08/05/2022 21:02:00
Arthur Johnson
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Week 3 Lecture Notes
Applications of Finance – Fixed-Income Securities – Bonds
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Fixed-income securities are claims on a specified periodic stream of cash flows
o In contrast to equity, uncertainty about cash flows is minimal as long as the issuer of
the security is sufficiently creditworthy
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Equity vs. Debt
o Equity
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Proportional ownership
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Voting rights
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Residual claimant in capital structure
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Unlimited maturity
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Discretionary dividend
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Limited liability
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Unlimited upside potential
o Debt
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No ownership
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No voting rights
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Usually more senior claimant in the capital structure
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Often debt is secured on collateral
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Fixed maturity
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Receive interest (coupon)
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Limited upside potential
A bond is a security that is issued in connection with a borrowing arrangement
o The bond is the basic debt security
o The borrower issues (sells) a bond to the lender (creditors) for some amount of cash
o The issuer agreed to make specified payments to the bond holder on specified dates
o In sum, bonds are securitised loans – they may have fixed, variable or no regular
interest payments
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In a typical coupon bond, the issuer makes semi-annual payments of interest for the life of
the bond – these are called coupon payments
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o Then the bond matures, the issuer repays the debt by paying the bond’s par value
(equivalently, its face value)
o The coupon rate of the bond determines the interest payment – the coupon rate can
be zero
o The annual payment is the coupon rate times the bond’s par value
𝐴𝑛𝑛𝑢𝑎𝑙 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 = 𝐶𝑜𝑢𝑝𝑜𝑛 𝑅𝑎𝑡𝑒 × 𝑃𝑎𝑟 𝑉𝑎𝑙𝑢𝑒
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Bond issuers include:
o National governments
o Government agencies
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i.e., Federal National Mortgage Association
o State and local governments
o Supranational institutions
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i.e., European Bank for Reconstruction and Development
o Companies
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Treasury bonds are issued with maturities ranging from 10 to 30 years
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T-notes mature anywhere between 1 and 10 years
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T-bills have the shortest maturity terms – from four weeks to a year
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Bond types
o Callable bonds
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These allow the issuing company to pay off their debt early
o Puttable bonds
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These provide the holder of a bond (investor) the right, but not the
obligation, to force the issuer to redeem the bond before its maturity date
o Floating-rate bonds
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These make interest payments tied to some measure of current market rates
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For example, the rate might be adjusted annually to the current T-bill rate
plus 2%
o Convertible bonds
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These give the bondholders an option to exchange each bond for a specified
number of shares of common stock of the firm
o Preferred stock
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Although preferred stock, strictly speaking, is considered to be equity, it is
often included in the fixed-income universe
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This is because, like bond, preferred stock promises to pay a specified cash
flow stream
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However, unlike bonds, the failure to pay the promised dividend does not
result in corporate bankruptcy
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In the event of bankruptcy, preferred stockholders’ claims to the firm’s assets
have lower priority than those of bond holders, but higher than those of
common stockholders
o Foreign bonds
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These are issued by a borrower form a country other than the one in which
the bond if sold
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The bond is denominated in the currency of the country in which it is
marketed
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i.e., bonds sold in pounds in the UK from the US
o Eurobonds
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These are denominated in one currency, usually the issuer, but sold in other
national markets
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i.e., bonds sold in dollars in the UK from the US
A bonds coupon and principal repayments all occur months or years in the future
o Therefore, the price an investor is willing to pay for the bond depends on the value
of dollars to be received in the future compared to the dollars in hand today (present
value)
𝐵𝑜𝑛𝑑 𝑉𝑎𝑙𝑢𝑒 = 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐶𝑜𝑢𝑝𝑜𝑛𝑠 + 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑃𝑎𝑟 𝑉𝑎𝑙𝑢𝑒
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If we call the maturity date 𝑇 and call the interest rate 𝑟, the bond value can be written as:
"
𝐵𝑜𝑛𝑑 𝑉𝑎𝑙𝑢𝑒 = :
!#$
𝐶𝑜𝑢𝑝𝑜𝑛 𝑃𝑎𝑟 𝑉𝑎𝑙𝑢𝑒
+
(1 + 𝑟)!
