A company has a position in bonds worth$6 million. The modified duration of the portfolio is your birth month (e.g., if you were born in March, then the duration is 3).Assume that only parallel shifts in the yield curve can take place, the mean of the daily yield change is 0, and that the standard deviation of the daily yield change (when yield is measured in percent) is 0.09. What is the change in the positions value if yields shifted down 10 bps (0.1%)?

Use the duration model to estimate the 20-day 90% VaR for the portfolio.

If the bond has convexity, explain why your analysis of VaR above is incorrect. How does this relate to the Gamma risk of an option?