
Margin leverage factor and levered return
 Leverage factor  1/margin%
 Levered return  HPR x Leverage factor

Relationships between k and g in dividend discount model
difference between k and g widens, value of stock falls

P/E = ?
P/E = Payout ratio/(kg)

Leading vs trailing P/E
 Leading P/E = price/forecast EPS next 12 months
 Trailing P/E = price/EPS for past 12 months

Bullet bonds, Serial bonds, Sinking fund provisions, Call provisions, Refunding provisions
 Bullet bonds  lump sum at maturity pays entire principal
 Serial bonds  pay off principal through series of payments over time
 Sinking fund provision  provide for bond retirement through predefined principal payments over life of the issue
 Call provision  issuer has right to retire all or part of an issuance at a set schedule and price
 Refunding provision  nonrefundable bonds prohibit premature retirement of an issue from proceeds of a lower coupon bond. Freely callable, but nonrefundable

Effective Duration
Average % movement (up or down)/value change in yield
takes embedded options into account, unlike modified duration
 Ex: P = 50
 if yield goes down .5%, P = 54
 if yield goes up .5%, P = 48
 Average movement = (5450 + 5048)/2 = 3
 Average % movement = 3/50 = 6%
 Duration = 6%/.5% = 12

Change in price using duration and convexity
%change in price = Duration*(change in yield in decimal form) + convexity*(change in yield in decimal form)^2
duration of a floater is the time to the next reset date
DURATION IS APPROXIMATE

Term structure theories (expectations, liquidity preference, market segmentation)
 Expectations hypothesis: yield curve shape reflects investor expectations about future behavior of shortterm rates
 Liquidity preference theory: investors prefer greater liquidity, so longer term bonds will include a liquidity risk premium
 Market segmentation: Market for debt securities is segmented on basis of investor maturity preferences. Each segment's interest rate is determined by supply and demand.

Interest rate risk approaches
full valuation > duration/convexity > duration
full valuation: start with market yield and price, estimate hypothetical changes in yields, recompute bond price using new yields, compare resulting price changes
duration/convexity and duration are summary measures that sacrifice accuracy for simplicity

debenture bond
unsecured, backed by the

coupon rate, current yield, ytm relation
current yield will always be between coupon rate and ytm
if selling at a premium, coupon rate > current yield > ytm
if selling at a discount, ytm > current yield > coupon rate

zspread
interest rate that is added to each zerocoupon bond spot rate that will cause the present value of the risky bond's cash flows to equal its market value
not used for bonds with options
zspread = option adjusted spread + cost of the call option in percent

$ Price change using duration
Price Value of a Basis Point
Dollar price change = yield change in decimal form*duration*(price+accrued interest)
Price Value of a Basis Point: how much the price will change given a 1 bp change in yield
PVBP = .0001*duration*(price+accrued interest)

Interest expense on a bond
total amount paid by issuer  amount received by issuer
 Ex. 10% coupon, 8% ytm, semiannual, 5 years, 1000, pv 923
 Interest expense = 10*40 + 1000  923

municipal bonds
not all are tax exempt
investors may be taxed on capital gains
moral obligation bong = no legal obligation to pay

technical bond default
issuer breaks bond covenants, like maintaining a certain debttoequity ratio

yield curve
time on x, yield on y

cum coupon, ex coupon
cum coupon  buyer has the right to the next coupon, and pays the seller accrued interest. This is the way bonds are traded in the U.S. and many other countries
ex coupon  buyer forfeits the right to the next coupon, which should be taken into account when calculating price

bond trading flat
issuer is in default and the bond is trading without accrued interest

floating rate bonds, how do the following affect volatility: fixed component (LIBOR + 2%)
cap
reset dates
a fixed component will increase volatility
a cap will increase volatility
reset dates that are farther apart will increase volatility

external enhancements
a third party guarantees bond performance
government, another firm, or insurance
rating can only be as high as the guarantor

regular redemption price, special redemption price
 regular redemption price: bonds are redeemed based on call provisions in the indenture
 special redemption price: bonds are redeemed to comply with sinking fund provisions

curtailment
a prepayment for a portion of the principal

price compression
the result of a call option on a bond, it hurts price appreciation

accrual bond
accrue interest over the life of the bond, then pay it out with the final principal or according to some schedule of future principal/interest payments

Bank DiscountBasis Yield, Money Market Yield, Bond Equivalent Yield
Bank DiscountBasis Yield:
Money Market Yield:
Bond Equivalent Yield:

