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.
518.
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。
用公式得出的BPV和题目中给出的BPV有什么不同？为什么要用公式计算出的BPV？
