Question Two: Bank XYZ$,$ a notable financial institution, manages a substantial inventory of AAA$-$rated, $10-$year zero$-$coupon bonds. These bonds, known for their high credit quality and lack of periodic interest payments, carry a total face value of $$300$ million. Currently, these bonds are yielding $8\mathrm{.}5$ percent in the over$-$the$-$counter market, reflecting the market's assessment of their value based on prevailing interest rates and the bank's risk profile. Given this financial landscape and the inherent interest rate risk associated with long$-$term fixed$-$income securities$,$ calculate the following requirements:

$(10$ points$)$

A$.$ Calculate the modified duration of these bonds to understand their sensitivity to interest rate changes.

B$.$ Assess the price volatility of these bonds assuming a potential adverse movement in yields of $35$ basis points.

C$.$ Calculate the Daily Earnings at Risk $($DEAR$)$ for this bond portfolio

D$.$ Considering a $95$ percent confidence limit and a mean historical change in daily yields of $0\mathrm{.}0$ percent, which indicates stable market conditions over the observed period. Based on this information, determine the implied standard deviation of daily yield changes to gauge the volatility and risk associated with the bond portfolio. This analysis is critical for Bank XYZ$\text{'}$s risk management strategy, as it provides insights into how changes in interest rates could impact the value of its holdings and its overall financial position.