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aileen20180623 · 2024年01月31日

这题

  1. CFA II
  2. Derivative

NO.PZ2023020101000004

问题如下：

Sheroda determined she was also underweight in one individual stock. Thirty days ago, she entered a long 60-day forward position on CHJ common stock, which does not pay a dividend. Sheroda has asked Parisi to calculate the value of her two forward positions today—that is, 30 days after the contracts were initiated. Parisi has collected the information in Exhibit 1 to carry out the valuation assignment.

Exhibit 1: Selected Financial Information for Sheroda Meeting

Based on the information in Exhibit 1 and assuming a 360-day year, the value of Sheroda’s forward contract on the CHJ stock is closest to:

选项：

A.

3.99 USD.

B.

–3.98 USD.

C.

–4.29 USD.

解释：

B is correct. The value of the forward contract is:

Vt(T) = PVt,T[Ft(T) – F0(T)]

= (96.31 – 100.30) /(1.003944)^(30/360)= –3.98

，您好，我不太理解里面的答案和助教的解释(已经贴在下方），首先疑惑助教解释：96.31=96*(1+rf)(30/360)这个地方，为什么拿stock来算forward，不是forward算一方，stock算一方？而且按照stock没有复利？

当前sotck在30后是96,30天后的forward当前时点价格是96.31（60天到期的0）,（60天到期的forward是96），不是用(96.31-96)*3.92%^(30/360)?




而且这题目还不全，看答案是有个复利3.92%



“” 此题是equity forward的valuation，按照教材的讲述，对于单个的stock而言，一般都不采用连续复利的，同学的疑问是对的。首先我们可以根据96.31=96*(1+rf)(30/360),反解出rf=3.94457%,Vt(T)=(96.31 – 100.30)/(1.00394457)(30/360)=-3.98。由于时间期限较短，所以采用连续复利和非连续复利计算的结果是一样的。这道题的解析确实存在一点问题，我们已经在后台做了处理。同学能够发现这个问题，证明同学对于此知识点的掌握是非常扎实的哦，非常棒“”

其次答案= e–0.0392(30/360)(96.31 – 100.30)? 不是long forward ?"Thirty days ago, she entered a long 60-day forward position on CHJ common stock, which does not pay a dividend."这题万全不用考虑96的stock？单独算forward这方？


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1 个答案

李坏_品职助教 · 2024年01月31日

嗨，努力学习的PZer你好：


96.31=96*(1+rf)(30/360)这个地方就是为了得出rf。


这个股票是没有dividend，所以PVD=0，根据讲义P21页：

远期价格FP = 股票价格S × (1+rf)^T, 远期合约是30天之前签订的，所以从今天开始算到合约到期日，还剩30天。

现在的FP是96.31，股票价格是96，所以是96.31=96*(1+rf)^(30/360)，rf = 3.94457%. 答案里写的是3.92%，那是用连续复利计算的，我写的rf是离散复利，在期限小于1年的情况下差异可以忽略不计。


在后面计算value of forward contract的时候，用的是这个公式（也是讲义21页）：

这个公式里面的FP指的是期初合约签订时的远期价格，应该是100.3，而St用的是现在的股价96。

V = 股票价格S - 远期价格FP / (1+3.94457%)^(30/360) = 96 - 100.3 / (1+3.94457%)^(30/360) = -3.98

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