Introduction to the Valuation of Debt Securities

Question 1

Valuation

Answer 1

the process of determining the fair value of a financial asset

Question 2

fundamental principle of financial asset valuation

Answer 2

its value is equal to the present value of its expected cash flows.

Question 3

valuing a financial asset steps

Answer 3

1. the expected cash flows must be estimated,
2. appropriate interest rates must be determined to discount the cash flows,
3. the present value of the expected cash flows is calculated

Question 4

Estimating cash flows

Answer 4

1. involves projecting the cash that is expected to be received in the future from an investment
2. can be difficult if the security has options such as callables, putables, or convertibles (risk of default)
3. the analysis must consider how future changes in interest rates and embedded option may affect cash flows

Question 5

cash flows of a fixed income security

Answer 5

are the collection of each period’s cash flow, which may be the interest income or payment of principal

Question 6

Future interest rate movements

Answer 6

the key factor in determining if the option will be exercised, and if they fall enough, the issuer/borrower may have an incentive to refinance.

Question 7

appropriate interest rate to discount cash flows

Answer 7

1. the yield available in the market on a default-free cash flow, which is the yield on a U.S. Treasury security
2. investors require a yield premium to reflect the added risks (non-government securities)
3. valued using an interest rate specific to its maturity, rather than a single interest rate

Question 8

final step in the valuation process

Answer 8

to value cash flows by discounting expected cash flows using the appropriate interest rate.

Question 9

The present value of a cash flow

Answer 9

1. depends on the timing of the cash flow and the interest rate (discount rate) used to calculate it.
2. value of a financial asset = add up the present values of all expected cash flows
3. PV = expected cash flow in period t/(1 + discount rate)^n
4. decreases as time elapses, making it important to use a suitable discount rate.
5. affected by the chosen discount rate, with higher rates leading to lower present values.

Question 10

A security’s value

Answer 10

1. determined by the present value of expected cash flows,
2. and inversely related to the discount rate;
3. a higher discount rate yields a lower security value, and vice versa

Question 11

option-free bond

Answer 11

1. The shape of the curve showing the inverse relationship between security value and discount rate is CONVEX;
2. it has implications for price volatility when interest rates change

Question 12

relationship between coupon rate, required market yield and price
relative to par value

Answer 12

1. when coupon rate > yield, price > par value (premium);
2. when coupon rate < yield, price < par value (discount);
3. when coupon rate = yield, price = par value

Question 13

Change in a Bond’s Value as it Moves Toward Maturity

Answer 13

1. its price will move to its par value
2. selling at a premium, its price declines as it moves towards
   maturity.
3. initially below the par value increases in price as it moves towards maturity.
4. changes due to both the change in the discount rate and cash flows as it moves towards maturity

Question 14

Decline of bond value due to an increase in discount rate

Answer 14

decomposed into two parts:
1. attributable to moving towards maturity and
2. increase in discount rate

Question 15

Valuation Using Multiple Discount Rates

Answer 15

The proper way to value the cash flows of a bond is to use a different discount rate that is unique to the time period in which a cash flow will be received

Question 16

Valuing Semiannual Cash Flows

Answer 16

For semiannual cash flows, simply adjust the coupon payments by dividing the annual coupon payment by 2 and adjust the discount rate by dividing the annual discount rate by 2.

Question 17

Valuing a Zero-Coupon Bond

Answer 17

For a zero-coupon bond, there is only one cash flow— the maturity value.

Question 18

Valuing a Bond Between Coupon Payments

Answer 18

1. When valuing a bond between coupon payments, the buyer pays the seller the present value of the cash flow, which includes accrued interest, which the buyer must compensate the seller for
2. price of the bond is computed using the present value calculations, including the accrued interest embodied in the full price, which is the amount the buyer pays.

Question 19

Computing the Full Price (Dirty Price)

Answer 19

1. The full price must be deducted by the accrued interest to determine the clean price of the bond
2. present value formula is modified to calculate the full price when a bond is purchased between coupons, using the fractional periods between the settlement date and the next coupon payment date.
3. the full price includes the accrued interest paid by the buyer to the seller

Question 20

Computing the Accrued Interest and the Clean Price

Answer 20

1. To calculate the clean price, the accrued interest must first be computed by subtracting the days between settlement and next coupon payment from the days in the coupon period
2. clean price is then calculated by multiplying the accrued interest by the semiannual coupon payment and subtracting it from the full price
3. Despite accruing interest, the buyer pays the seller the full price upfront.

Question 21

Day Count Conventions

Answer 21

1. The number of days in the numerator and denominator of the accrued interest formula is determined by the day count convention used in the bond market, which varies by security type
2. Treasury securities use the “actual/actual” day count convention between two coupon payment dates.
3. Settlement date is not counted when calculating the number of days between settlement and next coupon payment
4. Agency, municipal, and corporate bonds use the “30/360” day count convention, assuming each month has 30 days and 360 days in a year.

