NO.PZ201812020100001202
问题如下：
Chaopraya is an investment advisor for high-net-worth individuals. One of her clients, Schuylkill, plans to fund her grandson’s college education and considers two options:
- Option 1 Contribute a lump sum of $300,000 in 10 years.
- Option 2 Contribute four level annual payments of $76,500 starting in 10 years.
The grandson will start college in 10
years. Schuylkill seeks to immunize the contribution today.
For Option 1, Chaopraya calculates the
present value of the $300,000 as $234,535. To immunize the future single outfow,
Chaopraya considers three bond portfolios given that no zero- coupon government
bonds are available.
The three portfolios consist of non-callable,
fixed-rate, coupon-bearing government bonds considered free of default risk.
Chaopraya prepares a comparative analysis of the three portfolios, presented in
Exhibit 1.
Chaopraya evaluates the three bond portfolios and selects one to recommend to Schuylkill.
Schuylkill
and Chaopraya now discuss Option 2. Chaopraya estimates the present value of
the four future cash flows as $230,372, with a money duration of $2,609,700 and
convexity of 135.142. She considers three possible portfolios to immunize the
future payments, as presented in Exhibit 2.
Determine
the most appropriate immunization portfolio in Exhibit 2. Justify your
decision.
选项：
解释：
Answer:
Justification:
Portfolio
2 is the most appropriate immunization portfolio because it is the only one
that satisfies the following two criteria for immunizing a portfolio of
multiple future outflows:
- Money Duration: Money durations of all three possible immunizing portfolios match or closely match the money duration of the outflow portfolio. Matching money durations is useful because the market values and cash flow yields of the immunizing portfolio and the outflow portfolio are not necessarily equal.
- Convexity: Given that the money duration requirement is met by all three possible immunizing portfolios, the portfolio with the lowest convexity that is above the outflow portfolio’s convexity of 135.142 should be selected. The dispersion, as measured by convexity, of the immunizing portfolio should be as low as possible subject to being greater than or equal to the dispersion of the outflow portfolio. This will minimize the effect of non-parallel shifts in the yield curve. Portfolio 3’s convexity of 132.865 is less than the outflow portfolio’s convexity, so Portfolio 3 is not appropriate. Both Portfolio 1 and Portfolio 2 have convexities that exceed the convexity of the outflow portfolio, but Portfolio 2’s convexity of 139.851 is lower than Portfolio 1’s convexity of 147.640. Therefore, Portfolio 2 is the most appropriate immunizing portfolio.
The immunizing portfolio needs to be greater than the convexity (and dispersion) of the outflow portfolio. But, the convexity of the immunizing portfolio should be minimized in order to minimize dispersion and reduce structural risk
如题
