NO.PZ2020011303000208
问题如下：
The term structure is initially flat at 5%, and an investor buys a five-year bond with a face value of USD 100 and a coupon of 4% at a spread of ten basis points. At the end of six months the term structure is flat at 6% and the spread is zero. Carry out a P&L decomposition.
选项：
解释：
First we calculate the carry roll-down. The cash-carry is 2%. In this case, the assumption underlying the carry roll-down is that the term structure remains flat at 5%. (This is true for all three definitions of carry roll-down.) The initial price paid for the bond is
The price of the bond, if six months passes without rates changing or the spread changing, is
The carryroll-down is therefore: 2+95.626-95.199=2.427
This can also
be calculated as 0.0255 × 95.199.
The value of
the bond at the end of six months, assuming no spread change, is
After the
spread change is considered, the value of the bond is
This leads to
the following table
The bond price in six months is 92.214 and the investor receives a coupon of 2.000 just before
92.214 + 2.000－95.199 = ﹣0.985
The P&L decomposition splits this into:
(a) A carry roll-down of 2.427,
(b) The impact of a term structure change of -3.782, and
(c) A spread change of 0.370.
﹣0.985 = 2.427－3.782 + 0.370
The term structure is initially flat at 5%, and an investor buys a five-year bond with a face value of USD 100 and a coupon of 4% at a spread of ten basis points. At the end of six months the term structure is flat at 6% and the spread is zero. Carry out a P&L decomposition.
