FM formula sheet, Cheat Sheet of Financial Management

Download FM formula sheet and more Cheat Sheet Financial Management in PDF only on Docsity! MATH419: Actuarial Science. Exam-FM Formulas Interest: sum of geometric series Sn = a(1 − rn)/(1 − r) · Compound: A(t) = A(0)(1 + i)t = A(0)(1 − d)−t Simple: A(t) = A(0)(1 + it) · v = 1 1+i discount d = 1 − v. constant force of interest δ = ln(1 + i). · varying force of interest δ(t) = dA/dt A(t) . separate and integrate A(t) = A(0)e ∫ t 0 δ(s)ds. · interest earned from a to b = A(b)−A(a). X deposited at a accumulated till b is A(b) = Xe ∫ b a δ(s)ds Level Annuities: 5-button formula PV = PMTan + Fvn · PV immediate an = 1−vn i PV due än = (1 + i)an continuously paid an = an ( i δ ) · FV sn = (1 + i)nan = (1+i)n−1 i s̈n = (1+i)n−1 d perpetuity a∞ = 1 i ä∞ = 1 d · a(m) n means m payments per year for n years. i(12) nominal means i(12) 12 interest per month Varying Annuities: CF button, to enter PMTs and frequency. · geometric: increase e% per payment, calculate new interest rate 1 1+j = 1+e 1+i . · arithmetic: init P , increase Q: PV = Pan + Q i (an − nvn) Q is negative for decrease. P can be zero. ctsly payable - multiply by ( i δ ) · ctsly compounding, ctsly payable f(t): PV = ∫ n 0 f(t)vtdt · varying force of interest δ(t): PV = ∫ n 0 f(t)e− ∫ t 0 δ(r)drdt FV = ∫ n 0 f(t)e ∫ n t δ(r)drdt Loans: AMORT button after entering info into 5-buttons · L is principle, OBt is outstanding balance just after payment at t, · It is interest in tth payment, Pt is principle repaid tth payment. Pt + It = PMT . It = iOBt−1. · prospective: OBt = PMTan−t, present value of remaining payments. Pt = PMTvn−t+1, · retrospective: OBt = L(1+ i)t−PMTst, FVloan - FVpayments made. Pt = (1+ i)t−1(PMT −Li) Bonds: F = par = face, C = redemption amount, r = coupon rate, i = yield rate. · bond price PV = Fran + Cvn, book value is outstanding balance · write down is principal repaid: Pt = (Fr − Ci)vn−t+1, amortization of bond. · premuim=price-redemption. discount=redemption-price. NPV & IRR: CF, NPV, IRR (finds solution closest to zero only). · IRR is rate at which PV of flows equals 0, interest rate = cost of capital · dollar-weighted: simple interest rate that must have been in effect. solve for i. · time-weighted: (b/a)(c/b)(d/c) = 1 + i where a grew to b, b grew to c etc. solve for i. · investment year: interest rate depends on when deposited (row). · portfolio method: interest rate depends on current year (column). · new money rate: investment year rate for money deposited this year. Varying Rates: (1 + st−1) t−1(1 + ft) = (1 + st) t. spot rate: st rate for term t starting at 0. · forward rate: fa,b rate for term starting at a and ending at b. ft = ft−1,t. · modified duration DM = −dP/di P , equals t/(1 + i) for constant i and term t. · duration (Macaulay) D = (1 + i)DM , equals t for constant i and term t. D = ∑ t PVt∑ PVt · asset-liability matching: Asset income equals Liability due at all t. · Redington immunization: PVA = PVL at i0 and PVA > PVL for i near i0. · duration of assets = duration of liabilities dPVA di = dPVL di , and · convexity of assets > convexity of liabilities d2PVA di2 > d2PVL di2 . · full immunization: Asset income greater than or equal to Liability due for any i. Ch1: Derivatives: value determined by price of something else. long: buyer. short: seller. · insurance is risk-sharing. Insurance firms use reinsurance to share risk of extreme events. · diversifiable risk is unrelated to other risks and can be shared. non-diversifiable risk does not vanish when shared (it already affects everyone). · bid: price can sell at, ask: price can buy for. You always pay more than you get so ask > bid. Ch2: Forwards and Options: call: right to buy, put: right to sell, forward: obligation. · European: exercise at end. American: exercise anytime. Bermudan: exercise specified times between. · Option profit = payoff - FV(option price). Options are insurance, strike = value-deductable. Ch3: Insurance and Collars: Put-Call Parity C − P = FP − e−rtK · prepaid forward price FP : current price less the PV of dividends. · forward price F : FV of prepaid forward price.