1. Bond Prices and Yields
Chapter 12

2. A. Introduction Review different types of bonds, how bonds are quoted
E.g., Globeinvestor  Market Data  Bond Data
Some bonds are listed on organized exchanges, but most bonds are traded over the counter by bond dealers (via a proprietary platform or via phone)
U.S. OTC Corporate bond transaction database: FINRA TRACE: OTC represents 90%+ of total activity
New trend: NYSE and London Stock Exchange
Compared to the stock market, bond market has greater liquidity risk (treasury bonds much more liquid than corporate bonds)
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3. Real Return Bonds Inflation-indexed bonds
Bonds with an inflation hedge
Principal/par value is indexed to the Consumer Price Index (CPI)
Fixed coupon rate (e.g., 4%) is applied to the inflation- indexed principal
Hence, cash flow is fixed in real terms, because coupons are protected against inflation as well
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4. Cash Flow: Real Return Bond (4% coupon)
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5. Product developed in the 1980s
Real Return Bonds
Product developed in the 1980s
Treasury Inflation-Protected Securities (TIPS) in U.S., Real-Return Bonds (RRB) in Canada
Also available in many countries, e.g., Sweden, Australia, the U.K., France.
Small investors can participate through a real- return bond mutual fund, or through an ETF
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6. Real Return Bonds
For each inflation-indexed bond, there is a “real yield” plus an inflation protection (both are quoted by broker). The real yield is a proxy for the real rate of interest
Hence, (nominal yield – real yield) is a proxy for the market’s inflation expectation
E.g. U.S. 10-year Treasury yield minus 10-year TIPs yield
1.92% % = 1.75%
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7. Bond Valuation Intrinsic value How do we estimate this value?
PV of expected future cash flow
Inputs
Stream of expected future cash flows
Timing and frequency of cash flows
Most popular frequency for coupons: semi-annual
Discount rate
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8. Bond Pricing
PB = price of the bond Ct = interest or coupon payments T = number of periods to maturity r = “appropriate” discount rate
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9. Numerical Example PB = $810.71
Annual coupon = 8% (semiannual payments)
Par value = Term = 30 years
r = 5% (semi-annual discount rate)
PB = $810.71
In Excel: =PRICE(DATE(2013,11,13),DATE(2043,11,13),0.08,0.10,100,2)
= $81.07
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10. Bond Prices and Yields
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11. Relationship between Bond Prices and Yields
Bond prices and yields have a nonlinear inverse (convex) relationship
Sensitivity of bond prices to yield changes varies along the curve
When yields approach zero, the value of the bond approaches the sum of the expected future cash flows from the bond
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12. Yield to Maturity (YTM)
Rate of return most often quoted for investors
Promised compound rate of return based on the current market price if:
bond is held to maturity
coupons are reinvested at the same rate
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13. Solve the bond pricing formula for YTM
YTM equates the PV of expected cash flow to the market price
~ internal rate of return concept
Solve the bond pricing formula for YTM
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14. YTM Example 10-year Maturity Coupon Rate = 7%
Par value = Price = $950
Solve for YTM:
Semiannual YTM = %
In Excel:
=YIELD(DATE(2013,11,12),DATE(2023,11,12),0.07,95,100,2)/2
divide by 2 for the semiannual YTM
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15. YTM, Coupon Rate, and Bond Prices (8% Coupon Bond)
Note: in the text, market interest rate is synonymous with YTM of the bond
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16. Price Paths of Coupon Bonds
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17. Converting to an Annual Yield
Bond Equivalent Yield 3.86% x 2 = 7.72% Effective Annual Yield (1.0386)2 - 1 = 7.88% Current Yield (Annual coupon / Market Price) $70 / $950 = 7.37 %
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18. HPR where C = coupon(s) received over the period
P1 = price at the end of the period
P0 = purchase price at the beginning of the period
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19. HPR example Coupon = 8% ; YTM = 8%; Term =10 years
Semiannual compounding; P0 = $1000
In 6 months, YTM falls to 7%
New price
=PRICE(DATE(2014,5,13),DATE(2023,11,13),0.08,0.07,100,2) =$
Semi-annual HPR = 10.85% over the six months
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20. Yield to Call (YTC) Bonds may have a call provision Purpose of a call?
Especially popular in the U.S.
Purpose of a call?
When interest rates fall, PV of scheduled payments rises. If this PV > call price, firm will call the bond
Refinance at a lower interest rate
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21. YTC (cont’d) In other words, price of callable bond is capped
Yield to call may be more relevant to investors, especially if market price is close to the call price

22. YTC (cont’d) where CD is the call date
Example: U.S. municipal bond (Massachusetts Port Authority):
Mass Port 5 ¼% 7/1/18 call
Note:
1% call premium over par
May be called on July 1, 2008 or after