NO.PZ202112010200000102
问题如下:
A Sydney-based fixed-income portfolio manager is considering the following Commonwealth of Australia government bonds traded on the ASX (Australian Stock Exchange):
The manager is considering portfolio strategies based upon various interest rate scenarios over the next 12 months. She is considering three long-only government bond portfolio alternatives, as follows:
- Bullet: Invest solely in 4.5-year government bonds
- Barbell: Invest equally in 2-year and 9-year government bonds
- Equal weights: Invest equally in 2-year, 4.5-year, and 9-year bonds
The manager estimates that accelerated economic growth in Australia will increase the level of government yields-to-maturity by 50 bps.
Under this scenario, which of the three portfolios experiences the smallest decline in market value?
选项:
A.Bullet
portfolio
Barbell portfolio
Equally weighted portfolio
解释:
A is correct. The change in portfolio value due to a rise in Australian government rate levels may be calculated using Equation:
%∆PVFull ≈ -(ModDur × ΔYield) + [½ × Convexity × (ΔYield)2],where ModDur and Convexity reflect portfolio duration and convexity, respectively. Therefore, the bullet portfolio declines by 2.093%, or -2.093% = (-4.241 × 0.005) + [0.5 × 22.1 × (0.0052)],
followed by a drop of
2.343% for the equally weighted portfolio, or
-2.343% = (-4.779 ×
0.005) + [0.5 × 37.4 × (0.0052)],
and a drop of 2.468%
for the barbell portfolio, or
-2.468% = (-5.049 × 0.005) + [0.5 × 45.05 × (0.0052)].
我记得老师上课就有一道例题,说不能直接求一个平均的Duration和convexity,而是应该分别计算每一只债券的价格变动再加一起,为啥答案的算法直接取一个平均了呢