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Coupon Structures: 1. Zero-coupon bonds & 2. Accrual Bonds

Coupon structures:
1. Zero-coupon bonds - do not pay periodic interest or carry coupons
- sold at a deep discount from their par values.
- market convention dictates that semi-annual compounding should be used when pricing zero-coupon bonds.

2. Accrual Bonds - similar to zero-coupon bonds, BUT are sold originally @ Par Value.
- have a stated coupon rate
- but the coupon builds up at a compounded rate until maturity

Coupon Structures: 3. Step-up Notes & 4. Deferred Coupon Bonds

3. Step-up notes have coupon rates that increase over time at a specified rate.

4. Deferred-coupon bonds carry coupons, but the initial coupon payments are deferred for some period.
- at the end of deferral period, the accrued (compound) interest is paid, and the bonds then make regular coupon payments until maturity.

Floating rate securities

Floating (variable) rate securities - make varying coupon interest pmts which are set based on a specified interest rate or index (i.e. LIBOR) using the specified coupon formula

new coupon rate = reference rate ± quoted margin

Limits on Floating rate securities

Upper and Lower limits on Floating rate securities:

Upper limit = cap = max interest rate paid by the borrower; limits upside potential so disadvantage to bondholder
Lower limit = floor = min interest rate received by the lender; limits how low the rate could go, so disadvantage to the issuer.

Bond with both upper and lower limit → "collar"

Bond Valuation Process: 3 steps

Bond Valuation Process:
1. Estimate the CFs over life of security (both coupon pmts & principal)
2. Determine appropriate discount rate based on risk associated with estimated CFs
3. Calculate the PV of estimated CF

3 Difficulties in estimating Expected CFs

3 Difficulties in estimating expected CFs:
1. Timing of principal repayments is NOT known with certainty
2. Coupon pmts are NOT known with certainty
3. Bond = covertible or exchangeable into another security

Bond Prices can be expressed as..

Bond prices, established in the market, can be expressed as:
1. % of par value
2. Yield (YTM)

YTM for annual pay bonds =

Bonds that make annual payments:
Yield to maturity (YTM) is the ANNUAL discount rate that will make the PV of bond's promised ANNUAL CFs = Market Price

YTM (annual pay) = [ 1 + (YTM semi-annual / 2) ]² - 1

YTM for semi-annual pay bonds =

Bonds that make semi-annual payments:
Yield to maturity = 2 x Semiannual discount rate that will make the PV of semiannual coupon pmts = Market Price

YTM for a semi-annual pay bond = BEY

YTM (semi-annual pay) = 2 x [ (1 + YTM semi-annual /2)² - 1 ]

Relationship between semi-annual YTM (or a BEY) and Price for a bond with N years to maturity =

Bond Price = CPN₁ / (1 + YTM/2)
+ CPN₂ / (1 + YTM/2)²
+ CPN₃ / (1 + YTM/2)³ ......
+ CPN + Par Value / (1 + YTM/2)²ⁿ

Zero-coupon Bond Price & YTM =

Zero-coupon Bond Price = Face Value / [ 1 + (YTM/2) ]²ⁿ

Zero-coupon YTM = 2 x [ (face value/Price)¹/²ⁿ - 1 ]

Price-Yield relationship for a coupon-bond with N years to maturity is based on semi-annual YTM (or BEY by convention)

Bondholder will actually realize the YTM on his initial investment only if..

Bondholder will actually realize the YTM on his initial investment only if
(1) all payments are made as scheduled and
(2) bond is held to maturity and
(3) all interim CFs are reinvested @ YTM

Par-Yield Curve

Par Yield curve plots YTM vs. Bond Maturity
and is constructed with the YTMs for bonds trading @ par value

Spot Rates

Spot Rates are market discount rates for single payments to be received in the future and can be thought of, theoretically, as discount rates ≈ to market yields on zero-coupon bonds.

Given the spot-rate yield curve, we can discount each of a bond's promised CF @ its appropriate spot rate. Sum the resulting PVs = market value (Price) of bond.

Stripping the bond

Govt bond dealers can separate T bonds into their "pieces", with the individual coupon and principal CFs.
- individual pieces are a series of zero-coupon bonds with different maturity dates.
- each piece can be valued by discounting @ the spot rate for the appropriate maturity

Recombining Bonds

Since bond dealers can also recombine a bond's individual cash flows into a bond, arbitrage prevents the market P of the bond from being more or less than the value of the individual cash flows discounted at spot rates.
Spot rate = no-arbitrage values

Spot rate > Market P

If the spot rate (no-arbitrage value) > market P:
a bond dealer can BUY the bond, strip it and sell the pieces to earn an arbitrage profit.

