[SOLVED] 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 = sM : systematic risk non-diversifiable
si: idiosyncratic risk diversifiable
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 j) and the risk-free asset (fraction 1j)
ej =jeM +(1j)rf =rf +j(eM rf)

Alternative interpretation of
To infer j, regress the actual (historical) excess asset return,
Rj rf, on excess market return RM rf:
Rj rf =j +j(RM rf)
From econometrics, we remember that regression coefficient j = cov(Rj,RM)
Therefore, j indicates how the specific asset co-moves with the
> 1 asset is more volatile than the market
0 < < 1 asset is less volatile than the market < 0 asset moves in opposite direction rare and usefulWhat about j? It should be 0 in theory. Chasing . Security market lineWith different value, the required return for any asset is e=rf +(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 +j,1f1+,…,+j,KfK +j, Rj is the expected return of the asset (or portfolio) j j idiosyncratic, unexplained part of return E(j) = 0, E(Rj) = ej rf is the risk-free rate fk is the factor risk premium j,k is the sensitivity of portfolio j to factor k K is the number of factors.Assumptions (similar to standard OLS): exogeneity: j and factors fk are independent j for different assets are independentThis is not pure arbitrage, but statistical arbitrage CS: assignmentchef QQ: 1823890830 Email: [email protected]