futures contract 的beta

问题如下：

The number of BOVESPA futures contracts Tryon would have to buy to express the view on emerging markets is closest to:

选项：

350

402

462

解释：

A is correct.

Calculate the number of futures contracts needed on EM exposure of US$10 million, which at a BRL/USD exchange rate of 4.20 is equal to US$42 million. Adjust BOVESPA index exposure for beta of 1.15:

N_f=(β_T-β_s/β_f)(S/F)=(1.0-0/1.15)(42,000,000/104,456×1)=0.87×402.05=349.78≈350

where:

Nf = the number of contracts used,

βT = the target beta, and

βf = the beta of the futures contract.

B is incorrect. It uses the contract price in Brazilian reais to hedge the US$10 million: (10,000,000 × 4.2/104,465) = 402. This calculation does not adjust for beta of 1.15.

C is incorrect. It uses 1.15 in the numerator and 1.10 as the futures beta: 402.05 × 1.15 = 462.36.

中文解析：

本题考察的是用股指期货合约来管理equity risk。

注意题干中的汇率表达形式是错误的，应该是BRL/USD=4.2，因此10million的美元转换成巴西雷亚尔为42millionBRL

然后根据公式N_f=(β_T-β_s/β_f)(S/F)代入数字计算可知需要的份数约为350份。