Assume the CAPM holds. $R_f=4\%.$ The market portfolio has an expected return of $20\%$ and standard deviation $23\%.$

Portfolios A and B have the same expected return of $13\%$ and same standard deviation of $31\%.$

Based on the above information, the correlation coefficient between A and $B$ has to be higher than or equal to

tightest lower bound. Enter a decimal number, not a percentage. Round your answer to $3$ decimal places.$)$