Question

FRM EXAM2007 一道关于regression的试题，怎么用最小二乘法的公式来解决？

consider two stocks, A and B. Assume their annual returns are normally distributed, the marginal distribution of each stock has mean 2% and standard deviation 10%, and the correlation is 0.9. what is the expected annual return of stock A if the annual return of stock B is 3%?

the answer is 2.9%

Answer 1

这不是handbook上的题目么？我也是看答案看明白的。将A看成因变量，B看成自变量，做一个回归方程：A=(alpha)*B+(beta)
由于已知A与B的均值，对上面这个式子求均值就有2=(alpha)*2+(beta)
又由于已知方差和相关系数，我们有：0.9=(协方差）/0.1^2=(beta)*0.1/0.01
利用这两个式子接触alpha和beta，再将B=3%带入就可以求出A了

希望我说的你能明白