Market P > Spot rate

If Market P of bond > Spot rate (no-arbitrage value),
a bond dealer can BUY the pieces, combine them into a bond, and sell the bond to make a profit.

Nominal Yield spreads measure

Nominal yield spreads measure the difference between the market yields on 2 bonds.

Yield spreads are caused by:

Yield spreads are caused by differences in:
1. Credit quality
2. Call features
3. Tax treatments
4. Maturity

Absolute Yield Spread =

Absolute Yield Spread = Higher Yield - Lower Yield

Absolute yield spread quantifies the difference between nominal yields on two bonds or two types of bonds.
- typically this yield spread is calculated between a non-Treasury security and a benchmark Treasury security.

Relative Yield Spread =

Relative Yield Spread = [ Higher Yield / Lower Yield ] - 1

Quantifies the absolute spread as a % of the lower yield

Yield ratio =

Yield Ratio = HIgher Yield / Lower Yield

Credit Spread refers to the difference...

Credit spread refers to the difference in yield between two issues that are identical in ALL respects EXCEPT their credit ratings.
- credit spreads are a function of the state of the economy
Economic expansions → credit spreads ↓ as corporations are expected to have stronger cash flows
Recessions/Contractions → credit spreads ↑ since cash flows are pressured and there is a ↑ probability of default.

Sources of Bond Return

Sources of bond return -
(1) periodic coupon interest payments
(2) recovery of principal, (and any capital gain and loss)
(3) Reinvestment income

Current Yield =

Current Yield = Annual Coupon Payment / Bond Price

CY is based on actual cash received during the investment horizon and is typically composed of dividends and interest.

YTC computation

- calculated similarly to YTM. Both are essentially internal rate of return measures.
N = # of semi-annual periods until the call date under consideration
FV = call Price (replaces maturity value)

Key to YTC computations is using the right # of periods (to first call) and the appropriate terminal value (the call price)
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Accrued Interest

Accrued interest is the interest earned since the last coupon payment date and is paid by a bond buyer to a bond seller.

Clean Price vs. Full Price

Clean price is the quoted price of the bond without accrued interest.

Full price refers to the quoted price + accrued interest

Callable but non-refundable bonds

Callable but non-refundable bonds can be called prior to maturity, but their redemption cannot be funded by the issuance of bonds with a lower coupon rate.

Affirmative vs. Negative Covenants in Bond Indentures

Affirmative covenants - what borrower/issuer MUST perform.

Negative covenants - what borrower/issuer CANNOT do. .

A bond's indenture contains the obligations, rights and any options available to the issuer or buyer of a bond.

Which statement is LEAST accurate?
a) With zero-coupon bonds, investors have NO reinvestment risk
b) Graph of current corporate bond yields = spot yield curve
c) YTM on a zero-coupon bond is called spot interest rate

Least accurate: b) Graph of current corporate yields ≠ spot yield curve.
- The graph of yields on zero-coupon bonds (spot rates) is called the spot yield curve.
- Note: Return on zero-coupon bonds is based entirely on price appreciation.
- An investor in a default-free zero-coupon bond will NOT have to worry about reinvesting coupons to realize the YTM.

When a bond is trading "ex-coupon", what price does the buyer pay to the seller?

When a bond is trading "ex-coupon", the buyer will pay the CLEAN PRICE to the seller (or the price without accrued interest ~ the quoted price).

When a bond is trading "cum-coupon", the buyer will pay the DIRTY PRICE or full price to the seller.

If the issuer of a bond is in default, the bond will be trading...

If an issuer of a bond is in default (i.e. it has not been making periodic contractual coupon payments), the bond is traded WITHOUT accrued interest and is said to trade "FLAT".

Non-refundable bonds may be called, as along as...

Non-refundable bonds may be called as long as the firm does NOT use less expensive debt to do so. They may be refunded without outside capital (new debt or equity issues), just NOT cheaper debt

Regular redemption prices vs. Special redemption prices for callable bonds

Regular redemption price (can be at premium or at par) refers to bonds being called according to the provisions specified in the bond indenture.

When bonds are redeemed to comply with a sinking fund provision or because of a property sale mandated by govt authority, the redemption prices (typically par value) are referred to as "special redemption prices".
There is NO such thing as "specific redemption price".

The refunding provision found in nonrefundable bonds allows bonds to be retired UNLESS:
a) funds comes from a lower cost bond issue
b) funds come from the sale of a new common stock
c) market interest rates have increased substantially

(A) Refunding from a new debt issue at a higher interest rate is not prohibited, however their purchase cannot be funded by the simultaneous issuance of lower coupon bonds.

