經濟,財務,統計學,數理科學與政治評論

寫在前面:這裡我們將很簡單的介紹一下International CAPM,爾後就再回到Portfolio management的一些注意事項中,畢竟財務實務上面重視的還是評價,因此最後談的是Private Equity Valuation!!以後有機會的話,預計是七月之後,會跟大家談財務風險管理與其一些相關子議題!!

Hello there:

   這裡要簡單談一下International CAPM!!前提是:這是一個integrated world,所有人都能夠自由的用各國的無風險利率進行投資與借貸!!

(1)the foreign currency risk premium (FCRP)

  r(.):risk free rate of specified country,

  So: the direct-quote spot rate,

  a. the foreign currency risk premium

 = E[(S(T) - So)/So] - [r(domestic) - r(foreign)]

 = [E(S(T)) - So]/So - (F - So)/So

 = (E(S(T)) - F)/So 

  因為(F - So)/So = [r(domestic) - r(foreign)]

  by the covered interest rate parity

  b. 若F為S的不偏估計式,所以 F = E(S(T)),則the foreign currency risk premium為零!!!

     這裡面說明了當Forward rate為future spot rate的不偏估計式時,

     其中隱含的是foreign exchange rate可以完全透過Foreign exchange

     Forward rate contract來規避風險,因此所有的匯率風險就消失了,

     那International CAPM就回歸到傳統的CAPM了!!!

(2)先看一下relative PPP與real exchange rate的關係

 a. X: real exchange rate,

    S: direct-quote nominal exchange rate,

    P(FC): the price level of foreign currency,

    P(DC): the price level of domestic currency,

    X = S * [P(FC)/P(DC)]

  對上式取自然對數然後做微分,我們知道

  x = s - [Infl(DC) - Infl(FC)]

  其中 x = 實質匯率變動率,

       s = 名目匯率變動率,

      Infl(DC): the inflation rate of domestic,

      Infl(FC): the inflation rate of foreign.

 b. 若relative PPP是成立的,

    我們知道 s = [Infl(DC) - Infl(FC)], i.e., x = 0!!!

   => 名目匯率的變動率完全來自於兩地通貨膨脹率的差距!!

 c. 在international CAPM中, relative PPP並不成立!!!

    亦即名目匯率的變動不完全來自兩地通貨膨脹率的變動差異!!

(3)Asset Returns與Exchange Rate的關係

   V(DC): the value in terms of domestic currency,

   V(FC): the value in terms of foreign currency,

   S: the direct-quote exchange rate,

   V(DC) = V(FC) * S

  對上式取自然對數然後做微分,我們知道

   R = R(FC) + s

  => the hedged return is

     R = R(FC) + [F - So]/So

  a. unhedged case

  E(R) = E(R(FC)) + E(s)

       = E(R(FC)) + [E(S(T) - So]/So

  b. hedged case

  E(R) = E(R(FC)) + [F -So]/So 

  c. the difference between the unhedged case and the hedged case

     is the foreign currency risk premium!!

  FCRP = [E(S(T) - So]/So - [F -So]/So 

       = [E(S(T)) - So]/So - [r(domestic) - r(foreign)]

(4)The international CAPM

  E(R(i)) = Rf(Domestic)

          + Beta(i,world) *MRP(world)

          + Sum of (j = 1,2,....K; Sensitive(i,j) * FCRP(j)) 

(5)Currency exposure of a foreign asset

  Alpha = R/s

        = (R(FC) + s)/s

        = R(FC)/s + 1

        = Alpha(FC) + 1

  i.e., the currency exposure of a foreign asset is equal to its local currency exposure plus 1.

(6) the ex-post return

 R(DC) = E(R(FC)) + nominal change in FC w.r.t. DC

       = E(R(DC)) + real change in FC w.r.t. DC

 其中 E(R(.)) is the ex-ante expected return

note. 其他關於ICAPM的理論與實務等等,請自行參閱書籍與論文!!