Bonds Flashcards
Describe a bond?
(1) Holder: entitlement to set of fixed cash payments
(2) Borrower: obligation to pay set of fixed cash payments
(3) Regular interest payments, “coupons” (C),
(4) Face value (F), “principal” (aka “par value”) paid at maturity, T
What is “yield to maturity”?
“Yield to maturity” (YTM or yield) and is the return demanded by investors to hold the bond
Why is the bonds face value might be worth less today?
(1) Prices adjust through supply and demand -> yield comes from the opportunity costs
(2) Incorporates:
- >Real compensation for deferred consumption (e.g., apartment)
- > Expected inflation
- >Risk premium (interest rate risk, default, liquidity)
What are sources of dollar return for bond investors?
(i) the periodic coupon interest payments made by the issuer,
(ii) any capital gain (or capital loss—negative dollar return) when the bond matures (F-P), is called, or is sold, and
(iii) interest income generated from reinvestment of the periodic cash flows
What is the difference between Yield to maturity and coupon rate?
Yield to maturity (YTM), r, is what an investor earns buying a bond at the current market price and holding it to maturity (assuming coupon payments are reinvested at the yield)
– It is also the internal rate of return (IRR, or ‘discount rate’) that equates the bond’s discounted cash flows with its price
-> Takes into account (i) coupon interest + reinvestment of coupons, and (ii) capital gain (or loss)
Coupon rate, c, is the coupon divided by the face value,
-> Does not consider capital gain, and therefore can (and usually will) differ from yield to maturity
Yield and price relationship?
When:
– r > c then PF and bond trades at “premium” (might be willing to pay more if other opportunities give less return -> invest until it gives the same amount of return as other opportunities)
– r=c then P=F and bond trades at “par”
What happens to bond prices through time?
Clean prices converge to F as t -> T
Effective vs. stated rates
Effective annual rates (EAR) allow comparison between stated annual rates (SAR) (a.k.a. Annual Percentage Rate (APR)) of different compounding frequencies
Name three general principles of pricing bonds
- The cash flows cannot be changed so the interest rate has to be adapted to the cash flows
- The cash flow frequency defines the compounding frequency as each cash flow can be reinvested to earn interest on interest
- Thus the interest rate should be expressed so that its compounding matches the cash flow frequency, from which we get the effective rate per cash flow period
What is the indenture?
A written agreement between the corporation (borrower) and the lender (bondholder), a.k.a. deed of trust, containing terms and features of the debt, e.g.:
Describe features of bonds (maturity, form, security, seniority)
• Maturity
– “note” generally <10 years to maturity when issued – “bond” generally >10 years to maturity when issued
• Form
– “registered”: company maintains record of ownership and automatically makes payments
– “bearer”: certificate is evidence of ownership, request payments
• Security
– “secured”: assets pledged as collateral, in default collateral is possessed by lender
– “unsecured”: no collateral pledged, in default claim is to assets not pledged
• Seniority
– “senior” and “junior” or “senior” and “subordinated”: priority of claims
• Call provisions
• Repayment
– At maturity
– Before maturity (part)
What are call provisions?
– Allows company to repurchase (“call”) part or all of the bond issue at specified prices/times
– Used to refinance debt
– Deferred call provisions
– “Make-whole” call provisions: a guaranteed rate at which PV calculated when called
What is a Sinking fund?
Sinking fund: trustee account into which company makes annual payments to retire portions of debt
What are Protective covenants?
Limitations on company actions during life of bonds
– e.g., dividends, pledges of assets, mergers, additional debt, working capital requirements, financial statements
What is a Convertible bond?
– Allow holder to exchange bond for the company’s stock at conversion ratio
Risks associated with investing in bonds
Interest rate risk
– If an investor has to sell a bond prior to the maturity date, an increase in interest rates will mean the realisation of a capital loss
– Interest rate fluctuations cause systematic variation in bond prices (we will discuss measures of this risk in the next lecture)
– The major risk faced by a bond investor (in normal times)
Reinvestment risk
– Risk that the interest rate at which interim cash flows can be reinvested will fall; greater for longer holding periods and high- coupon bonds
– Offsets interest rate risk to a certain extent
Call risk
– Risk that a callable bond will be called when interest rates fall
Credit risk (default risk) – Risk that the issuer of a bond will fail to satisfy the terms of the obligation with respect to the timely payment of interest and repayment of the amount borrowed – Downgrade risk is the risk of a downgrade in credit rating which can lead to capital losses as yield rises (i.e., a form of idiosyncratic interest rate risk)
Liquidity risk
– Bond investor may not be able to sell a bond quickly at or near its value
Exchange rate risk
– If bond is denominated in a different currency
What is Securitization?
