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郎布斯吃苹果 · 2022年08月11日

ctd bond的bpv怎么算出来的?用题目给的数据算出的结果好像不等于给出的bpv?

* 问题详情,请 查看题干

NO.PZ201601050100001702

问题如下:

Global Mega (Global) is a diversified financial services firm. Yasuko Regan, senior trader, and Marcus Whitacre, junior trader, both work on the firm’s derivatives desk. Regan and Whitacre assist in structuring and implementing trades for clients in the financial services industry that have limited derivatives expertise. Regan and Whitacre are currently assisting one of Global’s clients—Monatize, an asset management firm—with two of its portfolios: Portfolio A and Portfolio B.

Portfolio A is a bond portfolio composed solely of US Treasury bonds. Monatize has asked Global to quote the number of Treasury futures contracts necessary to fully hedge this bond portfolio against a rise in interest rates. Exhibit 1 presents selected data on Portfolio A, the relevant Treasury futures contract, and the cheapest-todeliver (CTD) bond.


After an internal discussion, Monatize elects to not hedge Portfolio A but rather decrease the portfolio’s modified duration to 3.10. Regan asks Whitacre to compute the number of Treasury futures contracts to sell in order to achieve this objective. Regan tells Whitacre to assume the yield curve is flat.

Portfolio B is a $100,000,000 equity portfolio indexed to the S&P 500 Index, with excess cash of $4,800,000. Monatize is required to equitize its excess cash to be fully invested, and the firm directs Global to purchase futures contracts to do so. To replicate the return of Portfolio B’s target index, Whitacre purchases S&P 500 futures contracts, at a price of 3,300 per contract, that have a multiplier of $250 per index point and a beta of 1.00.

Monatize’s CFO and Regan discuss two potential hedging strategies for Portfolio B to protect against a hypothetical extreme sell-off in equities. Regan first suggests that Monatize could enter into a total return equity swap, whereby Monatize agrees to pay the return on the S&P 500 and receive a fixed interest rate at pre-specified dates in exchange for a fee.

Regan next suggests that Monatize could alternatively hedge Portfolio B using variance swaps. Monatize’s CFO asks Regan to calculate what the gain would be in five months on a purchase of $1,000,000 vega notional of a one-year variance swap on the S&P 500 at a strike of 15% (quoted as annual volatility), assuming the following:

■ Over the next five months, the S&P 500 experiences a realized volatility of 20%;

■ At the end of the five-month period, the fair strike of a new seven-month variance swap on the S&P 500 will be 18%; and

■ The annual interest rate is 1.50%.

Regan and Whitacre discuss the use of federal funds futures contracts to infer probabilities of future monetary policy changes. Whitacre makes the following three statements about fed funds futures contracts:

Statement 1

Typical end-of-month activity by large financial and banking institutions often induces “dips” in the effective fed funds rate.

Statement 2

Especially for the longer-term horizon, the probabilities inferred from the pricing of fed funds futures usually have strong predictive power

Statement 3

To derive probabilities of Federal Reserve interest rate actions, market participants look at the pricing of fed funds futures, which are tied to the Federal Reserve’s target fed funds rate.

Whitacre then proposes to Regan that Global explore opportunities in bond futures arbitrage. Whitacre makes the following two statements:

Statement 4

If the basis is positive, a trader would make a profit by “selling the basis.”

Statement 5

If the basis is negative, a trader would make a profit by selling the bond and buying the futures.


Based on Exhibit 1, the number of Treasury futures contracts Whitacre should sell to achieve Monetize’s objective with respect to Portfolio A is closest to:

选项:

A.

490.

B.

518.

C.

676.

解释:

A is correct.

Monetize wants to reduce Portfolio A’s modified duration to a target of 3.10. BPVT is calculated as follows:


The basis point value of Portfolio A (BPVP) is $130,342.94, and the basis point value of the cheapest-to-deliver bond (BPVCTD) is $127.05 with a conversion factor of 0.72382. The basis point value hedge ratio (BPVHR), which provides the number of futures contracts needed, is then calculated as follows:


Thus, to decrease the modified duration of Portfolio A to 3.10, Whitacre should sell 490 Treasury bond futures contracts

中文解析:

本题考察的是使用债券期货合约调节组合的duration。

根据题干信息可知,当前的目标duration是3.1,据此可以计算出BPVT =$44,402.54

然后仍然带入公式:


计算结果为-489.613,约等于490份,负号代表short。

如题。ctd bond的bpv怎么算出来的?用题目给的数据算出的结果好像不等于给出的bpv?

1 个答案

Hertz_品职助教 · 2022年08月11日

嗨,从没放弃的小努力你好:


同学你好

同学这里说的使用题目给的数据计算CTD的BPV,指的应该是使用futures的数据来计算,但是由于题目已经给到了CTD对应的BPV,所以咱们是用不到再计算。

为什么呢?

看一下框架图对应的公式:

 

BPVf和BPVctd是存在这样一个关系的,所以在求解BPVHR的时候,最初的公式可以认为是下面这样的公式:

只不过讲义中将分母的BPV_F,使用BPV_CTD/CF进行了替换。

所以呢?如果题目给到了CTD对应的BPV,就用它除以CF,得到对应的标准期货合约的价格,这也就是咱们用来调节久期真正用到的期货合约,因为CTD bond是双方实际交割的债券,这样对应计算出来的份数肯定是最准确的。而期货合约它是一个标准的合约,对应着很多标的债券,虽然有转换因子但并不如直接使用CTD自己的BPV计算来的准确。

因此,只有当题目没有直接给到CTD的BPV时,才选择使用futures的BPV来进行转换。


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NO.PZ201601050100001702问题如下 Baseon Exhibit 1, the number of Treasury futures contracts Whitacre shoulsell to achieve Monetize’s objective with respeto Portfolio A is closest to: A.490.B.518.C.676. A is correct. Monetize wants to rePortfolio A’s mofieration to a target of 3.10. BPVT is calculatefollows:The basis point value of Portfolio A (BPVP) is $130,342.94, anthe basis point value of the cheapest-to-liver bon(BPVCT is $127.05 with a conversion factor of 0.72382. The basis point value hee ratio (BPVHR), whiprovis the number of futures contracts nee is then calculatefollows:Thus, to crease the mofieration of Portfolio A to 3.10, Whitacre shoulsell 490 Treasury bonfutures contracts中文解析本题考察的是使用债券期货合约调节组合的ration。根据题干信息可知,当前的目标ration是3.1,据此可以计算出BPVT =$44,402.54然后仍然带入公式 计算结果为-489.613,约等于490份,负号代表short。 我是把bpv拆成mr和marketvalue算的,算下来数量级不一样但是选对了,请问market value of futures是不是需要乘以contrasize呢

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