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Bond(F) =

par value

Bond(r) =

coupon rate

Bond(Fr) =

coupon amount

Bond(C) =

redemption value (usually = F)

Bond(n) =

number of periods to redemption

Bond(P) =

price

Bond(i) =

yield per period to investor at price P

(Assuming F = C) Premium - Discount Formula:

P = F + F(r-i)an¬

(Assuming F = C) Makeham Formula:

P = K + (r/i)*(F - K), where K = Fv^n

Amortized amount in period k:

F(r-i)v^(n-k+1)

Maturity to use in pricing a callable bond (Premium Bond):

Earliest Possible Redemption Date

Maturity to use in pricing a callable bond (Discount Bond):

Latest Possible Redemption Date

Price Between Payment dates t=

number of days from last coupon date to settlement date / number of days in the bond period

Price-plus-accrued =

P0 (1+i)^t

Accrued interest =

t (Fr)

Price (Between Payment Dates)=

(Price-plus-accrued) - (Accrued interest)

Time Weighted Rates of Interest Ck, Bk, jk =

Ck = Contribution at time tk, Bk = Fund value at time tk, before contribution Ck is made, jk = effective rate over [t(k-1), tk]

Time Weighted Rates of Interest 1 + jk =

Bk / (B(k-1) + C(k-1)

Time Weighted Rates i =

1+j = (1+j1)(1+j2)...(1+jn)

Dollar Weighted Rate of Interest A,B,I,C =

A = Initial Fund Balance, B = Final Fund Balance, I = Interest Earned, C = Total Cash Contribution

Dollar Weighted Rate of Interest B,I, Ct =

B = A + C + I, I = B - A - C , Ct = Contributions/ Withdrawl at time t

Dollar Weighted Rate of Interest i =

I / (A + Sum(Ct(1-t)))

(Sport rates Sn, Forward rates i(n-1),n) 1 + i(n-1),n =

(1+Sn)^n / (1+S(n-1))^n-1

Macaulay Duration (Weighted Avg) D =

w1(t1) + w2(t2) + .... w1, w2 ... = (PV Pmts / PV Price)

Modified Duration (DM) =

neg (dP/Di) / P or D/(1+i)

Level Payments (D) =

(Ia)n¬ / an¬

Coupon Bond (D) =

(Fr(Ia)n¬ + nCv^n) / Bond Price

change in Price =

neg (D/(1+i)) P(i) change(i)

Portfolio (DM) =

w1 DM1 + w2 DM2 + ......

Dividend Growth Model P =

D / (i -g) D = Dividend g = growth

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