Finanzas Operativas Hoja de formulas Nombre y apellido: ______________________________ LU:_______________ Rendimiento de Activos Financieros 𝑟𝑡,𝑇 = 𝑃𝑇 + 𝐼𝑡,𝑇 − 𝑃𝑡 𝑃𝑡 Tasas de Interés 𝐶1 = 𝐶0 ∗ (1 + 𝑖0,1 ) 𝐶0 = 𝐶1 ∗ (1 − 𝑑0,1 ) 𝐼0,1 = 𝐶𝑜 ∗ 𝑖0,1 𝐷0,1 = 𝐶1 ∗ 𝑑0,1 𝑖𝑡 = 𝑇𝑁𝐴𝑡 ∗ 𝑡 365 𝑑𝑡 = 𝑇𝑁𝐴𝐴𝑡 ∗ 𝑡 365 𝑇𝑁𝐴𝑡 = 𝑖𝑡 ∗ 365 𝑡 𝑇𝑁𝐴𝐴𝑡 = 𝑑𝑡 ∗ 365 𝑡 𝑖𝑡 = 𝑑𝑡 1 − 𝑑𝑡 𝑖𝑞 = 𝑖𝑡 ∗ 𝑑𝑡 = 𝑞 𝑡 𝑖𝑡 1 + 𝑖𝑡 𝑑𝑞 = 𝑑𝑡 ∗ 𝑞 𝑡 𝑞 𝑖𝑞 = (1 + 𝑖𝑡 ) 𝑡 − 1 Capitalización Simple y Compuesta 𝐶𝑛 = 𝐶0 ∗ (1 + 𝑖1 + 𝑖2 + ⋯ + 𝑖𝑛 ) 𝐶𝑛 = 𝐶0 ∗ (1 + 𝑖1 ) ∗ (1 + 𝑖2 ) ∗ … ∗ (1 + 𝑖𝑛 ) 𝐶𝑛 = 𝐶0 ∗ (1 + 𝑖 ∗ 𝑛) 𝐶𝑛 = 𝐶0 ∗ (1 + 𝑖)𝑛 𝐼0,𝑛 = 𝐶0 ∗ (𝑖1 + 𝑖2 + ⋯ + 𝑖𝑛 ) 𝐼0−𝑛 = 𝐶0 ∗ [(1 + 𝑖1 ) ∗ (1 + 𝑖2 ) ∗ … ∗ (1 + 𝑖𝑛 ) − 1] 𝐼0,𝑛 = 𝐶0 ∗ 𝑖𝑡 ∗ 𝑛 𝐼0,𝑛 = 𝐶0 ∗ [(1 + 𝑖)𝑛 − 1] 𝑖0,𝑛 = 𝐶𝑛 −1 𝐶0 Fisher (1 + 𝑖𝑎 ) = (1 + 𝑖𝑟 ) ∗ (1 + 𝜋 ) Descuento simple 𝐶0 = 𝐶𝑛 ∗ (1 − 𝑑 ∗ 𝑛) 𝐷0,𝑛 = 𝐶𝑛 − 𝐶0 𝐶 𝑑0,𝑛 = 1 − 𝐶0 𝑛 1 Finanzas Operativas Nombre y apellido: ______________________________ LU:_______________ Rentabilidad y Riesgo de un Portafolio de “n” activos 𝑛 𝐸(𝑟) = 𝑟̅ = ∑ 𝑤𝑖 ∗ 𝑟̅𝑖 = 𝑤1 ∗ 𝑟̅1 + 𝑤2 ∗ 𝑟̅2 + ⋯ + 𝑤𝑛 ∗ 𝑟̅𝑛 𝑖=1 𝜎𝑝2 = 𝑤12 ∗ 𝜎12 + 𝑤22 ∗ 𝜎22 + ⋯ + 𝑤𝑛2 𝜎𝑛2 + 2 ∗ 𝑤1 ∗ 𝑤2 ∗ 𝜎1,2 + ⋯ + 2 ∗ 𝑤𝑛−1 ∗ 𝑤𝑛 ∗ 𝜎𝑛−1,𝑛 𝐶𝑂𝑉(𝑖, 𝑗) = 𝜎𝑖,𝑗 = 𝜌𝑖,𝑗 ∗ 𝜎𝑖 ∗ 𝜎𝑗 Rentabilidad y Riesgo de un Portafolio de 2 activos 𝐸(𝑟𝑝 ) = 𝑟̅𝑝 = 𝑤𝐴 ∗ 𝑟̅𝐴 + 𝑤𝐵 ∗ 𝑟̅𝐵 𝜎𝑝2 = 𝑤𝐴2 ∗ 𝜎𝐴2 + 𝑤𝐵2 ∗ 𝜎𝐵2 + 2 ∗ 𝑤𝐴 ∗ 𝑤𝐵 ∗ 𝜎𝐴,𝐵 𝐶𝑂𝑉(𝐴, 𝐵) = 𝜎𝐴,𝐵 = 𝜌𝐴,𝐵 ∗ 𝜎𝐴 ∗ 𝜎𝐵 Valor Futuro/ Valor Actual/ VAN 𝑖𝑡 = 𝑇𝑁𝐴𝑡 ∗ 𝑡 365 𝑉𝐴 = 𝐶 1 1 − (1 + 𝑖)−𝑛 ∗ [1 − ó 𝑉𝐴 = 𝐶 ∗ ] (1 + 𝑖)𝑛 𝑖 𝑖 𝑉𝐴 = 𝐶 1 1 − (1 + 𝑖)−𝑛 (1 ∗ [1 − ∗ + 𝑖) ó 𝑉𝐴 = 𝐶 ∗ ∗ (1 + 𝑖) ] (1 + 𝑖)𝑛 𝑖 𝑖 𝑉𝐹 = [(1 + 𝑖)𝑛 − 1] 𝐶 ∗ [(1 + 𝑖)𝑛 − 1] ó 𝑉𝐹 = 𝐶 ∗ 𝑖 𝑖 [(1 + 𝑖)𝑛 − 1] 𝐶 𝑛 [(1 (1 𝑉𝐹 = ∗ + 𝑖) − 1] ∗ + 𝑖) ó 𝑉𝐹 = 𝐶 ∗ ∗ (1 + 𝑖) 𝑖 𝑖 𝑉𝐴 = 𝑉𝐹 (1 + 𝑖)𝑛 𝑉𝐹 = 𝑉𝐴 ∗ (1 + 𝑖)𝑛 𝑉𝐴𝑁 = −𝐼𝑛𝑣. 𝐼𝑛𝑖𝑐𝑖𝑎𝑙 + 𝑉𝐴FF