Bonds

Question 1

Price of bond

Answer 1

P = C/r * (1-(1+r)^(-T)) + F/(1+r)^T

Question 2

EAR

Answer 2

EAR = (1 + APR/k)^k - 1

Question 3

ROI

Answer 3

ROI = Profit / How much you put up

Question 4

US quote 100:22

Answer 4

100:22 = ((100+22/32) / 100) * F

Question 5

Accrued interest

Answer 5

Acc. int. = time passed / coupon period

Question 6

Dirty price

Answer 6

Dirty price = Flat price + Accrued interest

Question 7

Duration

Answer 7

D = Sum( PV(CFs)/P * t ) | P - total price

Question 8

Duration for perpetuities

Answer 8

D = (1+n)/n

Question 9

Modified duration

Answer 9

MD = D / 1+EAR

Question 10

Convexity and MD

Answer 10

△P/P = -MD * △r + 0.5Convexity(△r)^2

Question 11

Future forward rate x2

Answer 11

1r2 = ( (1+r2)^2/(1+r1) ) - 1
(1+r2)^2 = (1+r1)*(1+1r2)

Question 12

F expected

Answer 12

F expected = pRFpromised + (1-p) * Fpromised (+coupon)

Question 13

Expected yield

Answer 13

P = Fexpected / (1+r)^T | Coupon adjustments

Question 14

Promised yield

Answer 14

P = Fpromised (+coupon) / (1+r)^T | Coupon adjustments

Question 15

Leverage effect

Answer 15

1% drop => 1/margin = 1/0.1 = 10%

Question 16

Hedge ratio

Answer 16

H = △portfolio / Profit on one futures contract

Question 17

Futures pricing

Answer 17

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

Question 18

Forward price

Answer 18

F = E * (1+rUS)^T / (1+rEU)^T

Question 19

PV of floating leg

Answer 19

PV = F + F*(r/T) | T is if needed