[SOLVED] 程序代写 Lesson 8: Capital Asset Pricing Model

Lesson 8: Capital Asset Pricing Model
Economics of Finance
School of Economics, UNSW

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Capital allocation line
A maximum Sharpe ratio is obtained for any portfolio on the straight line from rf tangent with the efficient frontier at M. This line is called capital allocation line (CAL).

Systematic vs Idiosyncratic Risk
sABC = sp + si
• sp = βsM : systematic risk – non-diversifiable
• si: idiosyncratic risk – diversifiable
• β ≡ x: share invested in the market portfolio to replicate e

Capital Asset Pricing Model
Capital asset pricing model (CAPM) is a model used to determine an appropriate expected return of any asset
• only systematic risk is valued
• replicate any desired expected asset return ej using the market portfolio (fraction βj) and the risk-free asset (fraction 1–βj)
ej =βjeM +(1−βj)rf =rf +βj(eM −rf)

Alternative interpretation of β
To infer βj, regress the actual (historical) excess asset return,
Rj −rf, on excess market return RM −rf:
Rj −rf =αj +βj(RM −rf)
From econometrics, we remember that regression coefficient βj = cov(Rj,RM)
Therefore, βj indicates how the specific asset co-moves with the
• β > 1 asset is more volatile than the market
• 0 < β < 1 asset is less volatile than the market• β < 0 asset moves in opposite direction – rare and usefulWhat about αj? It should be 0 in theory. “Chasing” α. Security market lineWith different β value, the required return for any asset is e=rf +β(eM −rf) Arbitrage Pricing Theory (APT)CAPM provides good benchmark, but reality is more complicated: market risk is just one factor, but there are othersRj =rf +βj,1f1+,…,+βj,KfK +εj,• Rj is the expected return of the asset (or portfolio) j• εj idiosyncratic, unexplained part of return E(εj) = 0, E(Rj) = ej• rf is the risk-free rate• fk is the factor risk premium• βj,k is the sensitivity of portfolio j to factor k• K is the number of factors.Assumptions (similar to standard OLS):• exogeneity: εj and factors fk are independent • εj for different assets are independentThis is not pure arbitrage, but statistical arbitrage程序代写 CS代考加微信: assignmentchef QQ: 1823890830 Email: [email protected]