Question 22

TRADITIONAL APPROACH TO VALUATION

Answer 22

uses the 10-year Treasury rate as a discount rate for all bonds, while the arbitrage-free approach uses theoretical rate that Treasury would have to pay if it issued a zero-coupon bond with a maturity date equal to the cash flow.

Question 23

spot rate

Answer 23

1. also called theoretical rate
2. the interest rate used to discount a default-free cash flow with the same maturity.

Question 24

THE ARBITRAGE-FREE VALUATION APPROACH

Answer 24

1. The value of a bond based on spot rates
2. The law of one price implies that the price of an asset that can be
   synthetically created by a package of assets must be equal to the price of the package

Question 25

Valuation Using Treasury Spot Rates

Answer 25

1. The spot rate curve used to value a Treasury security can be used to obtain an arbitrage-free value based on the present value of each period’s cash flow
2. The sum of the present values of the cash flows is the arbitrage-free value of the security.

Question 26

Reason for Using Treasury Spot Rates

Answer 26

1. If market participants value a security using the yield for the on-the-run Treasury, the security will trade close to its arbitrage-free value
   1.1 Stripping and the Arbitrage-Free Valuation
   1.2

Question 27

Stripping and the Arbitrage-Free Valuation

Answer 27

1. A dealer has the ability to strip the cash flows of a Treasury coupon security and create zero-coupon securities that can be sold at the Treasury spot rates.
2. arbitrage-free approach is referred to as such because the value
   determined by using the Treasury spot rates does not allow for the
   generation of an arbitrage profit.
3. If the market price of a Treasury security is less than its value using the arbitrage-free valuation approach, a dealer can buy the security, strip it, and sell off the Treasury strips to generate greater proceeds than the cost of purchasing the security

Question 28

Reconstitution and Arbitrage-Free Valuation

Answer 28

1. When a Treasury issue’s market price is greater than the arbitrage-free value, dealers use reconstitution to purchase a package of Treasury strips and create a synthetic Treasury coupon security worth more than the same maturity and coupon Treasury issue
2. Reconstitution means to assemble Treasury strips in a way that creates a new whole (a Treasury coupon bond), unlike stripping a coupon bond.

Question 29

Credit Spreads and the Valuation of Non-Treasury Securities

Answer 29

1. Discounting the cash flows of non-Treasury securities using Treasury spot rates plus a constant credit spread can provide their theoretical value.
2. The valuation of debt securities is based on the spot rate, which is the yield to maturity for bond cash flows.
3. Credit spreads, which represent the additional yield required for a non-Treasury security, are added to the benchmark spot rate curve to obtain the total yield requirement for the security
4. Credit spreads vary depending on the credit rating and market sector, and increase with the maturity of the bond

Question 30

term structure for credit spreads

Answer 30

1. typically estimated for each credit rating and market sector, with lower credit ratings having steeper term structures

Question 31

benchmark spot rate curve

Answer 31

used to value securities with the same credit rating and market sector

Question 32

VALUATION MODELS

Answer 32

1. provide the fair value of a security. Two common approaches for simple securities without embedded options are:
   1.1 the arbitrage-free valuation approach and
   1.2 the spot yield curve approach
2. Securities with embedded options require more complex valuation models like the binomial model and the Monte Carlo simulation model.

Question 33

binomial model and the Monte Carlo simulation model.

Answer 33

1. These models handle interest rate path dependent securities like callable bonds, putable bonds, floating-rate notes, mortgage-backed securities, and asset-backed securities.
2. assume expected volatility of short-term interest rates, generate different interest rate paths or branches, and are calibrated to the Treasury market
3. The binomial model cannot value mortgage-backed securities and asset-backed securities.

Question 34

five features are common to the binomial and Monte Carlo simulation valuation models

Answer 34

1. Each model begins with the yields on the on-the-run Treasury securities and generates Treasury spot rates.
2. Each model makes an ASSUMPTION about the expected volatility of short-term interest rates
3. different ‘‘branches’’ of an interest rate tree (binomial model) and interest rate ‘‘paths’’ (Monte Carlo model) are generated.
4. The model is calibrated to the Treasury market
5. Rules are developed to determine when an issuer/borrower will exercise embedded options

Question 35

modeling risk

Answer 35

1. Users of valuation models are susceptible to modeling risk, or the risk that the model output is incorrect because the assumptions it’s based on are wrong.
2. To reduce modeling risk, it’s important to subject the results of a valuation model to stress tests by altering the assumptions used in the model