Part 14. Intro to Fixed Income Valuation

Question 1

Relationship between price and yield:

Answer 1

1. A decrease (increase) in a bonds YTM will increase (decreases) its price.
2. If bond’s coupon rate is greater than YTM, its price will be at premium to par value, and less than YTM, its price will be at discount to par value.
3. The percentage decrease in value when YTM increases, by a given amount is smaller than increase in value when YTM decreases by same amount (price-yield relationship is convex).
4. All other things equal, the price of bond with lower coupon rate is more sensitive ti change in yield than price of bond with higher coupon rate.
5. All other things equal, price of bond with longer maturity is more sensitive to change in yield than price of bond with shorter maturity.

** calculated as if discount rate for every bond cash flow is the same.

Question 2

Constant-yield price trajectory

Answer 2

• this is a convergence to par value at maturity, as it shows how the bond’s price would change as time passes if its yield-to-maturity remained constant.

Question 3

Spot rates

Answer 3

• This is the market discount rates for a single payment to be received in the future, showing the reality of discount rates depending on the time period in which bond payment will be made.
• Discount rates for zero-coupon bonds are spot rates (zero coupon rates).
• to price a bond with spot rates, we sum PV of bonds payments each discounted at spot rate for the number of periods before it will be paid.

Question 4

No-arbitrage price (of bond)

Answer 4

• This is calculated using spot rates, as if a bond is priced differently there will be a profit opportunity from arbitrage among bonds.

Question 5

Full price of bond

Answer 5

• Coupon bond values calculated on date a coupon is paid, as PV of remaining coupons, but for most bond trades, the settlement date is when cash is exchanged for bond will fall between coupon dates.
• As time passes (future coupon payment dates get closer), the value of bond will increase.
• the value of bond between coupon dates can be calculated using its current YTM, as value of bond on its last coupon dated (PV) x (1+ YTM/#of coupon periods per year)^t/T, for a given settlement date.

t = no. of days since last coupon payment
T = no. of days in coupon period

Question 6

Max pricing

Answer 6

The method of estimating the required yield to maturity (or price) of bonds that are currently not traded.

• procedure is to use YTMs of traded bonds that have credit quality close to nontraded or infrequently traded bond similar in maturity and coupon, to estimate required YTM.

Question 7

Variation of matrix pricing

Answer 7

• This is used for pricing new bond issues focuses on spreads between bond yields and yields of a benchmark bond of similar maturity that is essentially default risk free.
• yields on Treasury bonds are used as benchmark yields for US dollar denominated corporate bonds.
• estimating YTM for new issue bond, the appropriate spread to yield of Treasury bond of same maturity is estimated and added to yield of benchmark issue.

Question 8

Periodicity of bond

Answer 8

The number of bond coupon payments per year.

A bond with a periodicity of 2 will have its yield to maturity, quoted on semi annual bond basis.

For a given coupon rate, the greater periodicity, the more compounding periods and the greater the annual yield.

Question 9

Street convention

Answer 9

• bond yields calculated using stated coupon payment dates.

Question 10

True yield

Answer 10

As coupon dates fall on weekends and holidays, coupon payments will actually be made next business date, this is the yield calculated using these actual coupon payment dates.

Some coupon payments will be made later when holidays and weekends are taken into account, so true yields will be slightly lower than street convention yields, only by few basis points.

Question 11

Current yield

Answer 11

This measure looks at just one source of return; a bonds annual interest income, not considering capital gains/losses or reinvestment income.

Question 12

Simple yield

Answer 12

This takes discount or premium into account by assuming that any discount or premium declines evenly over remaining years to maturity.

Simple yield = sum of annual coupon payments plus (minus) SL amortisation of a discount (premium) divided by flat price.

Question 13

Callable bond yields

Answer 13

• The investors yield will depend on whether and when bond is called.

yield to call = calculated for each possible call date and price.

yield-to-worst = the lowest of yield-to-maturity and the various yields-to-call.

Question 14

Option adjusted yield

Answer 14

This is calculated by adding value of call option to bonds current flat price,

The value of callable bond = value of bond without call option - value of call option (issuer owns call option).

This value will be < yield to maturity for callable bond as they have higher yields to compensate holders for issuers call option.

This can be used to compare yields of bonds with various embedded option to each other and similar option-free bonds.

Question 15

Floating rate note yields

Answer 15

• if issued by company that has more (less) credit risk than banks quoting LIBOR, the margin added to (subtracted from) LIBOR, the RR, with its liquidity and tax treatment also affecting margin.
• quoted margin = margin used to calculate bond coupon payments.
• required margin = the margin required to return the FRN to its par value.
• credit quality of FRN is unchanged, the QM = RM, and FRM returns to its par value at each reset date when next coupon payment is reset to current market rate (+/- appropriate margin).
• if credit quality of issuer decreases, QM RM and FRN will sell at premium to its par value.
• simplified calculation of the value of FRN on a reset date is to use the current RR plus QM to estimate the future cash flows for FRN, and discount future cash flows at RR plus R(discount)M.

