这道题干有问题吧？ t时刻 value of futures= change in prices，而不等于price
问题如下图：
选项：
A. 
B. 
C. 
解释：
NO.PZ2018113001000005 问题如下 The equity portfolio ha market value of $6,000,000, The pension funplans to use a futures contraprice$250,000 in orr to increase the beta from 0.9 to 1.2 for the perioof one month. The futures contraha beta of 0.95. One months later, the return of equity market is 5%, the market value of equity portfolio is $6,250,000, the priof futures contrais $262,000. The effective beta of the equity portion of the funis closest to: 1.15. 1.20 1.05 A is correct.考点计算effective beta解析将beta从0.9调整为1.2需要的合约数量为Nf=(βT−βSβS)(Sf)=(1.2−0.90.95)($6,000,000$250,000)=7.58N_f=(\frac{\beta_T-\beta_S}{\beta_S})(\frSf)=(\frac{1.2-0.9}{0.95})(\frac{\$6,000,000}{\$250,000})=7.58Nf=(βSβT−βS)(fS)=(0.951.2−0.9)($250,000$6,000,000)=7.58因此，需要买入8份期货合约。一个月之后期货合约所带来的利润=8×（262,000-250,000）=$96,000股票组合的市场价值变为6,250,000，加上期货合约的收益可以得到整个头寸的价值=$6,250,000+$96,000=$6,346,000，整个头寸的收益=$6,346,000/$6,000,000-1=0.0577又因为市场的收益率为5%，而组合的收益率为5.77%，所以组合的有效贝塔为0.0577/0.05=1.154 为什么期货的期初成本是0？
NO.PZ2018113001000005 问题如下 The equity portfolio ha market value of $6,000,000, The pension funplans to use a futures contraprice$250,000 in orr to increase the beta from 0.9 to 1.2 for the perioof one month. The futures contraha beta of 0.95. One months later, the return of equity market is 5%, the market value of equity portfolio is $6,250,000, the priof futures contrais $262,000. The effective beta of the equity portion of the funis closest to: 1.15. 1.20 1.05 A is correct.考点计算effective beta解析将beta从0.9调整为1.2需要的合约数量为Nf=(βT−βSβS)(Sf)=(1.2−0.90.95)($6,000,000$250,000)=7.58N_f=(\frac{\beta_T-\beta_S}{\beta_S})(\frSf)=(\frac{1.2-0.9}{0.95})(\frac{\$6,000,000}{\$250,000})=7.58Nf=(βSβT−βS)(fS)=(0.951.2−0.9)($250,000$6,000,000)=7.58因此，需要买入8份期货合约。一个月之后期货合约所带来的利润=8×（262,000-250,000）=$96,000股票组合的市场价值变为6,250,000，加上期货合约的收益可以得到整个头寸的价值=$6,250,000+$96,000=$6,346,000，整个头寸的收益=$6,346,000/$6,000,000-1=0.0577又因为市场的收益率为5%，而组合的收益率为5.77%，所以组合的有效贝塔为0.0577/0.05=1.154 请问effective beta在哪里讲过呢，这个题算不算超纲？
NO.PZ2018113001000005 问题如下 The equity portfolio ha market value of $6,000,000, The pension funplans to use a futures contraprice$250,000 in orr to increase the beta from 0.9 to 1.2 for the perioof one month. The futures contraha beta of 0.95. One months later, the return of equity market is 5%, the market value of equity portfolio is $6,250,000, the priof futures contrais $262,000. The effective beta of the equity portion of the funis closest to: 1.15. 1.20 1.05 A is correct.