NO.PZ2023032703000028
问题如下：
Chaopraya Av is an investment advisor for high-net-worth individuals. One of her clients, Schuylkill Cy, 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. Cy seeks to immunize the contribution today.
For Option 1, Av calculates the present value of the $300,000 as $234,535. To immunize the future single outflow, Av considers three bond portfolios given that no zero-coupon government bonds are available. The three portfolios consist of noncallable, fixed-rate, coupon-bearing government bonds considered free of default risk. Av prepares a comparative analysis of the three portfolios, presented in Exhibit 1.
Av evaluates the three bond portfolios and selects one to recommend to Cy.
Recommend the portfolio in Exhibit 1 that would best achieve the immunization. Justify your response.
选项：
解释：
Recommend the portfolio in Exhibit 1 that would best achieve the immunization. (circle one)
Portfolio A Portfolio B Portfolio C
Justify your response.
Portfolio A is the most appropriate portfolio because it is the only one that satisfies the three criteria for immunizing a single future outflow (liability), given that the cash flow yields are sufficiently close in value.
Market Value: Portfolio A’s initial market value of $235,727 exceeds the outflow’s present value of $234,535. Portfolio B is not appropriate because its market value of $233,428 is less than the present value of the future outflow of $234,535. A bond portfolio structured to immunize a single liability must have an initial market value that equals or exceeds the present value of the liability.
Macaulay Duration: Portfolio A’s Macaulay duration of 9.998 closely matches the 10-year horizon of the outflow. Portfolio C is not appropriate because its Macaulay duration of 9.503 is furthest away from the investment horizon of 10 years.
Convexity: Although Portfolio C has the lowest convexity at 108.091, its Macaulay duration does not closely match the outflow amount. Of the remaining two portfolios, Portfolio A has the lower convexity at 119.055; this lower convexity will minimize structural risk.
Default risk (credit risk) is not considered because the portfolios consist of government bonds that presumably have default probabilities approaching zero.
- 请问portfolio C的duration 比 10年小了一点，但是有最小的convxity。请问如果在这种情况下，我们是应该先优先比较duration，再比较convxity么？如果duration小于投资期，就算convexity小也不行是么？
- 可以麻烦老师看下我这样写的可以么？谢谢
Portfolio A would best achieve the immunization becuase of the following reasons:
- the present value of portfolio A is greater than the present value of liability.
- Macaulay duration of portfolio is close to liability's investment horizon.
- Portfolio A has the lower convexity. It can reduce the structural risk.