣𝑎𝑙𝑢𝑒 𝐵𝑜𝑛𝑑 𝑃𝑟𝑖𝑐𝑒 = ෍ 𝑡 + (1 + 𝑟) (1 + 𝑟)𝑇 𝑡=1 Same coupon for Coupon x Annuity factor(r,T): the duration of the bond → present 1 1 Coupon ∗ ∗ (1 − 𝑇 ) value of an 𝑟 1+𝑟 annuity Bond pricing 32 Bond pricing example 1/2 An example (14.2 from main textbook) A bond has an 8% coupon rate, has a maturity of 30 years with a par value of $1,000, and pays coupons semi-annually. If the market interest rate is 8% annually (or 4% per six-month period), what is the value of the bond? Answer: This means 60 semi-annual coupon payments of $40 each and 4% interest rate per six-month period: 60 40 1,000 𝐵𝑜𝑛𝑑 𝑃𝑟𝑖𝑐𝑒 = ෍ 𝑡 + (1 + 0.04) (1 + 0,04)60 𝑡=1 Bond pricing 33 Bond pricing example 2/2 1 1 1 𝐵𝑜𝑛𝑑 𝑃𝑟𝑖𝑐𝑒 = Coupon ∗ ∗ 1 − 𝑇 + 𝑃𝑎𝑟 𝑉𝑎𝑙𝑢𝑒 ∗ 𝑇 𝑟 1+𝑟 1+𝑟 1 1 1 𝐵𝑜𝑛𝑑 𝑃𝑟𝑖𝑐𝑒 = 40 ∗ ∗ 1− 60 + 1,000 ∗ 60 0.04 1 + 0.04 1 + 0.04 𝐵𝑜𝑛𝑑 𝑃𝑟𝑖𝑐𝑒 = 904.94 + 95.06 = 1,000 The price in this case is equal to the par value. This is because the interest rate is the same as the coupon rate! Bond pricing 34 Relationship between price and interest rates The relationship between the bond price and the interest rate is convex. If the coupon rate is the same as the interest rate then the price is the same as par value (check!) We say then that the bond “trades at par”. Corporate bonds typically issued at par. Bond pricing 35 Bond Price sensitivity to Interest Rate changes The main source of price sensitivity of fixed-income securities is interest rate exposure. You tied your money earning 8% → market rates increase → LOSS! You could be earning more in an alternative higher-paying investment. The longer the period for which your money is tied up, the greater the loss and the greater the drop in bond prices. This can be also seen from the formula. At “larger” t, a given change in r will have a bigger effect on the price because of exponentiation. Bond pricing 36 Coupon rate and bond prices Coupon rate = market interest rate → Bond sells at par Coupon rate < market interest rate → Bond sells below par (at a discount) When the coupon rate is lower than the market interest rate, investors can get better returns from newly issued bonds that offer higher rates. As a result, the bond with the lower coupon becomes less attractive because it pays less in interest compared to the market. To compensate for the lower coupon rate, the bond's price must drop (sell at a discount). Coupon rate > market interest rate → Bond sells above par (at a premium) Bond pricing 37 Bond Profitability Measures Credit risk 38 Bond returns Total bond return refers to the overall return an investor earns from holding a bond over a certain period. It includes two main components: Income Component: The periodic coupon payments received from the bond. Capital Gains or Losses: The difference between the price at which the bond is purchased and the price at which it is sold or its face value at maturity. If you buy the bond at par, then the coupon rate is the return of the bond. Once the bond’s price changes, this is no longer true. How to measure bond profitability? Bond pricing 39 Current Yield One option: current yield – the bond’s annual coupon payment divided by its current price. E.g., the current yield of the 8% 30-year bond, which pays coupon semi-annually trading at 1,276.76 is: 80/1,276.76 = 6.27% Improves on the coupon rate in that it considers the current price. Simple measure but: Ignores capital gains/losses. Ignores reinvestment of interest. Does not consider the maturity of the bond. Bond pricing 40 Holding Period Return [𝐶𝑜𝑢𝑝𝑜𝑛 + (𝑃2 − 𝑃1 )] 𝐻𝑜𝑙𝑑𝑖𝑛𝑔 𝑝𝑒𝑟𝑖𝑜𝑑 𝑅𝑒𝑡𝑢𝑟𝑛 = 𝑃1 Holding period return reflects both the coupon payments and capital gains/losses. The return you earn if you buy the bond at the beginning of the period and sell at the end. But it still has some limitations: HPR is specific to the holding period chosen. Difficult to compare across different bonds with different holding periods/maturities. Retrospective: you need to know the future price to calculate it. Need for forecasts… Bond pricing 41 Yield-to-Maturity (YTM) Yield to maturity (YTM) is the interest rate that makes the present value of a bond’s payments equal to its price. Most commonly used measure of bond profitability (although it is a bit abstract). Interpreted as a measure of the average rate of return that will be earned on a bond if it is bought now and held until maturity assuming coupons are re-invested at the same rate. To calculate YTM, we solve the bond price equation for the interest rate given the bond’s price. Bond pricing 42 Yield-to-Maturity (YTM) Suppose an 8% coupon 30-year bond with par value $1,000, which pays coupons semi-annually, is selling at $1,276.76. What is the yield to maturity of this bond? →This bond has 60 semi-annual coupon payments remaining, and we want to find the interest rate (that is, r) that will make the present value of all remaining cash flows from the bond equal to the current price of the bond (that is, $1,276.76): 60 40 1,000 Solve for r 1,276.76 = ෍ 𝑡 + (1 + 𝑟) (1 + 𝑟)60 𝑡=1 Bond pricing 43 Yield-to-Maturity (YTM) 60 40 1,000 1,276.76 = ෍ + (1 + 𝑟)𝑡 (1 + 𝑟)60 𝑡=1 Bond pricing 44 Holding period return vs. YTM Yield to Maturity Holding period return Current Yield Average return if the Rate of return over a Ratio of income to the bond is held to particular investment current price. maturity. period. Depends on the market Depends on coupon Depends on the bond’s price at the particular rate, maturity, and price at the end of the time and the coupon. par value. holding period, an Does not include the All of these are unknown future value. capital gain/loss. readily observable. Can only be forecasted. Simple and observable. Bond pricing 45 Bond Prices Over Time Credit risk 46 Bond prices over time Price will converge to par at maturity. Why? Premium Bonds: Offer higher coupon payments but may incur a capital loss if purchased above par and held to maturity. Discount Bonds: Provide lower coupon payments but the potential for capital gains as the price rises to par at maturity. Conclusion: in theory, the contribution of the income and capital gain components might change, but the total expected return needs to be the same for bonds with the same 1) maturity and 2) risk profile fair rate of return in competitive markets. Bond pricing 47 Examples Suppose the bond’s current yield > YtM; is the bond’s price smaller or larger than par value? current coupon income rate is “higher” than the average rate of return after including capital gains/losses. So, the contribution of capital gains is negative, i.e., this bond trades at a premium. Consider a bond with a 10% annual coupon and yield to maturity =8%. If the bond’s YTM remains constant, then in one year, will the bond price be higher lower or unchanged? the price will be lower. The bond is currently at a premium. As time passes, the bond price needs to approach par. Bond pricing 48 Zero-coupon bonds Only one payment on the maturity date of the bond (no coupon payments). Sell at a discount from par value. US Treasury bills common example of short-term zero-coupon instruments. Investors’ return comes in the form of price appreciation. Longer-term zero-coupon bonds: What should happen to the price of zeros as time passes? On their maturity date, zeros sell at par. Before maturity, they sell at a discount because of the time value of money. Zero-coupon bonds 49 Zero-coupon bonds Price of zero-coupon bond: 𝑝𝑎𝑟 𝑣𝑎𝑙𝑢𝑒 𝑃= (1 + 𝑟)𝑛 r: interest rate n: number of years until maturity Zero-coupon bonds 50 Python – lists and for-loops Credit risk 51 Lists Definition: A list is a collection of elements, which can be of different data types, stored in a particular order. First data structure to store multiple elements! Properties: Ordered (and indexed!). Mutable (modifiable). Creating a list: new_list = Allows duplicates. [element1, element2,…] Lists 52 Accessing List Elements Access the n-th element by writing “list[n]”. Lists are indexed starting from 0. Negative indexing allows access from the end; e.g., “list[-1]” accesses the last element. You can also access slices of a list to get multiple elements; e.g., “list[1:3]” (elements “higher” than 1st and “not lower” than 3rd). Lists 53 Modifying Lists Adding elements: list.append(item) Inserting an item at a specified position: list.insert(index, item) Remove the first occurrence of an item: list.remove(item) Delete the element at index n: del list[n] Change the value of an element using its index: list = new_value Update multiple elements at once: list[1:3] = [“a”,”b”] Lists 54 For-Loops Iterating – “going through” each element of a set. For example, we have 1,000 Excel files and we want to import and run our program on each of them. Not a good idea to do it manually! We want to iterate through the 1,000 files, i.e., run one piece of code that will repeat the program for each of them. Programming solution: “for-loop” (and its cousin, the “while loop”.) For-loops 55 For-Loops A for loop allows us to repeat a block of code a certain number of times or over a collection of items. It's a way to automate repetitive tasks. variable: A name used to represent each item in the sequence. sequence: This could be a list, range, or other iterable (more on this later). Indented code inside the loop runs for each item in the sequence. For-loops 56 For-Loop Examples An object that you can iterate through is called an iterable. You can iterate through lists, or their subsets as they are also lists. Function range(N) creates a list from 0 to N-1. Very useful to define sequences like this rather than creating new variables. For-loops 57 Price a bond in Python 6 years maturity, $1,000 par value, 5% coupon. Market rate 3%. For-loops 58  Very useful trick. len(list) returns the length of a list, Price a bond in Python then range() of that creates an iterable. 6 years maturity, $1,000 par value, 5% coupon. Market rate 3%. Updating the value of bond_price in each iteration. “+=“ means “previous value +” For-loops 59