第一步里的s需要用负数吗？

NO.PZ2018113001000079 问题如下 Herbert is a portfolio manager for a trust fun whihol stocks anon in its portfolio.Herbert expects interest rates to crease, sohe wants to use equity inx anbonfutures to aust current assetallocations. Exhibit 1 shows the current antarget asset allocations. Exhibit2 shows selecteta on the portfolio anthe relevant futures contracts.How many futures contracts shoulHerbertbuy or sell to achieve the sireasset allocation? Answer:Herbert nee to rethe equity allocation $15,000,000 = $65,000,000-$50,000,000The number of equity inx futures contracts requireNf=βT−βSβf×Sf=0−1.21×15,000,00030,000=−600N_f=\frac{\beta_T-\beta_S}{\beta_f}\times\frSf=\frac{0-1.2}1\times\frac{15,000,000}{30,000}=-600Nf​=βf​βT​−βS​​×fS​=10−1.2​×30,00015,000,000​=−600Herbert shoulsell 600 equity inx futures contracts.Herbert nee to increase the bonallocation $15,000,000 = $50,000,000-$35,000,000BPVHR=BPVT−BPVPBPVCTCFBPVHR=\frac{BPV_T-BPV_P}{BPV_{CT}\times CFBPVHR=BPVCTBPVT​−BPVP​​×CFBPVT=4.5×0.0001×15,000,000=6,750BPV_T=4.5\times0.0001\times15,000,000=6,750BPVT​=4.5×0.0001×15,000,000=6,750BPVHR=BPVT−BPVPBPVCTCF=6750−090×0.75=56.25BPVHR=\frac{BPV_T-BPV_P}{BPV_{CT}\times CF=\frac{6750-0}{90}\times0.75=56.25BPVHR=BPVCTBPVT​−BPVP​​×CF=906750−0​×0.75=56.25Herbert shoulbuy 56 bonfutures contracts (after rounng) 中文解析本题考察的是使用股指期货合约和债券期货合约进行资产配置。根据题干的意思可知，现在想要降低股票在组合中的占比，增加债券在组合中的占比。因此第一步是通过卖出股指期货合约来降低股票头寸，第二步再通过买入债券期货合约来增加债券头寸。具体合约的份数按照上述公式计算即可。 考试时间根本不够，这样写就可以了吧？to achieve target asset allocation，we shoulre$15000000 stoanincrease $15000000 bonN(f)=(0-1.2)x15000000/30000=-600N(f)=(4.5x0.0001x15000000/90)*0.75=56short 600 equity inx futures long 56 bonfutures

NO.PZ2018113001000079 问题如下 Herbert is a portfolio manager for a trust fun whihol stocks anon in its portfolio.Herbert expects interest rates to crease, sohe wants to use equity inx anbonfutures to aust current assetallocations. Exhibit 1 shows the current antarget asset allocations. Exhibit2 shows selecteta on the portfolio anthe relevant futures contracts.How many futures contracts shoulHerbertbuy or sell to achieve the sireasset allocation? Answer:Herbert nee to rethe equity allocation $15,000,000 = $65,000,000-$50,000,000The number of equity inx futures contracts requireNf=βT−βSβf×Sf=0−1.21×15,000,00030,000=−600N_f=\frac{\beta_T-\beta_S}{\beta_f}\times\frSf=\frac{0-1.2}1\times\frac{15,000,000}{30,000}=-600Nf​=βf​βT​−βS​​×fS​=10−1.2​×30,00015,000,000​=−600Herbert shoulsell 600 equity inx futures contracts.Herbert nee to increase the bonallocation $15,000,000 = $50,000,000-$35,000,000BPVHR=BPVT−BPVPBPVCTCFBPVHR=\frac{BPV_T-BPV_P}{BPV_{CT}\times CFBPVHR=BPVCTBPVT​−BPVP​​×CFBPVT=4.5×0.0001×15,000,000=6,750BPV_T=4.5\times0.0001\times15,000,000=6,750BPVT​=4.5×0.0001×15,000,000=6,750BPVHR=BPVT−BPVPBPVCTCF=6750−090×0.75=56.25BPVHR=\frac{BPV_T-BPV_P}{BPV_{CT}\times CF=\frac{6750-0}{90}\times0.75=56.25BPVHR=BPVCTBPVT​−BPVP​​×CF=906750−0​×0.75=56.25Herbert shoulbuy 56 bonfutures contracts (after rounng) 中文解析本题考察的是使用股指期货合约和债券期货合约进行资产配置。根据题干的意思可知，现在想要降低股票在组合中的占比，增加债券在组合中的占比。因此第一步是通过卖出股指期货合约来降低股票头寸，第二步再通过买入债券期货合约来增加债券头寸。具体合约的份数按照上述公式计算即可。 stock转bon中间不需要先转成cash头寸吗