Chapter 9: Fixed Income (Bond Characteristics, Prices, Yields, and Risks)

What is a bond?

A security that is issued in connection with a borrowing arrangement

What is a borrowing arrangement?

Debt obligations of issuers (borrowers) to bondholders (creditors)

What does the borrower do?

Issues or sells a bond to the lender for some specified amount of cash

What is the Face or Par Value?

Principal repaid at maturity, typically $1000

What does the Coupon Rate determine?

The interest payment (“coupon payments”), typically paid semiannually

What is the coupon rate quoted as?

An APR

Wheat does the issuer pay?

Coupon payments over the life of the bond and the face value of the bond on the maturity date

What are the different types of bonds?

• Treasury Bonds

• Zero-Coupon Bonds

• Corporate Bonds

• Callable Bonds

• Floating-Rate Bonds

• International Bonds

• Convertible Bonds

What is the maturity structure of treasury bonds?

• Treasury Bill Maturity ≤ 1 year

• 1 < Treasury Note Maturity ≤ 10 years

• 10 < Treasury Bond Maturity ≤ 30 years

What types of treasury bonds pay coupons?

T-notes and T-bonds pay semiannual coupons

What are Zero-Coupon Bonds?

Make no coupon payments. Investors receive par value at the maturity date but receive no interest payments until then

Do zero-coupon bonds allow borrowing at zero-interest?

No

Where does investors return come from in zero-coupon bonds?

From the difference between issue price and the payment of par value at maturity

Should the price of the zero-coupon bond be more or less than its face value?

Less, otherwise you lose money

What is the price or intrinsic value of a bond?

The sum of its expected discounted cash flows

What do the cash flows for a bond consist of?

• Periodic coupon payments

• The par value (face value) at maturity

When is the periodicity of coupon payments defined?

At the bond’s issuance

What is the formula for the Price of a Bond?

P = Sum of C_t/(1+r)^t

What is the other formula for the price of a bond?

P = C/r [1 - 1/(1+n)ⁿ)] + M/(1+r)ⁿ

What is the formula for the price of a zero coupon bond?

P = M/(1+r)ⁿ

What are the risks associated with bonds?

• Interest-rate risk

• Reinvestment risk

• Inflation risk

• Call risk

• Default risk

• Liquidity risk

• Volatility risk

• Exchange-rate risk

• Political risk

• Sovereign risk

What is Interest Rate Risk?

Price of a typical bond will move in the opposite direction from a change in interest rates

What happens if interest rates rise?

The price of a bond will fall (vice versa)

If an investor has to sell a bond prior to the maturity date, what does an increase in interest rates mean?

The realization of a capital loss

Why does the relationship between prices and yields of bonds hold?

If a bond has a higher coupon rate relative to the market, investor’s want to buy, so price increases

What is the shape of the bond price curve?

Convex

What does it mean the longer the maturity?

The more sensitive the bond’s price to changes in market interest rates

What happened during the Silicon Valley Bank Crisis?

• Very successful in the post-Global Financial Crisis tech boom

• Money invested in LT bonds

• Fed started raising interest rates, so existing bonds decreased in value

• Higher interest rates dried up funding for tech companies

• Tech companies needed to withdraw money, and SVB was forced to sell bonds at a loss

• Bank run

What are the different ways of measuring and quoting Bond Yields?

• Yield to Maturity (YTM)

• Bond Equivalent Yield (BEY)

• Effective Annual Yield

• Current Yield

• Yield to Call

What is Yield to Maturity (YTM)?

Interest rate that makes the present value of the bond’s payments equal to its price (bond’s internal rate of return)

What does the YTM have the same periodicity as?

Coupon Payments

How do you solve for YTM?

Solve the bond price formula for r

What does YTM measure?

The average per period return from holding a bond until maturity

What is the YTM for a bond that pays coupons at different times?

• Once a year = annual rate

• Twice a year = 6-month rate

• Four times a year = 3-month rate

What is the Bond Equivalent Yield (BEY) always?

An annual rate

What is the BEY for a bond that pays coupons at different times?

• Once a year = YTM

• Twice a year = YTM*2

• Four times a year = YTM*4

If the BEY is equal to the coupon rate, then the bond sells at?

At par (price = face value)

If the BEY is greater than the coupon rate, then the bond sells at?

At a discount (price < face value)

If the BEY is less than the coupon rate, then the bond sells at?

At a premium (price > face value)

What is the formula for the Effective Annual Yield?

(1 + YTM)ⁿ - 1

What is the formula for the Current Yield?

Annual Coupon Amount/Bond Price

What happens to prices over time with a premium bond?

