As an analyst at an investment bank, you are asked to estimate the Sharp$-$Ratio $($SR$)$ parameter $({}_{SR})$

for the two stocks Tesla and Apple Inc. The SR is defined as:

${}_{SR}=\frac{{}_R-R_f}{{}_R}$

where ${}_R,R_f,$ and ${}_R$ denote the expected returns, the risk$-$free interest rate, and the expected

standard deviation $($volatility$)$ for returns, respectively. It is evident that SR is a measure of risk$-$

adjusted excess returns. In this case, the risk$-$free interest rate equals $R_f=0\mathrm{.}0025,$ and the volatility

parameter ${}_R$ equals $0\mathrm{.}20$ for Tesla and $0\mathrm{.}10$ for Apple Inc.

The following returns during the period of August $2020$ to March $2021$are observed:

a$)$ Which stock has the highest estimated Sharp$-$Ratio?

b$)$ For both Tesla and Apple Inc, calculate a $95\%$ confidence interval for ${}_{SR}.$ Can you argue that

these two Sharp$-$Ratios are different?