True/False: An investor concerned about premature redemption is indifferent between a noncallable bond and a nonrefundable bond.

False! The term "refunding" specifically means redeeming a bond with funds raised from a new bond issued at a lower coupon rate.
Even a sinking fund is a type of redemption, which refers to the retirement of bonds.
An investor concerned with "premature redemption" would prefer a noncallable bond because a noncallable bond cannot be called for ANY reason.
A bond that is callable, but nonrefundable can be called for any reason OTHER than refunding.
A nonrefundable bond can be redeemed with funds from operations or a new equity issue.

Retiring funds via sinking fund vs. accelerated sinking fund

A sinking fund actually retires the bonds based on a schedule.
- accomplished through either a) payment of cash or b) delivery of securities
An accelerated sinking fund provision allows the company to retire more than is stipulated in the indenture.

Which of the following is LEAST LIKELY an amortizing security:
a) Coupon Treasury Bonds
b) Bonds with sinking fund provisions
c) Mortgage-backed securities (MBS)

A) Coupon Treasury Bonds ≠ amortizing security
Coupon Treasury bonds and most corporate bonds are non-amortizing securities because they pay only interest until maturity. At maturity, these bonds repay the entire par value or face value.
MBS is backed by pools of loans that generally have a schedule or partial principal payments, making these "amortizing securities".
A sinking fund provision is another example of an amortizing feature of a bond. This feature is designed to pay a part of the entire total of the issue by the maturity date.

Characteristics and examples of embedded options that benefit the issuer

Embedded options that benefit the issuer
- ↓ bond value
- ↑ bond yield
to a bond buyer.
- Call Provisions
- Accelerated Sinking Fund Provisions
- Caps (maximum interest rates) on floating rate bonds

Characteristics and examples of embedded options that benefit the bondholders

Embedded options that benefit the bondholder:
- ↑ bond value
- ↓ bond yield
to a bond buyer.
- Conversion options (the option of bondholders to convert their bonds into shares of the bond issuer's common stock)
- Put options (option of bondholders to return their bonds to the issuer at a predetermined price). Even if the put is out of money, it still has value to the bondholder.
- Floors (minimum interest rates) on floating rate bonds.

What are two ways institutions can finance secondary market bond purchases?

Institutions can finance secondary market bond purchases by
a) margin buying (borrowing some of the purchase price, using the securities as collateral) OR
b) repurchase agreements (repo) - an arrangement in which the institution sells a security with a promise to buy it back at an agreed-upon higher price @ a specified date in the future.
- repo agreements are more commonly used.

Risks associated with fixed income securities: Interest rate risk

Interest rate risk - uncertainty about bond prices due to changes in market interest rates
- probability of an ↑ in interest rates causing a bond's price ↓

Risks associated with fixed income securities: Call Risk

Call Risk - the risk that a bond will be called (redeemed) prior to maturity under the terms of the call provision and that the funds must then be reinvested at the then-current (lower) yield

Risks associated with fixed income securities: Prepayment Risk

Prepayment risk - the uncertainty about the amount of bond principal that will be repaid prior to maturity.

Risks associated with fixed income securities: Yield Curve Risk

Yield curve risk - the risk that changes in the shape of the yield curve will reduce bond values

Risks associated with fixed income securities: Credit Risk

Credit Risk - includes
- the risk of default
- the risk of a ↓ in bond value due to a ratings downgrade
- the risk that the credit spread ↑ for a particular rating

Risks associated with fixed income securities: Liquidity Risk

Liquidity risk - the risk that an immediate sale will result in a price < fair value price (or the prevailing market price)

Risks associated with fixed income securities: Exchange Rate Risk

Exchange Rate Risk - the risk that the domestic currency value of bond payments in a foreign currency will ↓ due to exchange rate changes

Risks associated with fixed income securities: Volatility Risk

Volatility Risk - the risk that ∆ in expected interest rate volatility will affect the values of bonds with embedded options

Risks associated with fixed income securities: Inflation Risk

Inflation risk - the risk that actual inflation > expected inflation
- this erodes the purchasing power of the cash flows from a fixed income security.

Risks associated with fixed income securities: Event Risk

Event Risk - the risk of ↓ in a security's value from disasters, corporate restructurings, or regulatory changes that negatively affect the firm.
- anything that ↓ issuer's earnings or ↓ asset values.
- takeovers or restructurings that can have negative effects on the priority of bondholder's claims.
- regulatory changes that can ↓ issuer's earnings or narrow the market for a particular class of bonds.

Risks associated with fixed income securities: Sovereign Risk

Sovereign Risk - the risk that governments may refuse to pay or repudiate debt or not be able to make debt payments in the future.
- possibly due to poor economic conditions and government deficit spending.

