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請問大家幫忙回答有關投資學計算問題? +10點喔

1.A nine-year bond has a yield of 10% and a duration of 7.194 years. If the bond's yield changes by 50 basis points, what is the percentage change in the bond's price?

2.Find the duration og a 6% coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of 6%. What is hte duration if the yield to maturity is 10%?

3.A pension plan is obligated to make disbursements of $1 million, $2million, and $1 million at the end of each of the next three years, respectively. Find the duration of the plan's obligations if the interest rate is 10% annually?

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    1 0 年前
    最佳解答

    公式:Duration=(∑CF(t)×t/(1+y)^t)/(∑CF(t)/(1+y)^t)=(∑PV(CF(t))×t)/(Bond Price)

    債券價格上漲(下跌)幅度(%)=成交殖利率下跌(上漲)幅度(%) ×該期債券目前之存續期間 ∆P/P=∆i/(1+i)×D

    <sol>:1. ∆P/P=0.5%×7.194=3.597%

    2.(1)因為票面利率與到期殖利率相等,所以債券價格為面額$1,000(你沒告之面額為多少,所以我就自己假設為$1,000)

    Duration=(60/1.06+2×60/1.06^2+3×1060/1.06^3)/1000=2.8334

    (2)當到期殖利率=10%時,債券價格為60/1.1+60/1.1^2+1060/1.1^3=900.53

    所以Duration=(60/1.1+2×60/1.1^2+3×1060/1.1^3)/900.53=2.8238

    3.為了計算方便,我把“萬”給省了。

    這三筆退休金的現值為100/1.1+200/1.1^2+300/1.1^3=481.59

    所以Duration=(100/1.1+2×200/1.1^2+3×300/1.1^3)/481.59=2.2793

    2007-06-08 20:56:57 補充:

    對不起,第1題漏了一部分

    ∆P/P=0.5%/1.1×7.194=3.27%

    2007-06-10 19:37:32 補充:

    因為你第1題只寫利率變動50基本點,所以若是上揚50基本點,則債劵價格下跌3.27%;若下跌50基本點,則債劵價格上漲3.27%。價格與利率走勢呈反比。

    我應把公式重新寫過 ∆P/P=-∆i/(1+i)×D

    參考資料: 自己
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