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[CFA Level 1] 请教一道LV1题目。急。

an investor has a 1-year, 10% semiannual coupon bond with a price of $975. if the 6-month Treasury bill(T-bill) has a holding period yield of 6%, what is the 1-year theoretical spot rate on a bond equivalent basis?

A6.4% B.8.7% C.9,9% D. 12.8%

我算了好久,不知道怎么算,大家帮帮忙,谢谢!

50/(1 + 6%) + 1050/(1+X%)^2 = 975

calculate X%: 6.38%

so, 1-year theoretical spot rate on a bond equivalent basis is 2 * 6.38% = 12.76%

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能给解释一下为什末这样计算吗?看不大懂。

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不同意二楼的算法。

我对Treasury bill(T-bill) has a holding period yield of 6%的理解为 annual yield 6%.

975 = 50/(1+6%/2) + 1050/(1+x/2)^2

answer x = 12.9%.

D.

how?

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QUOTE:
以下是引用kimbol在2007-4-28 0:11:00的发言:

不同意二楼的算法。

我对Treasury bill(T-bill) has a holding period yield of 6%的理解为 annual yield 6%.

975 = 50/(1+6%/2) + 1050/(1+x/2)^2

answer x = 12.9%.

D.

how?

同意!

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The period during which you own an investment is called its holding period, and the return for that period is the holding period
return (HPR).

HPR=Ending Value of Investment/Beginning Value of Investment

holding period yield (HPY). The HPY is equal to the HPR minus 1

To derive an annual HPY, you compute an annual HPR and subtract 1. Annual HPR is found by:
       Annual HPR = HPR^1/n, where: n = number of years the investment is held

So, holding period yield of 6% should be semi-annual rate

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HPR和HPY就是一个,看notes book1 P107对holding period yield的解释就知道了

2楼的做法正确

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不好意思,50和1050是哪里来的?

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QUOTE:
以下是引用MrChildren在2007-5-8 10:12:00的发言:

HPR和HPY就是一个,看notes book1 P107对holding period yield的解释就知道了

2楼的做法正确

同意,HPY并没有要求annualize,treasury bill是6个月的话,那么6%就是6个月的yield.

从另外一方面讲,如果答案是12.9%,不可能四舍五入到12.8%,只有12.76%可能round up到12.8%。

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QUOTE:
以下是引用ysheen在2007-5-10 18:07:00的发言:
不好意思,50和1050是哪里来的?

把bond看作是几段不同时间的cash flow,6个月时有$50的coupon,到了1年的时候,有另外$50的coupon和$1000的principal,加在一起就是$1050。换句话说就是把一个bond拆成n段cash flow,其中n=2*t (t是time to maturity),把每一段cash flow看做是一个zero coupon bond来找它的yield

找1-yr的spot rate其实就是找1-yr的zero coupon bond的yield,因为bond一般都是半年算一次coupon,所以找yield的时候都每半年discount一次。

对于第一段6-month cash flow - $50,treasury bill的yield就可以直接使用,因为treasury bill本身就是一个zero coupon bond. 对于第二段1-yr cash flow - $1050,则需要用要求的yield每半年discount一次来找到present value。

所以得到 975=50/(1+6%)+1050/(1+x/2)^2,解出来x=12.76%,2楼正解。

这种方法叫做bootstrapping,经常用于construct yield curve。

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