Interest rate risk for a bond refers to the fact that when interest rates:
a) ↓...the realized yield on the bond < YTM
b) ↑...the bond's value ↓
c) ↑...prepayments of principal will ↓

(B) Interest rate risk is the risk that the bond's value will ↓ because interest rates ↑.
Reinvestment risk is the risk that a bond's CFs will be reinvested at lower-than-expected rates.
Prepayment risk refers to the fact that prepayments of a mortgage-backed security's principal may differ from the expected rate.

When a bond's coupon rate < market yield, how does this affect the bond value?

When a bond's coupon rate < market yield, the bond will trade at a DISCOUNT to its par value

When a bond's coupon rate > market yield, how does this affect the bond value?

When a bond's coupon rate > market yield, the bond will trade at a PREMIUM to its par value

The level of a bond's INTEREST RATE RISK or duration is positively and negatively related to...

The level of a bond's interest rate risk (=duration) is:
- ↑ Maturity, ↑ Interest Rate Risk
- ↓ Coupon rate, ↑ Interest Rate Risk
- ↓ Market YTM, ↑ Interest Rate Risk

Less over some ranges for bonds with embedded options

What type of bonds have the highest interest rate risk?

Zero-coupon bonds have the highest interest rate risk because they deliver all their cash flows at maturity.
- another way to think of this: a zero-coupon bond has the lowest coupon (0.00%), so it has the highest price volatility, since the coupon rate is inversely related to price volatility.

For a given change in yield, which will experience a smaller change in price?
a) higher coupon bond
b) lower coupon bond

(A) In addition to market yields, the timing and magnitude of cash flows affect price volatility.
For a given change in yield, a higher coupon bond will experience a SMALLER change in price than a lower coupon bond.

True/False Price sensitivity is lower when the level of interest rates is higher.

True! The price sensitivity is lower when the level of interest rates is higher. Put another way, a bond that has the lowest duration is therefore the least sensitive to changes in interest rates.

All else equal, the lower the bond's YTM, the:
a) longer the duration and higher the interest rate risk
b) shorter the duration and lower the interest rate risk
c) shorter the duration and higher the interest rate risk

(A) A lower yield to maturity would result in a longer duration and higher interest rate risk.

Price of a callable bond =

Price of a callable bond = Price of an identical option-free bond - value of the embedded call.

As interest rates decrease, how does the issuer value the call option?

As interest rates ↓, the issuer values the call option more because the company has the potential to "call" the bond and replace existing debt with lower-coupon (and thus lower cost) debt.

Who does the call option benefit: issuer or the investor? Is the call price the ceiling or the floor on the value of a callable bond?

The call option benefits the issuer - not the investor. The call price acts as a ceiling on the value of a callable bond.
Value of a callable bond will always be ≤ otherwise identical non-callable bond.

Difference between the curves of callable and noncallable bonds:

The noncallable bond has the traditional PY shape.
The callable bond bends backwards.
The difference between the two curves = value of the option

What kind of risk can floating-rate bonds have between reset dates?

Floating-rate bonds have INTEREST RATE RISK between reset dates.
- their prices differ from their par values, even at reset dates, due to changes in liquidity or in credit risk after they have been issued.

Does holding a floating-rate bond eliminate price fluctuations?

Holding floating-rate bonds MINIMIZES, but does not eliminate price fluctuations.
- with a perfect, continuously resetting coupon rate, a floating-rate bond's value would always = par value
- a cap rate can ↑ price volatility of a floating-rate bond.

In general, the longer the time until the next reset date of a floating-rate security affects interest rate risk by...

In general, the longer the time until the next reset, the greater the interest rate risk of the floating-rate security.
- the interest rate risk of a floating-rate security ↓ as the reset date approaches because the coupon reset will return the price to par, as long as the margin above the reference rate accurately reflects the bond's risk.

True/False The greater the time lag between reset dates, the greater the amount of price fluctuation in floating-rate securities.

True. The more frequent the reset dates, the less the time lag that causes volatility. So, the greater the gap between reset dates, the greater the amount of price fluctuation.

True/False A fixed margin coupon exposes the bond to more price fluctuations than an adjustable margin (as is the case with an extendible reset bond)

True! A fixed margin coupon exposes the bond to more price fluctuations than an adjustable margin (as is the case with an extendible reset bond)

What is cap risk in a floating-rate bond?

Cap risk refers to when market interest rates rise to the point that the coupon on a floating rate security hits the cap and the bond begins to behave like a fixed coupon bond, which has more price fluctuations.
- this is a risk to the holder of a floating-rate bond.

