Formula Sheet - FII - Lösningar och formler för fek 2 och introduction to financial derivatives PDF

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Lösningar och formler för fek 2 och introduction to financial derivatives...

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Finance II – Formula sheet Arithmetic average =

∑𝑛𝑖=1 𝑟𝑖 𝑛 1

Geometric average = [(1 + 𝑟1 )(1 + 𝑟2 )(1 + 𝑟3 ) … (1 + 𝑟𝑛 )] 𝑛 − 1 Holding Period Return (HPR) = [(1 + 𝑟1 ) ∗ (1 + 𝑟2 ) ∗ (1 + 𝑟3 ) … (1 + 𝑟𝑛 )] − 1 Asset return (one asset) =

𝑃1−𝑃0 𝑃0

Expected Return (probabilities) = E(r) = ∑𝑛𝑖=1 𝑝𝑖 𝑟𝑖 Expected Return (weights) = E(r) = ∑𝑛𝑖=1 𝑤𝑖 𝑟𝑖 Variance (probabilities) = 𝜎𝑟2 = ∑ 𝑛𝑖=1 𝑝𝑖 [𝑟𝑖 − 𝐸(𝑟)]2 Variance (historical) = 𝜎𝑟2 =

∑𝑛𝑖=1 (𝑟𝑖 −𝑟 )2 (𝑛−1)

Variance (portfolio) = 𝜎𝑝2 = 𝑤𝑆2 𝜎𝑆2 + 𝑤𝐵2 𝜎𝐵2 + 2𝑤𝑆 𝑤𝐵 𝐶𝑂𝑉𝑆,𝐵 Covariance (S,B) = 𝐶𝑂𝑉𝑆,𝐵 = 𝜎𝑆,𝐵 = 𝜌𝑆,𝐵 𝜎𝑆 𝜎𝐵 Beta = 𝛽𝑖 =

𝐶𝑂𝑉𝑖,𝑚 𝜎𝑚2

CAPM = 𝐸(𝑟𝑖 ) − 𝑟𝑓 = 𝛼𝑖 + 𝛽𝑖 [𝐸(𝑟𝑚 ) − 𝑟𝑓 ] Sharpe ratio =

(𝑟𝑝 −𝑟𝑓) 𝜎𝑝

Treynor measure =

(𝑟𝑝−𝑟𝑓) 𝛽𝑝

M2 performance measure = 𝑟𝑝∗ − 𝑟𝑚

where 𝑟𝑝∗ = 𝑟𝑝 ∗

𝜎𝑚 𝜎𝑝

𝜎

+ 𝑟 𝑓 ∗ (1 − 𝜎𝑚) 𝑝

𝐸

Return in home currency = 1 + 𝑟(𝐻𝑂𝑀𝐸) = [1 + 𝑟(𝐹𝑂𝑅𝐸𝐼𝐺𝑁)] 𝐸 1 0

𝑤ℎ𝑒𝑟𝑒 𝐸 = 𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒 𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑒𝑑 𝑖𝑛 𝐻𝑂𝑀𝐸 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑜𝑓 𝐹𝑂𝑅𝐸𝐼𝐺𝑁 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑀𝑎𝑟𝑔𝑖𝑛 =

𝐸𝑞𝑢𝑖𝑡𝑦 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠

=

(𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒𝑠 ∗ 𝑠ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒 − 𝑑𝑒𝑏𝑡) 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒𝑠 ∗ 𝑠ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒 1

Utility function = 𝑈 = 𝐸(𝑟) − 𝐴𝜎 2 where U = Utility and A = risk aversion 2

Weight in asset D to optimize Optimal Risky Portfolio (given a two asset portfolio consisting of D and E):

Weight in the Optimal Risky Portfolio for an individual’s Optimal Complete Portfolio = y Maculay Duration =

∑𝑇𝑡=1

𝑡 ∗ 𝑤𝑒𝑖𝑔ℎ𝑡𝑡, where 𝑤𝑒𝑖𝑔ℎ𝑡𝑡 =

=

𝐸(𝑟𝑝) −𝑟𝑓 𝐴𝜎𝑝2

𝐶𝐹𝑡 /𝑝𝑟𝑖𝑐𝑒 (1+𝑦)𝑡

𝐶𝐹𝑡 = 𝑐𝑎𝑠ℎ𝑓𝑙𝑜𝑤 𝑜𝑓 𝑡ℎ𝑒 𝐵𝑜𝑛𝑑 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡 (t = years to maturity) y = discount rate price = price of the Bond Put-Call-Parity: 𝐶 + C = Price of Call T = time to maturity

𝑋 (1+𝑟𝑓 )𝑇

= 𝑆0 + 𝑃 X = Strike price 𝑆0 = Price of underlying asset at time 0

𝑟𝑓 = Risk free rate P = Price of Put...