Bonds Flashcards
Price of bond
P = C/r * (1-(1+r)^(-T)) + F/(1+r)^T
EAR
EAR = (1 + APR/k)^k - 1
ROI
ROI = Profit / How much you put up
US quote 100:22
100:22 = ((100+22/32) / 100) * F
Accrued interest
Acc. int. = time passed / coupon period
Dirty price
Dirty price = Flat price + Accrued interest
Duration
D = Sum( PV(CFs)/P * t ) | P - total price
Duration for perpetuities
D = (1+n)/n
Modified duration
MD = D / 1+EAR
Convexity and MD
△P/P = -MD * △r + 0.5Convexity(△r)^2
Future forward rate x2
1r2 = ( (1+r2)^2/(1+r1) ) - 1 (1+r2)^2 = (1+r1)*(1+1r2)
F expected
F expected = pRFpromised + (1-p) * Fpromised (+coupon)
Expected yield
P = Fexpected / (1+r)^T | Coupon adjustments
Promised yield
P = Fpromised (+coupon) / (1+r)^T | Coupon adjustments
Leverage effect
1% drop => 1/margin = 1/0.1 = 10%
Hedge ratio
H = △portfolio / Profit on one futures contract
Futures pricing
F = S * (1+rf-y)^T | y - dividend yield for indices
F = S * (1+rf)^T - Dt | Dt - FV of dividends
F = S * (1+rf)^T | no dividends in the contract period
F = S * (1+rf+u-y)^T | u - saved storage costs;
| y - convenience yield
Forward price
F = E * (1+rUS)^T / (1+rEU)^T
PV of floating leg
PV = F + F*(r/T) | T is if needed