SecurityAhasreturnRA~N(0.3,0.52)andsecurityBhasreturnRB~N(0.08,0.252).SecurityAhasreturnRA~N(0.3,0.5^2)andsecurityBhasreturnRB~N(0.08,0.25^2).Thereturnsofthesetwosecuritiesareperfectlynegativelycorrelated.Whatvaluefort

Question

Security A has return RA~N(0.3,0.52) and security B has return RB~N(0.08,0.252).
Security A has return RA~N(0.3,0.5^2) and security B has return
RB~N(0.08,0.25^2). The returns of these two securities are perfectly negatively
correlated. What value for the risk free rate in the economy is implied by these
figures? Explain your reasoning and show all necessary calculations.

Answer 1

两个证券完全负相关,可以建立一个零方差的组合,此组合的收益率就是无风险收益率.
投资A证券x,投资B证券1-x,建立组合
组合方差=(0.5x)^2+[0.25(1-x)]^2-2x(1-x)*0.5*0.25=0
求解x=1/3
这样组合的收益率为0.3*1/3+0.08*2/3=0.153%,也就是无风险收益率