考点计算effective beta解析将beta从0.9调整为1.2需要的合约数量为Nf=(βT−βSβS)(Sf)=(1.2−0.90.95)($6,000,000$250,000)=7.58N_f=(\frac{\beta_T-\beta_S}{\beta_S})(\frSf)=(\frac{1.2-0.9}{0.95})(\frac{\$6,000,000}{\$250,000})=7.58Nf=(βSβT−βS)(fS)=(0.951.2−0.9)($250,000$6,000,000)=7.58因此，需要买入8份期货合约。一个月之后期货合约所带来的利润=8×（262,000-250,000）=$96,000股票组合的市场价值变为6,250,000，加上期货合约的收益可以得到整个头寸的价值=$6,250,000+$96,000=$6,346,000，整个头寸的收益=$6,346,000/$6,000,000-1=0.0577又因为市场的收益率为5%，而组合的收益率为5.77%，所以组合的有效贝塔为0.0577/0.05=1.154 题目已经告诉了市场的收益率是5%了，又说股票市值达到6250，这个逻辑在哪？认可6250，股票收益率是4.167% ；认可收益率是5%，股票市值应该为6300？？
NO.PZ2018113001000005 问题如下 The equity portfolio ha market value of $6,000,000, The pension funplans to use a futures contraprice$250,000 in orr to increase the beta from 0.9 to 1.2 for the perioof one month. The futures contraha beta of 0.95. One months later, the return of equity market is 5%, the market value of equity portfolio is $6,250,000, the priof futures contrais $262,000. The effective beta of the equity portion of the funis closest to: 1.15. 1.20 1.05 A is correct.考点计算effective beta解析将beta从0.9调整为1.2需要的合约数量为Nf=(βT−βSβS)(Sf)=(1.2−0.90.95)($6,000,000$250,000)=7.58N_f=(\frac{\beta_T-\beta_S}{\beta_S})(\frSf)=(\frac{1.2-0.9}{0.95})(\frac{\$6,000,000}{\$250,000})=7.58Nf=(βSβT−βS)(fS)=(0.951.2−0.9)($250,000$6,000,000)=7.58因此，需要买入8份期货合约。一个月之后期货合约所带来的利润=8×（262,000-250,000）=$96,000股票组合的市场价值变为6,250,000，加上期货合约的收益可以得到整个头寸的价值=$6,250,000+$96,000=$6,346,000，整个头寸的收益=$6,346,000/$6,000,000-1=0.0577又因为市场的收益率为5%，而组合的收益率为5.77%，所以组合的有效贝塔为0.0577/0.05=1.154 这里算整个头寸收益的时候，为什么不在分母加上买期货的成本？
NO.PZ2018113001000005 问题如下 The equity portfolio ha market value of $6,000,000, The pension funplans to use a futures contraprice$250,000 in orr to increase the beta from 0.9 to 1.2 for the perioof one month. The futures contraha beta of 0.95. One months later, the return of equity market is 5%, the market value of equity portfolio is $6,250,000, the priof futures contrais $262,000. The effective beta of the equity portion of the funis closest to: 1.15. 1.20 1.05 A is correct.考点计算effective beta解析将beta从0.9调整为1.2需要的合约数量为Nf=(βT−βSβS)(Sf)=(1.2−0.90.95)($6,000,000$250,000)=7.58N_f=(\frac{\beta_T-\beta_S}{\beta_S})(\frSf)=(\frac{1.2-0.9}{0.95})(\frac{\$6,000,000}{\$250,000})=7.58Nf=(βSβT−βS)(fS)=(0.951.2−0.9)($250,000$6,000,000)=7.58因此，需要买入8份期货合约。一个月之后期货合约所带来的利润=8×（262,000-250,000）=$96,000股票组合的市场价值变为6,250,000，加上期货合约的收益可以得到整个头寸的价值=$6,250,000+$96,000=$6,346,000，整个头寸的收益=$6,346,000/$6,000,000-1=0.0577又因为市场的收益率为5%，而组合的收益率为5.77%，所以组合的有效贝塔为0.0577/0.05=1.154 如果这个题没有告诉 the market value of equity portfolio is $6,250,000，让求？怎么求？6000000x(1+betax5%),是不是应该用这个方法求解？那这里面的贝塔 选哪个呢？
