經濟,財務,統計學,數理科學與政治評論

Hello there:

 (III) Macroeconomic Factor Model與Fundamental Factor Model

  a. Macroeconomic Factor Model 

R(i) = E(R(i)) + Sum of (j = 1,2,3,...,n; b(i,j) * F(j)) + Errorterm(i)

  其中

   E(F(j)) = 0 , E(Errorterm(j)) = 0,

   F(j): Surprise  in the factor j, j = 1,2,...,n

   Errorterm(j) : 無法由Factors來解釋的證券i個別因素

   E(R(i)) is the expected return from the APT idea!!

  這裡的b(.,.)數值是需要透過迴歸去估計的!!

  而F(j)透過兩個資訊求出,一個是預期,一個是真實,因此相減後為surprise!!

  b. Fundamental Factor Model

R(i) = a(i) + Sum of (j = 1,2,3,...,n; b(i,j) * F(j)) + Errorterm(i)

   其中

  a(i) is the coefficient estimate from the regression

  b(i,j)為Standardized beta, E(Errorterm(j)) = 0,

  b(i,.)

 = [Asset i's attribute value - Average attribute value]/SD(Attribute values)

   這個 factor sensitive value是事前給定的,

   我們要估計的是F(.),the factor return through regression!!

   E(R(i)): the expected return of specified stock or asset!!

(IV) Active Poertfolio with respective risk ideas

    a. Tracking Error(TE) and Information Ratio(IR)

    TE(Portfolo,Benchmark) = SD(R(Portfolio) - R(Benchmark)),

    SD(.) is the standard deviation

    IR = [E(R(Portfolio)) - E(R(Benchmark))]/TE(Portfolio,Benchmark),

    E(.) is the expectation of specified portfolio

    b. Active return

    = R(Portfolio) - R(Benchmark)

    = Sum of [j = 1,2,...,n; (Portfolio sensitivity(j) - Benchmark sensitivity(j)) * Factor return (j)] + Asset selection

    =  Beta-type risk component + Alpha-trye risk component

    Active Return risk

    = Active factor risk (Beta-type risk)

     + Active specific risk or asset selection risk (Alpha-type risk)