Q.3943 A liquidity division for HTC bank invests in shares and a commodity. The mid-market value of the position in shares is $W$ while the mid-market value of the position in the commodity is $413. The mean and standard deviation of the bid-offer spread for the shares are $1.24 and $1.02, respectively. On the other hand, the mean and standard deviation of the bid-offer spread for the commodity are $0.67 and $0.34. Further, the mean and standard deviation of the proportional bid-offer spread for the shares is 0.0721 and 0.0675, respectively, while the mean and standard deviation of the proportional bid-offer spread for the commodity is 0.00524 and 0.00463, respectively. Assuming that the distribution of the spreads is normal, and the cost of liquidation at the 99% confidence level in a stressed market condition is $95.062, calculate W, the mid-market value of the position in shares.