Fixed Income

Question 1

U.S. Treasury Bonds

Answer 1

•Bonds and notes may be purchased directly from the Treasury
–Note maturity is 1-10 years; Bond maturity is 10-30 years
•Denomination can be as small as $100, but $1,000 is more common
•Bid price of 100:08 means 100 8/32 or $1002.50

Question 2

Calculate Pre-Tax Equivalent Yield

Answer 2

= (after-tax yield) / (1 - tax rate)

Question 3

Commercial Paper

Answer 3

unsecured short term debt obligations issued by corporations with maturities of less than one year

Question 4

Bond indenture

Answer 4

contract between the issuer and the bondholder that specifies the coupon rate, maturity date, and par value

Question 5

Determinants of Bond Safety (5 ratios)

Answer 5

–Coverage ratios
–Leverage ratios, debt to equity ratio
–Liquidity ratios
–Profitability ratios
–Cash flow to debt ratio

Question 6

Macaulay Duration

Answer 6

Named for creator Frank Macaulay, duration measures the present value of future interest payments and the length of time needed to reach par value. The average time to receive the present value of a bond’s cash flows (aka “weighted average term to maturity”).

Question 7

Assumptions in duration calculation

Answer 7

Duration assumes yields remain constant and reinvestment risk does not exist, which is actually only true during the life of the bond for zero coupon bonds.

Question 8

Important Duration Observations

Answer 8

All else being equal, the greater the present value of the cash flow that is received as part of the coupon payment (i.e., versus principal received at maturity), the lesser the duration.
 All else being equal (credit risk, maturity), the higher the coupon rate, the lesser the duration.
 All else being equal, a longer maturity bond (relative to a shorter maturity one) will have a longer duration.
 A zero coupon bond’s duration will normally equal its maturity.
 The greater the duration, the greater the percentage price change from a change in interest rates.

Question 9

Modified Duration

Answer 9

Modified Duration measures price sensitivity when there is a change in interest rates or a change in yield to maturity.

Question 10

Duration of a level perpetuity

What is it?

Answer 10

The duration of a level perpetuity is equal to:
(1 + y ) / y

A perpetuity is a series of payments made forever along equal. intervals of time

Question 11

Interest Rate Risk

Answer 11

Interest Rate Sensitivity

1. Bond prices and yields are inversely related
2. An increase in a bonds yield to maturity results in a smaller price change than a decrease of equal magnitude
3. Long term bonds tend to be more price sensitive than short term bonds
4. As maturity increases, price sensitivity increases at a decreasing rate
5. Interest rate risk is inversely related to the bonds coupon rate
6. Price sensitivity is inversely related to the yield to maturity at which the bond is selling

Question 12

YTM

Answer 12

YTM is the rate of return of a bond if it is held to maturity
Interest rate that makes the present value of the bond’s payments equal to its price is the yield to maturity (YTM)
•expressed as an annual rate
•assumes all interest payments are reinvested at the bond’s current yield

Question 13

Relationship of coupon rate to current yield to YTM for premium and discount bonds

Answer 13

For premium bonds Coupon rate > Current yield > YTM

For discount bonds reversed

Question 14

YTM and Default Risk

Answer 14

There is a difference between the yield based on expected cash flows and yield based on promised cash flows

The difference between the expected YTM and
the promised YTM is the default risk premium

Question 15

Bond Yields: Yield to Call

Answer 15

• If interest rates fall, price of straight bond can rise considerably
• The price of the callable bond is flat over a range of low interest rates because the risk of repurchase or call is high
• When interest rates are high, the risk of call is negligible and the values of the straight and the callable bond converge

Question 16

Credit Default Swaps (CDS)

Answer 16

–Acts like an insurance policy on the default risk of a corporate bond or loan
–Buyer pays annual premiums
–Issuer agrees to buy the bond in a default or pay the difference between par and market values to the CDS buyer

Question 17

Convexity

Answer 17

• Bonds with greater convexity have more curvature in the price yield relationship
• Duration rule is a good approximation for only small changes in bond yields

Question 18

Why Do Investors Like Convexity?

Answer 18

• Bonds with greater curvature gain more in price when yields fall than they lose when yields rise
• The more volatile interest rates, the more attractive this asymmetry
• Bonds with greater convexity tend to have higher prices and/or lower yields, all else equal

Question 19

Negative convexity in callable bonds and Mortgage backed securities

Answer 19

Callable bonds have negative and positive convexity. Negative as interest rates approach call. Use effective duration = [(change in P)/P]/(change in rate)

MBSs are based on a portfolio of callable amortizing loans (since homeowners can pay off loans at any time), so MBSs have negative convexity as well.

Question 20

Immunization

Answer 20

– A way to control interest rate risk that is widely used by pension funds, insurance companies, and banks
– In a portfolio, the interest rate exposure of assets and liabilities are matched
• Match the duration of the assets and liabilities
• Price risk and reinvestment rate risk exactly cancel out
• As a result, value of assets will track the value of liabilities whether rates rise or fall