Securitization is a process that involves:
– (i) Pooling assets (e.g., loans, bonds), then
– (ii) Selling packages of cash flows with different ‘priorities’, backed by the asset pool
What is Tranching?
Tranching: (a.k.a. credit enhancement) using seniority to split off “tranches” of CDOs with different levels of risk and therefore different credit ratings:
– Principal and interest are paid in order of seniority.
– If the underlying asset pool becomes insufficient to make payments on the securities (e.g., when underlying loans default), the loss is absorbed first by the subordinated tranches, and the upper-level tranches remain unaffected until the losses exceed the entire amount of the subordinated tranches.
– Used to, e.g., sell bundles of subprime mortgages to pension funds
Dangers of CDOs:
- Pricing is VERY sensitive to key underlying parameter
estimates, particularly default correlation
– Default correlation is difficult to estimate, particularly because defaults are rare, and is NOT constant through time
– CDO-squared (and higher orders) are particularly sensitive to errors in parameters potential for substantial mispricing of risk - CDOs have high proportion of systematic risk compared
to single name corporate bonds of equal credit rating
– Neglectingthisfact,theiryieldslookedveryattractivehigh demand strong pressure on banks to lend more so that more CDOs could be createdirresponsible lending
– Credit ratings may have been misleading because (i) they did not distinguish systematic vs idiosyncratic, (ii) naively extrapolated parameters from good market conditions
What is a Repo?
A repurchase agreement (repo) is a form of short-term borrowing for dealers in government securities. In the case of a repo, a dealer sells government securities to investors, usually on an overnight basis, and buys them back the following day at a slightly higher price. That small difference in price is the implicit overnight interest rate. Repos are typically used to raise short-term capital. They are also a common tool of central bank open market operations.
Why repos are needed?
– Maybe someone needed the cash to speculate on Nasdaq OMX Riga stocks
– Maybe someone had excess cash and wanted a safe investment that pays interest
– Maybe someone thought someone could sell my LV bond today and buy a similar one for cheaper in a year’s time before returning it to me
What is Interest rate risk?
Interest rate risk is the sensitivity of the bond’s price to changes in yields
How to measure interest rate risk?
Duration is a measure of the sensitivity of the price of a bond or other debt instrument to a change in interest rates. A bond’s duration is easily confused with its term or time to maturity because they are both measured in years. However, a bond’s term is a linear measure of the years until repayment of principal is due; it does not change with the interest rate environment. Duration, on the other hand is non-linear and accelerates as time to maturity lessens.
What is modified duration?
Modified duration is the percentage change in bond price
per change in yield:
- > Also known as bond “volatility”
- > Useful to calculate price changes in response to small parallel changes in interest rates
What is dollar duration?
Dollar duration is the dollar change in price for a change
in yield
What is Effective duration?
Callable bonds and bonds with embedded options (e.g., convertibles) are difficult to analyze with Macaulay’s or modified duration because future cash flows are no longer known.
-> By definition effective duration is equal to the proportional change in bond price for a unit change in market interest rates
Characteristics of duration
- Duration of zero-coupon bond is time to maturity, T
- Ceteris paribus, higher coupons => lower duration
- Ceteris paribus, longer maturity => higher duration
- Ceteris paribus, higher yield => lower duration
- For bonds – duration is always between 0 and T
What is convexity?
Think of convexity as an “adjustment” for the error made by duration in approximating the price-yield curve
• Convexity => larger price increases when rates fall and smaller price declines when rates rise
Duration and convexity of a callable bond
When interest rates are high, probability of call is low and curve is as per a non-callable bond
-> in this region duration and convexity unaffected by call option
As rates fall, price approaches the limiting call price and convexity becomes negative
-> convexity and duration of callable bond are less than or equal to those of non-callable bond equivalent
