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Lemonade · 2022年11月01日

不是低于1.55%的取不到吗?

* 问题详情,请 查看题干

NO.PZ201712110200000307

问题如下:

John Smith, an investment adviser, meets with Lydia Carter to discuss her pending retirement and potential changes to her investment portfolio. Domestic economic activity has been weakening recently, and Smith’s outlook is that equity market values will be lower during the next year. He would like Carter to consider reducing her equity exposure in favor of adding more fixed-income securities to the portfolio.

Government yields have remained low for an extended period, and Smith suggests considering investment-grade corporate bonds to provide additional yield above government debt issues. In light of recent poor employment figures and two consecutive quarters of negative GDP growth, the consensus forecast among economists is that the central bank, at its next meeting this month, will take actions that will lead to lower interest rates.

Smith and Carter review par, spot, and one-year forward rates (Exhibit 1) and four fixed-rate investment-grade bonds issued by Alpha Corporation which are being considered for investment (Exhibit 2).

Exhibit 1.₤Par, Spot, and One-Year Forward Rates (annual coupon payments)

Exhibit 2.₤Selected Fixed-Rate Bonds of Alpha Corporation

Note: All bonds in Exhibit 2 have remaining maturities of exactly three years

Carter tells Smith that the local news media have been reporting that housing starts, exports, and demand for consumer credit are all relatively strong, even in light of other poor macroeconomic indicators. Smith explains that the divergence in economic data leads him to believe that volatility in interest rates will increase. Smith also states that he recently read a report issued by Brown and Company forecasting that the yield curve could invert within the next six months.

Smith develops a binomial interest rate tree with a 15% interest rate volatility assumption to assess the value of Alpha Corporation’s bonds. Exhibit 3 presents the interest rate tree.

Exhibit 3.₤Binomial Interest Rate Tree for Alpha Corporation 15% Interest Rate Volatility


Carter asks Smith about the possibility of analyzing bonds that have lower credit ratings than the investment-grade Alpha bonds. Smith discusses four other corporate bonds with Carter. Exhibit 4 presents selected data on the four bonds.

Exhibit 4.₤Selected Information on Fixed-Rate Bonds for Beta, Gamma, Delta, and Rho Corporations


Notes: All bonds have remaining maturities of three years. OAS stands for option-adjusted spread.


Based on Exhibit 2 and Exhibit 3, the market price of Bond 4 is closest to:

选项:

A.

100.0000.

B.

100.5123.

C.

100.8790.

解释:

A is correct.

The market price of callable Bond 4 with no protection period cannot exceed 100.

为什么到PV0的时候要用1%折现?callable bond不是低于1.55%就取不到了吗?难道折现到0时刻不应该用1.55%吗

2 个答案

吴昊_品职助教 · 2024年10月15日

嗨,从没放弃的小努力你好:


每道题的条件是不一样的,所以结果也对应不同。这道题中,callable bond是没有任何保护期的(without any protection periods),换句话说,就是每个时间点都是可以执行权利的,包括零时间点。既然每个时间点都可以行使权力,那就说明价格不会超过call price(100)。一旦超过就会调整回call price.

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吴昊_品职助教 · 2022年11月02日

嗨,爱思考的PZer你好:


1.55%对应的是债券的coupon rate,而不是折现率。每一期的折现率应该使用的是表三中的二叉树。折现到零时刻就应该用1%。

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加油吧,让我们一起遇见更好的自己!

James · 2024年10月15日

老师我记得在前面有一道题你说过p0是可以大于100的,为什么这道题不行呢?

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NO.PZ201712110200000307 问题如下 Baseon Exhibit 2 anExhibit 3, the market priof Bon4 is closest to: A.100.0000. B.100.5123. C.100.8790. A is correct.The market priof callable Bon4 with no protection periocannot excee100. 还是需要用二叉树算,如果高于100,就只能取到100

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