Prices converge to eventually go down (opposite for discount bond)

What does the price of callable bonds look like?

It’s flat over a range of low interest rates because the risk of repurchase or call is high

What is the risk of a call when interest rates are high?

Risk is negligible and the value of the straight and callable bond converge

What do we use to compute yield to call?

Compute the yield (average return) from holding the bond until the first possible call date

What is the Realized Yield?

The rate of return from holding the bond and reinvesting the coupons at the prevailing rate

What is the Realized Yield affected by?

The rate at which coupon payments are reinvested

If coupons are always reinvested at the YTM, then what is the realized yield equal to?

The YTM

Which way does YTM look vs. Realized Yield?

• YTM is forward looking

• Realized Yield is backward looking

How can we compare and contract YTM and HPR?

YTM:

• Average return if the bond is held to maturity

• Depends on coupon rate, maturity, and par value

• All of these are readily observable

• Can be computed before purchasing the bond

HPR:

• Rate of return over the particular investment period

• Depends on the bond’s price at the end of the holding period, an unknown future value

• Can only be forecasted or computed after selling bond

What are Corporate Bonds?

Corporations, like governments, will borrow through the issuance of bonfs

What is Preferred Stock?

Hybrid between a corporate bond and a stock

What is a Convertible Bond?

Can be exchanged for shares of the firm’s common stock

What is a Puttable Bond?

Give the bondholder an option to retire or extend the bond. The holder can demand early repayment of principal at pre-specified levels

What are Floating-Rate Bonds?

Have adjustable coupon rate

What are the characteristics of Preferred Stock?

• Dividends are paid in perpetuity

• Nonpayment of dividends does not mean bankruptcy

• Preferred dividends are paid before common

• No tax break

• Can be cumulative or noncumulative

What happens if preferred stock is cumulative?

• More expensive

• Missed dividends on that preferred stock will be paid out before any future common stock dividends

Why might an investor like a Convertible Bond?

Profit from the upside

Why might an issuer like a Convertible Bond?

Lower coupon payment than another one

If you were a bond purchaser, would you require a higher or lower yield on a convertible bond than a similar bond that was not convertible?

Accept lower yield because you have an option value

What is the Conversion Ratio?

Gives the number of shares for which each bond may be exchanged

What is the Conversion Value?

The market price of equity times the conversion ratio

What is the Conversion Premium?

Excess of the bond price over the conversion value

What is the convertible bond arbitrage?

An investment/trading strategy that involves trading the convertible bond and the associated firm’s stock to take advantage of relative mispricing between the two (takes into account the “embedded option” of a convertible bond)

What do Floating-Rate Bonds do?

Make interest payments that are tied to some measure of current market rates

What are the two categories of international bonds?

• Foreign Bonds

• Eurobonds

What is a Foreign Bond?

Issued by a borrower from a country other than the one in which the bond is sold

What is a Foreign Bond dominated in?

In the currency of the country in which it is marketed

What are the relationships of a Foreign Bond?

• US Company can access foreign capital markets

• European investors can obtain exposure to US without exchange rate risk

What are Eurobonds?

Bonds issued in the currency of one country but sold in other national markets

What does the Eurodollar market refer to?

Dollar-denominated bonds sold outside the U.S., with London being the biggest market for these bonds

What are the relationships of a Eurobond?

• U.S. company can obtain credit in Chinese Yen (or another country)

• U.S. investors can obtain exposure to another country’s economy

What is Default Risk (or Credit Risk)?

The possibility of the issuer defaulting on the payments of the bond

When does Default Risk happen?

When the issuer is unable to make timely principal and interest payments to the bondholders

What must bonds with default risk pay?

A higher coupon rate than treasuries (which are typically considered free of default risk)

Who provides measures of default risk?

Ratings companies

What are the ratings categories?

Highest rating is AAA or Aaa

What are Investment Grade bonds?

Rated BBB or Baa and above

What are High Yield/Speculative Grade/Junk Bonds?

Have ratings below BBB or Baa

Why can some firms issue debt at lower rates than others?

Ability to pay (credit risk or probability of default) differs across firms

When a firm becomes less creditworthy, then how should the price of their bonds react? Why?

Price should fall

How do we determine the creditworthiness of firms?

Evaluate firm fundamentals (use ratings)

When does the credit spread (difference in yields) between investment grade and high-yield bonds widen?

During crisis periods and recessions

What is a Credit Default Swap (CDS)?

An insurance contract that pays the holder of the swap in the event of a “credit event” (default of similar) in the reference entity firm (bond issuer)