As a business analyst, you are monitoring a stock whose total return volatility is $50\%,$ while its idiosyncratic volatility is $10\%.$ Suppose the beta is $3.$ Based on your analysis, the stock's return should have a covariance of $-0\mathrm{.}1$ with the SDF$.$ The level of the risk$-$free rate is currently $5\%.$ The volatility of the market's return is $15\%.$

$(1)$ Compute the stock's expected total return.

$(2)$ What is the expected return of the market

$(3)$Supposethat the level of correlation between the market's return and the stock's return is bounded, what is the minimum stock total return volatility that you could consider?