Duration of a bond vs. Dollar Duration of a bond

Duration of a bond = approximate %Price∆ for a 1% change in yield

$ Duration of a bond = approximate $Price∆ for a 1% change in yield.

For a zero-coupon bond, duration is approximately equal to...?

For a zero-coupon bond, duration is approximately equal to the # of years to maturity. We use the term "approximately" because it ignores the curvature of the price/yield curve.

True/False A bond's percentage change in price and dollar change in price are both tied to the underlying price volatility.

True! A bond's %∆ in price and $∆ in price are both tied to the underlying price volatility.

Effective duration & basis points

The effective duration formula result is for 1.00% change in interest rates.

100 basis points = 1.00% = 0.01 (in decimal form).
1 basis point = 0.0001

True/False If a bond has an effective duration of 7.5, it means that a 1% change in rates will result in a 7.5% change in price.

True! Because of convexity, it will be approximately 7.5% change in price, not an actual 7.5% change in price. The readings are very explicit about this distinction.

How is duration related to maturity and coupon rate and YTM?

Duration ↑
...Maturity ↑
A longer term bond pays its cash flows later than a shorter term bond, increasing the duration.
...Coupon Rate ↓
A lower coupon bond pays lower annual cash flows than a higher coupon bond and thus has less influence on duration.
...YTM ↓
Because the bond's price (or present value) is inversely related to interest rates. When market yields ↓, the value (or cash flows) of a bond ↑ WITHOUT increasing the time to maturity.

How is duration related to a bond's cash flows?

Duration is approximately equal to the point in years where the investor receives half of the PV of the bond's cash flows. Therefore, the later the cash flows are received, the ↑ duration. This rationale is similar to price volatility.

What is the indirect relationship between coupon rate and duration?

The higher the coupon rate, the shorter the duration. Why? A higher coupon bond pays higher annual cash flows than a lower coupon bond and thus has more influence on duration.

What type of bonds have the highest price volatility and the longest duration?

Zero-coupon bonds have the highest price volatility and the longest duration (at approximately ≈ maturity). This is because zero-coupon bonds pay all cash flows in one lump sum at maturity.

In what way is duration a function of volatility or risk?

Duration is also a function of volatility (risk). Higher volatility (risk) = higher duration. A ↑ coupon bond has a ↓ duration relative to similar bond with a lower coupon, because the bond holder is getting more of their cash value sooner (because of the higher coupon). This ↓ the overall risk of the bond resulting in ↓ duration.

Duration of zero-coupon bonds vs. coupon paying bonds

The duration of a zero-coupon bond is approximately equal to its time to maturity.
For coupon-paying bonds, duration < maturity. Any coupon amount will shorten duration because some cash flow is received prior to maturity.

Yield curve risk of a bond portfolio -

Yield curve risk of a bond portfolio is the risk (in addition to interest rate risk) that the portfolio's value may ↓ due to a non-parallel shift in the yield curve (change in its shape).

What happens to the duration of a bond portfolio when a yield curve has a non-parallel shift?

When yield curve shifts are not parallel - the duration of a bond portfolio does NOT capture the true price effects because the yield on various bonds in the portfolio may change by different amounts.

TRUE/FALSE If long-term rates are low, the PV of cash flows far into the future will be high, and the bond's value will be high.

True! If long-term rates are low, the PV of cash flows far into the future will be high and the bond's value will be high. The value of a bond is comprised of discounted cash flows and a lower discount rate translates to higher cash flows.

What does the yield curve plot?

The yield curve plots
Term to maturity vs. Yield to Maturity (<< YTM, not coupon rate!)

Why does the yield curve usually have a non-zero slope?

The yield curve usually has a nonzero slope because the rates change by different basis points across maturities.

Portfolio duration -

Portfolio duration is a measure of a portfolio's interest rate risk.
- measures the sensitivity of the portfolio's value to an equal change in yield for all the bonds in the portfolio.
- calculated as the weighted average of the individual bond durations using the proportions of the total portfolio value represented by each of the bonds.
- does not capture the effect of changes in the yield curve (term structure)

What are the disadvantages to an investor of a callable or prepayable security:

- Timing of cash flows = uncertain
- Principal is most likely to be returned early when interest rates are available for reinvestment are low.
- Potential price appreciation is < than that of option-free bonds.

Compared to a callable bond, the yield on a non-callable bond is... more or less?

When compared to a callable bond, the yield on a noncallable bond is LESS. With a noncallable bond, the issuer does not have to compensate the investor for call risk/cash flow uncertainty with any premium.

Call Risk is a combination of...

Call risk is a combination of cash flow uncertainty and reinvestment risk.

When a bond is called, the investor faces a disruption in cash flow and a reduced rate of return.

