Problem $1.$ Imagine you are a rational $($utility maximizing$)$ investor and assume you are in the case of one risky and one riskless asset. You have just decided upon you capital allocation for the next year.

a$)$ You realize that you have underestimated both the expected return and the standard deviation of the risky asset by $4\%.$ Will you increase, decrease, or leave unchanged your allocation to risk$-$free T$-$Bills? $($Hint: You can argue graphically using the CAL and indifference curves.$)$

b$)$ Upon careful introspection, you decide that you are really more risk tolerant than you first thought. How will you change your asset allocation?