Question 16

Money market securities yields

Answer 16

This can be stated as discount from face value or as add-on yields, based on 360 day or 365 day basis.

US Treasury bills quoted as annualised discounts from face value based on 360 day year.

LIBOR and bank CD quoted as add on yields.

we need to be able to:

1. Calculate actual payment on MMS given its yield and knowledge of how yield was calculated.
2. Compare the yields on two securities quoted on different yield bases.

Question 17

Yield curve

Answer 17

• This shows yields at maturity.
• Constructed for yields of various types and important to understand which yield is being shown.
• term structure = of IR, yields at different maturities (terms) for like securities or interest rates.

Question 18

Spot rate yield curve

Answer 18

• the appropriate yields and hence discount rates for single payments to be made in the future.
• we calculated value for bond by discounting each separate payment by spot rate corresponding to time until payment will be received.
• usually quoted on semi annual bond basis, so directly comparable to YTMs quoted for coupon government bonds.

Question 19

Yield curve for coupon bonds

Answer 19

• This shows the YTMs for coupon bonds at various maturities.
• yields are calculated for several maturities and yields for bonds with maturities between these are estimated by linear interpolation.
• yields expressed in semi annual bond basis.

Question 20

Par bond yield curve

Answer 20

This is not calculated from yields on actual bonds but constructed from spot curve.

This yield reflects the coupon rate that a hypothetical bond at each maturity would need to have to be priced at par.

Alt. considered as YTM of a par bond at each maturity.

Question 21

Forward rates

Answer 21

• These are yields for future periods.
• The rate of interest on 1 year loan that would be made 2 years from now.

forward yield curve = this shows future rates for bonds or MMS for the same maturities for annual periods in the future.

• a typical forward curve would show yields of 1 year securities for each future year, quoted on semi annual bond basis.

Question 22

Yield spread

Answer 22

• The difference between the yields of two different bonds, typically quoted in basis points.

Question 23

Benchmark spread

Answer 23

• A yield spread relative to benchmark bond.
  e. g. if 5 year corporate bond has yields of 6.25% and benchmark, the 5 year Treasury note has yield of 3.5%, the corporate bond has benchmark spread of 625 - 350 = 275 bp.
• floating rate securities use LIBOR as benchmark rate.

Question 24

G-spread

Answer 24

• for fixed coupon bonds, on-the-run government bond yields for same or nearest maturity frequently used as benchmarks.
• this benchmark may change during bonds life, for 5 year corporate bond, when issued, the benchmark spread is stated relative to 5 year government bond yields, but 2 years later ( when it has 3 years remain to mature).
• its benchmark spread will be stated relative to 3 year government bon yields, where this is yield spread over government bond.

Question 25

Interpolated spreads/ I-spreads

Answer 25

• an alt. to using government bond yields as benchmarks is to use rates for interest rate swaps in same currency, with same tenor as bond.
• this is yields spreads relative to swap rates, with i-spreads frequently stated for bonds denominated in euros.

Question 26

Uses of yield spreads

Answer 26

• for analysing factors that affect bond’s yield, for CB yields increases from 6.25% to 6.50%, this may be caused by factors affect all bond yields, or by firm specific/industry specific factors.
• if bond yield increases, but yield spread remains the same, yield on benchmark must also increase, suggesting macroeconomic factors caused bond yields in general to increase.
• if yield spread increases, this suggests increases in bonds yield caused by microeconomic factors such as credit risk or issues liquidity.

Question 27

Disadvantages of G-spreads & I-spreads:

Answer 27

• They are theoretically correct only if spot yield curve is flat so yields are approx. the same across maturities.
• normally spot yield curve is upward sloping (i.e. LT yields are higher than ST yields).

Question 28

Zero volatility spread/Z-spread

Answer 28

• for deriving bonds yield spread to a benchmark spot yield curve that accounts for the shape of the yield curve is to add an equal amount to each benchmark spot rate and value bond with those rates.
• we find an amount which when added to benchmark spot rates produces a value equal to market price of the bond, we have the appropriate yield curve spread.

Question 29

Option adjusted spread (OAS)

Answer 29

• This is used for bonds with embedded options, and takes option yield component out of Z-spread measure.
• The government spot rate curve that the bond would have if it were option-free.
• if we calculated an OAS for callable bond, it will be less than bonds Z-spread.
• option value = the extra yield, where the difference in extra yield required to compensate bondholders for call option.