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天天_mama · 2021年01月31日

问一道题:NO.PZ201812020100000601 第1小题 [ CFA III ]

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问题如下:

The portfolio strategy implemented by McLaughlin last year is mostly likely to be described as:

选项:

A.

a carry trade.

B.

a barbell structure.

C.

riding the yield curve.

解释:

C is correct.

Last year, McLaughlin expected the yield curve to be stable over the year. Riding the yield curve is a strategy based on the premise that, as a bond ages, it will decline in yield if the yield curve is upward sloping. This is known as "roll down"; that is, the bond rolls down the (static) curve. Riding the yield curve differs from buy and hold in that the manager is expecting to add to returns by selling the security at a lower yield at the horizon. This strategy may be particularly effective if the portfolio manager targets portions of the yield curve that are relatively steep and where price appreciation resulting from the bond’s migration to maturity can be significant. McLaughlin elected to position her portfolio solely in 20-year Treasury bonds, which reflect the steepest part of the yield curve, with the expectation of selling the bonds in one year.

老师,不太明白何璇老师讲的,在intra-market carry trade 中futures的FP=(P-PVC)(1+r)的T次方,为什么要减掉PVC? 

1 个答案

发亮_品职助教 · 2021年02月01日

嗨,从没放弃的小努力你好:


“在intra-market carry trade 中futures的FP=(P-PVC)(1+r)的T次方,为什么要减掉PVC? ”


先忽略PVC0,我们Futures的定价为:

FV = PV ×(1+Rf)^T



上面公式的意思是:我们约定在未来T时刻买入债券,买入价就是现在债券现值PV复利到未来T时刻。

注意,债券的PV现值,是债券未来所有现金流的折现求和。Futures约定在未来T时刻购买债券,用现值PV进行复利到T时刻定价实际上是不公平的。

 


PV现值是债券未来所有现金流的折现求和,他既包括T时刻之前的Coupon,也包括T时刻之后的Coupon,我们Long futures的一方是约定在T时刻购买债券,只能拿到T时刻之后的Coupon,无法拿到T时刻之前的Coupon,因此在给Futures定价时,定的T时刻买价只能是T时刻之后的现金流折到T时刻。

由于我们是以0时刻的PV为基础计算Futures里约定的价格,PV包含T时刻之前的Coupon,我们需要把T时刻之前的Coupon从PV里扣掉,这样剩余部分只是T时刻之后现金流在0时刻的现值,我们再把这些现金流复利到T时刻就是T时刻Futures定的买价了。

我们把拿不到的Coupon在0时刻的现值记为PVC0;所以定价公式为:

FV = (PV-PVC0) ×(1+Rf)^T

也就是债券的现值,减去T时刻之前拿不到的Coupon的现值,以此为基础再复利到T时刻,就是我们Long方在T时刻购买债券的价格。


这是一个十分公平的购买价,因为Long方只能拿到T时刻以后的现金流,所以在T时刻的购买价也刚好扣掉了T时刻之前的Coupon。


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