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%

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?

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

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％。

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。

gosh...这道题看一眼，最多用20秒，就知道只能选d,不需要计算具体结果。