源_品职助教 · 2017年03月14日
这道题要求在最大化组合夏普比率的情况下求解每种资产的配比权重，因为BENCHMARK的夏普比率是不变的，所以就是等同于求在最大化组合信息比率的情况下每种资产的配比权重，那就要套用公式先把组和的超额风险水平算出来SDT(RA)，再用SDT(RA)除以INDIGO FUND的ACTIVE RISK，就求得了INDIGO FUND的权重，那么标普500的权重也就有了。
之后的解答过程只是证明了在这个权重下，组合的夏普比率是最大的即0.365（该数值是由前一题（12题）算得的）思路就是分别求得现在配比情况下组合的ACTIVE RETURN 和 RISK,然后前者除以后者就OK啦。
NO.PZ2015121810000013 问题如下 Whiof the following pairs of weights wouluseto achieve the highest Sharpe ratio anoptimamount of active risk through combining the Ingo Funanbenchmark portfolio, respectively? A.1.014 on Ingo an–0.014 on the benchmark B.1.450 on Ingo an–0.450 on the benchmark C.1.500 on Ingo an–0.500 on the benchmark A is correct.The optimamount of active risk is:σA=IRSRBσB=0.150.333×18%=8.11%\sigma_A=\frac{IR}{SR_B}\sigma_B=\frac{0.15}{0.333}\times18\%=8.11\%σA=SRBIRσB=0.3330.15×18%=8.11%The weight on the active portfolio (Ingo) woul8.11%/8.0% = 1.014 anthe weight on the benchmark portfolio woul1 – 1.014 = – 0.014. 考点Optimamount of active risk解析Optimamount of active riskσA=IRSRBσB=0.150.333×18%=8.11%\sigma_A=\frac{IR}{SR_B}\sigma_B=\frac{0.15}{0.333}\times18\%=8.11\%σA=SRBIRσB=0.3330.15×18%=8.11%Ingo Fun在的active risk是8%，为了使active risk达到最优水平，就将Ingo Funbenchmark再做组合，形成active risk最优的combinefun假设Ingo Fun权重为那么σA=cσAfun 8.11%=c8%, c=1.014\sigma_A=c\sigma_A^{fun,\;8.11\%=c8\%,\;c=1.014σA=cσAfun,8.11%=c8%,c=1.014因此，benchmark的权重为1-1.014=-0.014 如题
NO.PZ2015121810000013问题如下Whiof the following pairs of weights wouluseto achieve the highest Sharpe ratio anoptimamount of active risk through combining the Ingo Funanbenchmark portfolio, respectively?A.1.014 on Ingo an–0.014 on the benchmarkB.1.450 on Ingo an–0.450 on the benchmarkC.1.500 on Ingo an–0.500 on the benchmark A is correct.The optimamount of active risk is:σA=IRSRBσB=0.150.333×18%=8.11%\sigma_A=\frac{IR}{SR_B}\sigma_B=\frac{0.15}{0.333}\times18\%=8.11\%σA=SRBIRσB=0.3330.15×18%=8.11%The weight on the active portfolio (Ingo) woul8.11%/8.0% = 1.014 anthe weight on the benchmark portfolio woul1 – 1.014 = – 0.014. 考点Optimamount of active risk解析Optimamount of active riskσA=IRSRBσB=0.150.333×18%=8.11%\sigma_A=\frac{IR}{SR_B}\sigma_B=\frac{0.15}{0.333}\times18\%=8.11\%σA=SRBIRσB=0.3330.15×18%=8.11%Ingo Fun在的active risk是8%，为了使active risk达到最优水平，就将Ingo Funbenchmark再做组合，形成active risk最优的combinefun假设Ingo Fun权重为那么σA=cσAfun 8.11%=c8%, c=1.014\sigma_A=c\sigma_A^{fun,\;8.11\%=c8\%,\;c=1.014σA=cσAfun,8.11%=c8%,c=1.014因此，benchmark的权重为1-1.014=-0.014 大盘的SR大于单个基金的SR，要想组合SR最大就要尽可能多买大盘，ABC三个中A投资大盘的比例最高，所以选A，这样做行不行？
