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小台chirly · 2022年04月13日

老师这个题计算没看懂

NO.PZ2017121101000013

问题如下:

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

Explain how Ko can use this information to understand potential movements in the current federal funds rate.

选项:

解释:

First, Ko knows that the FFE rate implied by the futures contract price of 97.175 is 2.825% (= 100 – 97.175). This is the rate that market participants 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% FFE rate implied by the futures signals a fairly high chance that the FOMC will increase rates by 25 bps from its current target range of 2.50%–2.75% to the new target range of 2.75%–3.00%. She calculates the probability of a rate hike as follows:

(2.825%-2.625%)/(2.875%-2.625%)=0.80 or 80%

Ko can now incorporate this probability of a Fed rate hike into her forecast of short-term US interest rates.

中文解析:

97.175期货合约价格隐含的FFE汇率为2.825%(= 100 - 97.175)。这是市场参与者预期的当月联邦基金平均利率。

P = expected FFE rate - current federal funds rate / 25bp

= [ 2.825% - 1/2(2.5%+ 2.75%) ] / 25bp =0.80


按照公式的话


effective federal funds rate implied by futures contract = 100-97.125 = 2.825%

current federal funds rate = (2.5%+2.75%)/2 = 2.625%


题目里面没看到哪里说 expected rate要增加,看其他问答写的是增加25BP

那么 the probability of a change in the federal funds rate = 0.25%


把上述都带进公式的话:

0.25% = (2.825% - 2.625%)/(rate hike - 2.625%)

rate hike = (2.825% - 2.625%)/ 0.25% + 2.625% = 3.425


好像完全没对。。

请老师解答

2 个答案
已采纳答案

Hertz_品职助教 · 2022年04月14日

嗨,爱思考的PZer你好:


同学你好

你列式中分母位置是不对的哈,应该是“(2.875%-2.625%)”,分子位置是正确的。

分母位置有两种计算方法:

1.     直接带入25bp,不论题目怎么说,直接带入这个数字即可,因为这个公式的成立就是基于美联储每次调整都是以25bp的幅度调整的,所以带入这个数字不会出错。

2.     第二种方法是根据上面截图的公式,它是怎么计算的呢?

分母位置是说用接下来的FFR减去当前的FFR。注意是取中间数哈

当前的FFR,题目说了“The current federal funds rate target range is set between 2.50% and 2.75%”,所以分母位置中当前的FFR为1/2(2.5%+2.75%)=2.625%

然后计算分母位置中被减数位置的FFR,这里怎么判断呢?

仍然是基于美联储每次加息或者降息的幅度都是25bp,然后根据 fed funds futures contract倒推出来的FFE rate是2.825%,高于当前的2.625%,因此判断是加息。

所以在当前2.50% and 2.75%都加上25bp,然后再取平均即可。即2.75%–3.00%求平均就是2.875%。

因此,分母位置是2.875%-2.625%。

3.     通过上面两个方法可见,其实分母位置直接带入25bp即可哈

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Hertz_品职助教 · 2022年04月14日

嗨,爱思考的PZer你好:


同学你好

是的,这句话的意思是说假设利率被上调后的联邦基金利率,也就是调整后的FFR了

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