When yield volatility increases, what happens to both (puts and calls) embedded options?

Embedded options (puts and calls) increase in value when volatility increases. In the formula, The value of a putable bond is calculated by ADDING the option to a straight bond. The value of a callable bond is calculated by SUBTRACTING the option from a straight bond.

What characteristics cause a bond to have more reinvestment risk?

A security has more reinvestment risk when it has a...
- HIGHER coupon
- is callable
- is an amortizing security
- has a prepayment option

Why does a prepayable amortizing security have greater reinvestment risk?

A prepayable amortizing security has greater reinvestment risk because of the probability of accelerated principal payments when interest rates (including reinvestment rates) ↓

True/False Zero-coupon bonds have NO reinvestment risk over their term.

Zero-coupon bonds have NO reinvestment risk over their term ONLY if they are held till maturity. Reinvestment risk means that a bond investor risks having to reinvest bond cash flows (both coupon and principal) at a rate lower than the promised yield.

How do maturities and coupon amounts impact reinvestment risk?

Reinvestment risk ↑ with
longer maturities and higher coupons.

Can an investor ever eliminate reinvestment risk?

While a bond investor can eliminate price risk by holding a bond until maturity, he usually cannot eliminate bond reinvestment risk.
ONE EXCEPTION: zero-coupon bonds have no reinvestment risk as long as they are held to maturity.

True/Falso Short-term bonds should be purchased if the investor anticipates higher reinvestment rates.

True! If an investor expects interest rates to rise, he would want a bond with a shorter maturity so that he receives his CFs sooner and could reinvest at the higher rate. Also, there is less prepayment risk with shorter maturities.

Why is reinvestment risk important to consider? And when does reinvestment risk become the least important?

Reinvestment risk is important because the yield-to-maturity (YTM) calculation for a bond assumes that the investor can reinvest cash flows at exactly the coupon rate. It is the risk that if the rates fall, cash flows will be reinvested at lower rates, resulting in a holding return < expected return (at the time of bond purchase).

Reinvestment risk is least important with the combination of shorter maturity and lower coupon rate.

Do mortgage-backed securities face reinvestment risk?

Yes! Mortgage backed and other asset backed securities have HIGH reinvestment risk because in addition to cash flows from periodic interest payments (like bond coupons), these securities have repayment of principal. The ↓ interest rates, the ↑ chances of prepayments.

What kind of security has
a) high interest rate risk AND
b) low reinvestment risk?

A zero-coupon bond can have high interest rate risk (because its single cash flows subjects it to the full amount of discounting when interest rates change) and low reinvestment risk (the single cash flow minimizes prepayment risk).

Order the following securities from least reinvestment risk to most: callable bonds, straight coupon bonds, mortgage-backed securities, and zero-coupon bonds

Least to Most Reinvestment risk:
1) Zero-coupon bonds (noncallable & held to maturity)
2) Straight coupon bonds (no prepayment risk, but do have periodic coupon payments).
3) Callable Bonds (the right to prepay principal compounds reinvestment risk. A call option is one form of prepayment right that benefits the issuer (and not the bondholder).
4) Mortgage-backed securities - most reinvestment risk because of high prepayment risk, periodic interest payments, and repayment of principal.

Credit Risk includes what 3 types of risk:

Credit risk includes:
1) Default Risk - probability of default
2) Downgrade Risk - probability of a reduction in the bond rating
3) Credit Spread Risk - uncertainty about the bond's yield spread to T-bonds ("Treasuries") based on its bond rating.

Credit Ratings

Credit ratings are designed to indicate to investors a bond's relative probability of default.
Lowest probability of default - AAA

Credit ratings for Investment grade vs. Speculative or high yield bonds...

Investment grade Bonds: AA, A, and BBB
Speculative or high yield bonds: BB or lower

TRUE/FALSE When a rating agency downgrades a security, the bond's price usually falls.

TRUE! The market will likely demand a higher yield from the downgraded bond (the risk premium has increased) and thus the price will likely fall.

Technical Default -

Technical default refers to an issuer's violation of bond covenants, such as debt ratios, rather than the failure to pay interest or principal. In the event of a default, the holder (lender) may recover some or all of the investment through legal action or negotiation. The percentage recovered = "recovery rate"

Credit spread Risk (or the yield on a risky asset) formula:

Yield(risky) = Yield (risk-free) + RP

RF = default - free rate

The yield differential above the return on a benchmark security measures...

The yield differential above the return on a benchmark security measures the CREDIT SPREAD risk.
Credit Spread risk = Risk Premium = "Spread"

Call Risk is composed of what three components:

Call Risk is composed of:
1) unpredictability of the cash flows
2) compression of the bond's price
3) reinvestment risk (or the high prob that when the bond is called, the investor will be faced with less attractive investment ops)

How does a lack of liquidity affect portfolio values?

