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Kokonoi Hajime · 2025年06月28日

公式

NO.PZ2022123002000047

问题如下:

Sarah Ko, a private wealthadviser in Singapore, is developing a short-term interest rate forecast for herprivate wealth clients who have holdings in the US fixed-income markets. Koneeds to understand current market expectations for possible upcoming centralbank (i.e., US Federal Reserve Board) rate actions. The current price for thefed funds futures contract expiring after the next FOMC meeting is 97.175. Thecurrent federal funds rate target range is set between 2.50% and 2.75%.

Explain how Ko can use thisinformation to understand potential movements in the current federal fundsrate.

解释:

Correct Answer

First, Ko knows that the FFE rate implied by the futures contractprice of 97.175 is 2.825% (= 100 – 97.175). This is the rate that marketparticipants expect to be the average federal funds rate for that month.

Second,Ko should determine the probability of a rate change. She knows the 2.825% FFErate implied by the futures signals a fairly high chance that the FOMC willincrease rates by 25 bps from its current target range of 2.50%–2.75% to thenew target range of 2.75%–3.00%. She calculates the probability of a rate hikeas follows:


Ko cannow incorporate this probability of a Fed rate hike into her forecast ofshort-term US interest rates.

答案里的公式没看懂,求老师解析

1 个答案

李坏_品职助教 · 2025年06月28日

嗨,努力学习的PZer你好:


current price for the fed funds futures是97.175,根据这个条件可以算出FFE rate = (100 - 97.175)/100 = 2.825%.


the probability of a rate change的公式如下:

分子上的effective fed funds rate就是刚算出来的FFE = 2.825%.

而current fed funds rate是2.50% and 2.75%的平均数,也就是2.625%.


分母的fed funds rate assuming a rate hike意思是,当加息25个bp,也就是加了0.25%之后,那么fed funds rate会从现在的2.625%变成2.625% + 0.25% = 2.875%.


所以最后的probability = (2.825% - 2.625%) /(2.875% - 2.625%)= 80%

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