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holicess · 2024年01月04日

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NO.PZ202208260100000404

问题如下:

A client seeking advice on her fixed-income portfolio observes the price and yield-to-maturity of one-year (r1) and two-year (r2) annual coupon government benchmark bonds currently available in the market. Which of the following statements best describes how the analyst can determine a breakeven reinvestment rate in one year's time to help decide whether to invest now for one or two years?

选项:

A.

As the two-year rate involves intermediate cash flows, divide the square root of (1 + r2 ) by (1 + r1) and subtract 1 to arrive at a breakeven reinvestment rate for one year in one year's time.

B.

Since the first year's returns are compounded in the second year, set (1 + r1 ) multiplied by 1 plus the breakeven reinvestment rate equal to (1 + r2 )2 and solve for the breakeven reinvestment rate.

C.

Since the breakeven reinvestment involves a zero-coupon cash flow, first substitute the one-year rate r1 ) into the two-year bond price equation to solve for the two-year spot or zero rate (z2 ), then set (1 + r1 ) × (1 + breakeven reinvestment rate) = (1 + z2 )2 and solve for the breakeven reinvestment rate.

解释:

Solution

C is correct.

The one-year annual rate equals the one-year zero rate, as it involves a single cash flow at maturity (z1 = r1). Since the breakeven reinvestment rate involves a single cash flow at maturity, substitute the one-year rate (r1) into the two-year bond price equation to solve for z2, then set (1 + r1) × (1 + breakeven reinvestment rate) = (1 + z2)2 and solve for the breakeven reinvestment rate (IFR1,1).

中文解析:

本题考察的是计算Implied forward rates(IFR),也就是题干说的:观察到市场上现有的一年期(r1)和两年(r2)年期政府基准债券的价格和到期收益率,想确定一年内的盈亏平衡再投资率。

考察的公式为:


基于此公式,只有C选项描述正确。

这几个rate怎么区分?r1/r2/z2/breakeven point rate

1 个答案

pzqa35 · 2024年01月04日

嗨,从没放弃的小努力你好:


这道题问的是breakeven reinvestment rate的计算,也就是求implied forward rate

而implied forward rate都是基于zero-rate来做计算,也就是零息债券的收益率。根据题目我们可以看到这个债券是按年付息的,那么r1只有一笔现金流就是到期日才会拿到,所以就是零息债券,那么r1=z1,但是r2是会有期间现金流的,所以需要把r2转化成z2,最终求的IFR。转化的过程就是【CF1/(1+z1)】+【CF2/(1+z2)2】=债券价格,最终计算出Z2.

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努力的时光都是限量版,加油!

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