(1 + 𝑟)"
o The coupon strean is an annuity and can be valued using the annuity formula
approach, namely:
"
:
!#$
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𝐶𝑜𝑢𝑝𝑜𝑛
1
1
=
𝐶𝑜𝑢𝑝𝑜𝑛
×
>1
−
@
(1 + 𝑟)!
(1 + 𝑟)"
𝑟
o Where 𝑇 is the number of periods to maturity and 𝑟 is the semi-annual discount rate
or the semi-annual yield to maturity
o As seen, there is an inverse relationship between price and yield (interest rate or 𝑟)
o This is a central feature of fixed-income securities
o This is because the interest rate fluctuations represent the main source of risk in the
fixed-income market
o The sensitivity of the bond price to the interest rate fluctuations depends on the
maturity of the bond
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The longer the maturity of the bond, the greater the sensitivity of price to fluctuations in the
interest rate
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The yield-to-maturity (YTM) is defined as the interest rate that makes the present value of a
bond’s payments equal to its price
o It is often 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
o To calculate the yield to maturity, we solve the bond price equation for the interest
rate given the bond’s price
o It can be interpreted as the compound rate of return over the life of the bond (under
the assumption that all bond coupons can be reinvested at that yield)
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Therefore, it is widely accepted as a proxy for average return
The financial press reports on an annualised basis which is called the bond equivalent yield
(BEY)
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When the coupon rate > interest (discount, yield) rate, price > par (premium bonds)
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When the coupon rate = interest (discount, yield) rate, price = par (premium bonds)
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When the coupon rate < interest (discount, yield) rate, price < par (premium bonds)
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Yield can be used as a measure of risk
o We need to discount the bonds cash flows at appropriate discount rate
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Reflects the opportunity cost of capital
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i.e., the return on similar risk investments that could be made today
o Because the yield to maturity is backed out of the current price, it gives us a sense of
how market participants view the risk of that particular bond
o If yields are increasing, it means that the market is discounting future cash flows more
heavily as a consequence of increased risk
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The dividend yield tells us how much income we get as a proportion of what we would have
to currently pay to buy the stock:
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑡 𝑌𝑖𝑒𝑙𝑑 =
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑
𝑆ℎ𝑎𝑟𝑒 𝑃𝑟𝑖𝑐𝑒
o The bond market equivalent of this measure is called the current yield
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑌𝑖𝑒𝑙𝑑 =
𝐴𝑛𝑛𝑢𝑎𝑙 𝑑𝑜𝑙𝑙𝑎𝑟 𝐶𝑜𝑢𝑝𝑜𝑛 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡
𝑃𝑟𝑖𝑐𝑒
o The current yield is a very simplistic proxy
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It only considers coupons (not principal repayment or capital gains
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Doesn’t discount future cash flows
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Thus, a measure known as the YTM addresses these concerns and is
ubiquitous in bond markets
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The yield curve is the graphical depiction of the relationship between the yield on bonds of
the same credit quality but different maturities
o The yield curve is usually constructed from observation of prices and yields
o A rising yield curve shows that bonds offering yields higher than those of short-term
bonds
o A downward-sloping yield curve shows long-term bonds offering yields lower than
those of short-term bonds
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A credit spread is the difference in yield between a US Treasury bond and another debt
security of the same maturity, but different credit quality
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Zero-coupon bonds are original-issue discount bonds
o They are less common that coupon bonds issued at par
o Zero-coupon bonds carry no coupons and provide all of their return in the form of
price appreciation
o More explicitly, zero-coupon bonds provide only one cash flow to their owners, on
the maturity date of the bond
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The top bond rating is AAA (SP, Fitch) or Aaa (Moody’s), a designation awarded to very few
firms
o Moody’s modifies each rating class with a 1,2, or 3 suffix (e.g., Aaa1, Aaa2, or Aaa3)
to provide a finer gradation of ratings
o Those rated BBB or Baa and above are considered investment-grade investments
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Lower-rated bonds are classified as speculative-grade bonds or junk bonds
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Defaults on low-grade issues are not uncommon
Bond rating agencies base their quality ratings largely on an analysis of the level and trend of
some of the issuer’s financial ratios
o The key ratios used to evaluate safety are:
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Coverage
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Leverage
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Ratio of company income to assets
Cash flow-to-debt
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Ratio of company current assets to current liability
Profitability
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Ratio of company debt to equity
Liquidity
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Ratios of company earnings to fixed cost
Ratio of total cash flow to outstanding debt