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3. Asset Pricing Theory Apt Notes

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This is an extract of our 3. Asset Pricing Theory Apt document, which we sell as part of our Corporate Finance Notes collection written by the top tier of University Of London (examined By LSE) students.

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Arbitrage Pricing Theory (APT)
Single-factor Model and Multi-factor Model
Single-factor Model ri = i + 1ii F1i + i r = Actual E(Ri)
 = E(R)
 = sensitivity to F
F = common factor (e.g. Index, Inflation, Interest Rate Risk, Oil Price, etc.)
 = Random Shock / Idiosyncratic Return / Unsystematic Risk
Capturing Surprise Changes
 E() = 0
 E(F) = 0
 Cov(i, F1i) = 0, Cov(i, j) = 0
Multi-factor Model (N factors)
ri = i + 1ii F1i + 2ii F2i + 3ii F3i + … + Ni F1i + i
Factor-replicating Portfolio (2-factor Model)
ri = i + 1ii F1i + 2ii F2i + i
Relation between Expected Returns and Factor Sensitivities
E(R) = RF + 1i P1i + 2i P2i+ … + N PN
P = Risk Premium of Factor
Note:  = 0, as Portfolio A, B & C are assumed to be well-diversified
Portfolio A:

rA = A + 1iA F1i + 2iA F2i

Portfolio B:

rB = B + 1iB F1i + 2iB F2i

Portfolio C:

rC = C + 1iC F1i + 2iC F2i

Weighting ()
Weighting for Portfolio A = A
Weighting for Portfolio B = B
Weighting for Portfolio C = C

1i

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