Finance Cheat Sheet- Formulae and Terminology

FINANCE FORMULAE


1+𝑔 𝑛
1−( 1+𝑟 ) (1+𝑟)𝑛 −(1+𝑔)𝑛
Annuity: PV = 𝐶 ( ) 𝑭𝑽 = 𝐶 ( )
𝑟−𝑔 𝑟−𝑔




𝐶 𝐷𝑡+1
Perpetuity: PV = & 𝑃0 =
𝑟−𝑔 𝑟𝑒−𝑔



𝑅𝑞𝑜𝑢𝑡𝑒𝑑 𝑚
EAR = (1 + ( 𝑚
) )−1




𝐷𝑡+1 +𝑃𝑡+1 −𝑃𝑡 𝐸(𝐷𝑡+1 )+𝐸(𝑃𝑡+1 )
Realized Return Rate: Rt+1 = Pt =
𝑃𝑡 1+𝐸(𝑟)



𝑇
Forward Price: F0, T = 𝑆0 (1 + 𝑟𝑟𝑓 )


𝐾
Put-Call-Parity: 𝐶 0 + 𝑇 = 𝑆0 + 𝑃0
(1+𝑟𝑟𝑓 )



𝐵 𝐶 −𝐶 𝑢𝐶𝑑−𝑑𝐶𝑢
Replicating portfolio Option price = 𝑆0 ∆ + 1+𝑟 , where ∆= 𝑆𝑢 −𝑆 𝑑 & 𝑩=
𝑟𝑓 𝑢 𝑑 𝑢−𝑑



𝑞𝐶𝑢 +(1−𝑞)𝐶𝑑 1+𝑟𝑟𝑓 −𝑑
Risk Neutral method: 𝐶0 = 1+𝑅𝑟𝑓
, where 𝑞 = 𝑢−𝑑
𝑎𝑛𝑑 𝑖𝑠 𝑟𝑖𝑠𝑘 𝑛𝑒𝑢𝑡𝑟𝑎𝑙 𝑝(𝑢𝑝𝑠ℎ𝑖𝑓𝑡)

• Cu & Cd are in relation to K whereas u & d are in relation to S0




E(R) = ∑ 𝑃𝑖𝑅𝑖
1
Var(R)= volatility2 = 𝜎 2 = ∑(𝑅𝑖 − 𝑅̅)2 = 𝑆𝐷2
𝑁−1

• 𝜎𝑅2 = ∑ 𝑃𝑖(𝑅𝑖 − 𝐸(𝑟))2