A factor portfolio has a sensitivity of one to one factor and a sensitivity of zero for all other factors (in this case, a pure bet on industrial production). We need to create a factor portfolio (a combination of portfolios J, K and L) that has a factor sensitivity of zero to the confidence risk factor and a sensitivity of one to the industrial production factor. The three simultaneous equations to solve are:

Equation 1: w_J + w_K + w_L = 1 (portfolio weights sum to 1)

Equation 2: 1.50w_J + 0.80w_K + 1.00w_L = 0 (confidence risk portfolio sensitivity equals 0)

Equation 3: 1.00w_J + 1.20w_K + 2.00w_L = 1 (production portfolio sensitivity equals 1)