You may need the following definitions:

$x_i$ is the daily log return of the hedging instrument $($like futures$).$

$y_i$ is the daily log return of the hedged product $($for example, Apple Stock$).$

$S_{}={\displaystyle \underset{i=1}{\overset{n}{}}}(x_i-(\stackrel{}{x}){)}^2$

$S_{yy}={\displaystyle \underset{i=1}{\overset{n}{}}}(y_i-(\frac{?}{\text{b}\text{a}\text{r}}(y)){)}^2$

$S_{xy}={\displaystyle \underset{i=1}{\overset{n}{}}}(x_i-(\stackrel{}{x}))(y_i-(\frac{?}{\text{b}\text{a}\text{r}}(y)))$

${}_x=\frac{{\displaystyle \underset{i=1}{\overset{n}{}}}(x_i-(\stackrel{}{x}){)}^2}{n-1}$

${}_y=\frac{{\displaystyle \underset{i=1}{\overset{n}{}}}(y_i-(\frac{?}{\text{b}\text{a}\text{r}}(y)){)}^2}{n-1}$

${}_{xy}=\frac{{\displaystyle \underset{i=1}{\overset{n}{}}}(x_i-(\stackrel{}{x}))(y_i-(\frac{?}{\text{b}\text{a}\text{r}}(y)))}{n-1}$Which one is NOT the correct formula to calculate the minimum variance hedge ratio? Write down

the number in the space provided.

$(1)h^{**}=\frac{{}_{xy}}{{}_x{}_x}$

$(2)h^{**}=\frac{S_{xy}}{S_{}}$

$(3)h^{**}=\frac{{}_{xy}}{{}_x{}_y}$

$(4)\frac{{}_y}{{}_x}$ where $$ is a correlation coefficient