Lack of liquidity can have ADVERSE effects on calculated portfolio values and therefore, on performances measures for a portfolio.
- this makes liquidity a concern for a manager even though sale of the bonds is not anticipated.

How is liquidity important to institutional investors and dealers?

Liquidity is important to institutional investors that must determine market values for NAVs and to dealers in the repurchase market for collateral valuation.

Bonds bought with cash flows denominated in a foreign currency...

An investor who buys a bond with CFs denominated in a foreign currency (not $$) will see the value of the bond ↓...
- if the foreign currency depreciates OR
- the exchange value of the foreign currency declines
relative to the investor's home currency.

True/False Appreciation of the Swiss Franc benefits the US investor holding Swiss bonds.

True! The appreciation of the foreign currency (Swiss Franc) benefits domestic investors (US citizens) who own foreign (Swiss) bonds.
- when the Swiss Franc appreciates, each Swiss franc buys more of the US dollar than before.
- So, the US investor gains by owning foreign bonds because the investor realizes (a) return from the bond and (b) gain from the foreign currency appreciation.

What happens if the inflation increases unexpectedly?

If inflation increases unexpectedly, the purchasing power of a bond's future cash flows is decreased and bond values ↓

True/False Treasury securities are considered immune to inflation and liquidity risk

False! The statement that T securities are considered immune to inflation and liquidity risk is partially true - T securities are immune to liquidity risk, but fixed-coupon T securities have high inflation risk and generally low real returns.

True/False The short term inflation premium < long term premium

The ST inflation premium < LT inflation premium because investors are better able to predict inflation in the short term. Inflation risk ↑ as time ↑ and so investors want to be compensated for this uncertainty.

True/False The real return on a fixed coupon bond is variable.

True! The real return on a fixed coupon is variable. An investor's real return is not fixed - even though an investor may hold a fixed-rate coupon bond, the real return depends on a variable - inflation.
↑ inflation rates result in a ↓ purchasing power of bond payments.

How does ↑ Yield volatility impact put and call options embedded in bonds?

↑ Yield volatility, ↑ value of put and call options embedded in bonds...thus:
- ↓ value of a callable bond (cuz the bondholder is short the call)
- ↑ value of a putable bond (cuz the bondholder is long the put)

Value of a callable bond =

Value of callable bond = Value of a Straight bond - Call Option
Remember: the call option is subtracted from the bond value because the call option is of value to the issuer and not the bondholder.
↑ Yield volatility, ↑ Call OPTION value, ↓ Callable BOND value → Bondholder loses.

Value of a putable bond =

Value of a putable bond = Value of a Straight Bond + Put Option Value
Remember: the put option is added to the bond value because it is of value to the bondholder and not the issuer.
↓ Yield Volatility, ↓ Put OPTION value, ↓ Putable BOND value

US Treasuries are the ______ debt of the US Government

US Treasury securities are SOVEREIGN debt of the US government and are considered free of credit risk.
- Sovereign debt refers to the debt obligations of governments.
- Sovereign debt of other countries has varying degrees of credit risk.

Sovereign debt is typically issued using 4 methods:

Sovereign debt is typically issued using one of 4 methods:
1. Regular auction cycle with the entire issue sold at a single price
2. Regular auction cycle with bonds issued at multiple prices.
3. Ad Hoc auction system with no regular cycle
4. Tap system, auctioning new bonds identical to previously issued bonds.

Ad Hoc auction system

The Ad Hoc auction system is a method in which a central government distributes new government securities via auction when it determines that market conditions are advantageous.

True/False When a central government issues securities, those securities can only be denominated in the local currency regardless of where the bonds are issued.

False! When a central government issues securities, those securities are generally denominated in the currency of the issuing country, but a government can issue bonds denominated in any currency.
- Also, Sovereign bonds are not necessarily free from default risk.

3 types of US Treasury securities:

Securities issued by the US Treasury include:
1. Bills - pure discount securities maturing in 4 weeks, 3 months, or 6 months
2. Notes - coupon securities maturing in 2, 5, and 10 years
3. Bonds - coupon securities maturing in 20 or 30 years


Treasury Inflation Protected Securities (TIPS) are US Treasury issues in which:
- Coupon rate = FIXED
- Par Value = adjusted periodically for inflation, based on changes in the CPI.

On the run vs. Off the run issues

US Treasuries from the most recent auction are referred to as "on the run" issues, while Treasuries from previous auctions are referred to as "off the run" issues.

