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Margin leverage factor and levered return
- Leverage factor - 1/margin%
- Levered return - HPR x Leverage factor
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Relationships between k and g in dividend discount model
difference between k and g widens, value of stock falls
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P/E = ?
P/E = Payout ratio/(k-g)
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Leading vs trailing P/E
- Leading P/E = price/forecast EPS next 12 months
- Trailing P/E = price/EPS for past 12 months
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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
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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 = (54-50 + 50-48)/2 = 3
- Average % movement = 3/50 = 6%
- Duration = 6%/.5% = 12
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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
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Term structure theories (expectations, liquidity preference, market segmentation)
- Expectations hypothesis: yield curve shape reflects investor expectations about future behavior of short-term 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.
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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
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debenture bond
unsecured, backed by the
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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
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z-spread
interest rate that is added to each zero-coupon 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
z-spread = option adjusted spread + cost of the call option in percent
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$ 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)
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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
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municipal bonds
not all are tax exempt
investors may be taxed on capital gains
moral obligation bong = no legal obligation to pay
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technical bond default
issuer breaks bond covenants, like maintaining a certain debt-to-equity ratio
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yield curve
time on x, yield on y
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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
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bond trading flat
issuer is in default and the bond is trading without accrued interest
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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
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external enhancements
a third party guarantees bond performance
government, another firm, or insurance
rating can only be as high as the guarantor
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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
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curtailment
a prepayment for a portion of the principal
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price compression
the result of a call option on a bond, it hurts price appreciation
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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
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Bank Discount-Basis Yield, Money Market Yield, Bond Equivalent Yield
Bank Discount-Basis Yield:
Money Market Yield:
Bond Equivalent Yield:
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