# 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?

### 1 個解答

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Lv 5
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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