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李晨 · 2022年07月15日

a于c之间,在mac.duration 和 convexity之间做选择,可以理解为convexity的影响相比duration比较小,所以最后还是选了duration吗?

NO.PZ2018120301000036

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.

Recommend the portfolio in Exhibit 1 that would best achieve the immunization. Justify your response


选项:

解释:


Justification:

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:

1. 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.

2. 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.

3. 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.

Default risk (credit risk) is not considered because the portfolios consist of government bonds that presumably have default probabilities approaching zero.

谢谢老师

1 个答案

pzqa015 · 2022年07月16日

嗨,爱思考的PZer你好:


不是的

mac D和convexity相比,convexity的顺序相对靠后,只有mac D条件满足后,才要比较convexity的条件。

portfolio C的mac D是9.503,是小于负债的投资期10年的,所以,直接排除,用不到convexity的条件。

PortfolioA与portfolioB的mac D分别是9.998和10.002,与负债投资期10年相近,所以,需要在portfolioA与portfolioB两个中做选择,这个时候,需要用到convexity的条件,portfolioC的convexity大于portfolioA的convexity,所以,PortfolioA是最好的。

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