經濟,財務,統計學,數理科學與政治評論

Hello there:

  這裡要替後面的Interest Rate相關的證券進行理論與基礎的鋪陳!

-----------------------------------------------------------------

 幾個概念請自行參閱相關資料與書籍:

  1. Yield Curve Shapes:Parallel Shift, Nonparallel Shift, Positive Butterfly Shift, Negative Butterfly Shift 

  2. Treasury Bond Yields --> Bootstrapping --> Treasury Spot rates

  3. The beneficial of Swap rates information over the traditional Treasury yield curve

     (no sovereign but only credit risk)

  4. Pure (Unbiased) Expectation Theory 

     (the implications of upward-sloping, flat or downward-sloping yield curve)

  5. Liquidity Preference Theory (the liquidity premium)

  6. Preferred Habitat Theory

    a. positive or negative risk premium instead of liquidity premium

    b. the risk premium is not necessary related to maturity

 (小結)4,5,6均能用來解釋Yield Curve的變動,但甚麼Yield curve變動都能解釋的是5或6!!!

-----------------------------------------------------------------

 The Key Rate Duration

  傳統的Duration概念是用在殖利率曲線的small parallel shift上面,對於non-parallel shift採用key rate duration是比較好的!!

  1. The total change in value if all rates change by the same number of basis points is the effective duration of a security or portfolio to a parallel shift in rates.

  2. 一般教科書對於Key Rate Duration的定義是 a. Yield curve risk is measured by changing the spot rate for a particular key maturity and determining the sensitivity of a security or portfolio to the change holding the spot rate for other key maturities constant. b. The sensitivity of the change in value to a particular change in spot rate is called rate duration. The Key Rate Duration is not one rate duration, but a vector of durations representing each maturity on the spot rate curve.

  用簡單的中文來說就是:今天我們可能遇到兩個portfolios其各自的effective duration是相同的,但其key rate duration的rate duration vector是不同的,因此除非今天遇到的是所有考量中的rate duration都平行上升或下降同樣basis points才會使得duration數值相同,否則我們將發現其durations數值是不同的!!

  至於計算請參閱Thomas S.Y. Ho "Key Rate Durations: Measure of Interest Rate" Journal of Fixed Income (Sep.,1992)

 舉一個例子好了:有兩個投資組合,組合一持有5mil. 2-yr bond與5 mil. 30-yrs bond,組合二持有10mil. 16-yrs bond.今天我們知道去採用三個key rates,分別為2-yr, 16-yr與30-yr!!今天其effective duration均為16(亦即對於三個key rates,當有100 bps下降時,其價格會上升16%),但組合一的key rate duration為[1,0,15],而組合二的key rate duration為[0,16,0]!相對上Key rate duration確實能夠應付non-parallel yield shift的情境!!