NO.PZ2015121810000013问题如下Whiof the following pairs of weights wouluseto achieve the highest Sharpe ratio anoptimamount of active risk through combining the Ingo Funanbenchmark portfolio, respectively?A.1.014 on Ingo an–0.014 on the benchmarkB.1.450 on Ingo an–0.450 on the benchmarkC.1.500 on Ingo an–0.500 on the benchmark A is correct.The optimamount of active risk is:σA=IRSRBσB=0.150.333×18%=8.11%\sigma_A=\frac{IR}{SR_B}\sigma_B=\frac{0.15}{0.333}\times18\%=8.11\%σA=SRBIRσB=0.3330.15×18%=8.11%The weight on the active portfolio (Ingo) woul8.11%/8.0% = 1.014 anthe weight on the benchmark portfolio woul1 – 1.014 = – 0.014. 考点Optimamount of active risk解析Optimamount of active riskσA=IRSRBσB=0.150.333×18%=8.11%\sigma_A=\frac{IR}{SR_B}\sigma_B=\frac{0.15}{0.333}\times18\%=8.11\%σA=SRBIRσB=0.3330.15×18%=8.11%Ingo Fun在的active risk是8%，为了使active risk达到最优水平，就将Ingo Funbenchmark再做组合，形成active risk最优的combinefun假设Ingo Fun权重为那么σA=cσAfun 8.11%=c8%, c=1.014\sigma_A=c\sigma_A^{fun,\;8.11\%=c8\%,\;c=1.014σA=cσAfun,8.11%=c8%,c=1.014因此，benchmark的权重为1-1.014=-0.014 这道题的思路是根据 sigema （portfolio+benchmark）=C*sigema portfolio这个式子算出C，然后再看是long short。有几个问题1、不太明白optimamount of active risk算出来的是sigema （portfolio+benchmark），还是sigema portfolio ？2、请问讲义244页的optimamount of active risk=12%，是sigema （portfolio+benchmark），还是sigema portfolio？是怎么看出来的？3、为什么算sigema （portfolio+benchmark）用的是 表格中return stanrviation，而算sigema portfolio用的却不是return stanrviation，而是active risk4、可以用讲义243页关于“sigema P 平方”的那个公式来算sigema portfolio吗？有点晕，求老师耐心解答，谢谢！
NO.PZ2015121810000013 问题如下 Whiof the following pairs of weights wouluseto achieve the highest Sharpe ratio anoptimamount of active risk through combining the Ingo Funanbenchmark portfolio, respectively? A.1.014 on Ingo an–0.014 on the benchmark B.1.450 on Ingo an–0.450 on the benchmark C.1.500 on Ingo an–0.500 on the benchmark A is correct.The optimamount of active risk is:σA=IRSRBσB=0.150.333×18%=8.11%\sigma_A=\frac{IR}{SR_B}\sigma_B=\frac{0.15}{0.333}\times18\%=8.11\%σA=SRBIRσB=0.3330.15×18%=8.11%The weight on the active portfolio (Ingo) woul8.11%/8.0% = 1.014 anthe weight on the benchmark portfolio woul1 – 1.014 = – 0.014. 考点Optimamount of active risk解析Optimamount of active riskσA=IRSRBσB=0.150.333×18%=8.11%\sigma_A=\frac{IR}{SR_B}\sigma_B=\frac{0.15}{0.333}\times18\%=8.11\%σA=SRBIRσB=0.3330.15×18%=8.11%Ingo Fun在的active risk是8%，为了使active risk达到最优水平，就将Ingo Funbenchmark再做组合，形成active risk最优的combinefun假设Ingo Fun权重为那么σA=cσAfun 8.11%=c8%, c=1.014\sigma_A=c\sigma_A^{fun,\;8.11\%=c8\%,\;c=1.014σA=cσAfun,8.11%=c8%,c=1.014因此，benchmark的权重为1-1.014=-0.014 请问求出optimactive risk 8.122% 以后为什么不用它除 portfolio 的active return viation 而是除portfolio的 active risk？风险组合的active return 的标准差和 aktive risk 有什么区别？
此题为什么不能通过最大的sharp ratio求解权重的，最大的sharp ratio是0.365。rf=0.03，这样算出来的权重为啥和答案不一致了？『0.105x+（1-x ）0.09-0.03 』/0.25x+(1-x)0.18=0.365这样算出来的权重x为啥不对？