Impact of deflation on a TIPS

If deflation (inflation ↓) occurs over the life of a TIPS, the Treasury will redeem the security for its initial face value of $1000 at maturity.
Remember: The principal of a TIPS adjusts semi-annually and then the FIXED coupon rate x (new principal value) = new inflation-adjusted interest payment.

How are T-bond prices quoted?

Bond prices are quoted in 32nds. Ex: a quote for 94 10/32.
Divide 10/32 = 0.3125. Now you have 94.3125%.
So, the bond price = $943.125 for a $1000 T-bond.
Ex: a quote for 96 27/32 = 96.84. So, bond price = $9684.38 for a $10,000 bond.

If a T-bond is quoted at 92-16, the price of the bond is:

Bond prices are quoted in 32nds.
Quote: 92-16, which means 92 16/32 = 92.5% of par value
0.925 x $1000 (par value) = $925

Treasury strips are traded in 2 forms

Treasury strips are traded in 2 forms:
1. Coupon strips
2. Principal Strips
and are taxed by the IRS on the basis of accrued interest, like other zero-coupon securities.

How often are US Treasury notes issued?

US Treasury notes are issued quarterly.

True/False Taxable investors holding zero-coupon bonds can have negative cash flow prior to maturity

True! It is possimpible that taxable investors will have (-) cash flows from holding zero-coupon securities, since there is no cash income, but taxes must be paid at least annually on the implicit interest.

Securities issued by the US Federal agencies

Agencies of the US government, inc federally related institutions and govt sponsored enterprises, issue bonds that are not obligations of the US Treasury but are considered to be almost default risk free.

This type of security redistributes the prepayment risk among the investors through tranches.

A collaterized mortgage obligation (CMO), and NOT a passthrough security, redistributes the prepayment risk among the investors through tranches.
- CMOs are split into tranches, with each tranche having a different claim and risk structure on the pool of CFs.

This type of security may be retired before maturity at face value with no penalty.

Because the mortgage holders may prepay the mortgage, a passthrough security may indeed be retired before maturity at face value with no penalty.

True/False Government sponsored enterprises (GSE) are owned by the US government and therefore have essentially no credit risk.

False! Government sponsored enterprises (GSE) are privately owned, and therefore investors assume some credit risk.

Which of the following is NOT a GSE (government-sponsored enterprise)?
a) Federal Farm Credit System
b) Government National Mortgage Association
c) Student Loan Marketing Association

(B) Government National Mortgage Association (Ginnie Mae) is NOT a GSE.
Federally related (or government-owned) agencies are arms of the federal government. Both the "Federal Farm Credit System" & "Student Loan Marketing Assoc" are GSE's.

Mortgage Passthrough Security

Mortgage Passthrough security
- backed by a pool of amortizing mortgage loans (the "collateral")
- has monthly CFs that include:
a) interest payments
b) scheduled principal payments
c) prepayments of principal.

Is prepayment risk significant for Investors in passthrough securities?

Yes, Prepayment risk is significant for investors in passthrough securities because most mortgage loans contain a prepayment option which allows the issuer (borrower - you) to make additional principal payments at any time.

Collaterized Mortgage Obligations (CMOs)

Collaterized Mortgage Obligations are customized claims to the principal and/or interest payments of mortgage passthrough securities
- redistribute the prepayment risk and/or maturity risk of the securities.

Sequential Tranches

Sequential tranches issued as a CMO do not have proportionate claims on the CFs from the pool
- Have sequential claims
- shortest term tranche receives principal and interest payments until it is paid off.
- CFs then go to the second tranche until it is paid off and so on.
- This structure allows securities with different timings and risk profiles to be issued from the same pool of certificates.

How is prepayment of a mortgage like an embedded call option feature?

A borrower who prepays a mortgage is in effect exercising a call option, similar to a corporate bond issuer who calls a bond and prepays the principal.
- therefore the pool of mortgages and the securities created from it behave as if they had an embedded call feature.


If a prepayment of principal is for an amount < full outstanding loan balance...then it is known as "curtailment".

What are CMOs created to do?

CMOs are created to ↓ borrowing costs by:
a) redistributing prepayment risk or
b) altering the maturity structure better suit investor preferences.
CMOs redistribute the risk between tranches on an UNEQUAL basis, and not on a random basis.

Munis and Interest Payments

Interest payments on state and local government securities ("munis") are usually exempt from US Federal taxes, and from state taxes in the state of issuance.

Municipal bonds include:
1) Tax-backed bonds
2) Revenue bonds

Municipal bonds include:
1) Tax-backed (general obligation) bonds backed by the taxing authority of the governmental unit issuing the security.
2) Revenue bonds, backed only by the NET revenues from the project specifically financed by the bond issue.

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