Convexity: You are in a meeting and talking about how you are concerned that the Fed has signaled it will

be increasing interest rates several times this year. You explain to your boss that you believe the portfolio

$($which consists primarily of $15-30$ year maturity bonds$)$ is overly exposed to these potential interest rate

risks and want to hedge your position. Your boss condescendingly pats you on the head and says $$Look$,$

kid. I appreciate your work ethic but I$$ve been doing this for $40$ years. And back in $1980$ I managed a huge

portfolio of short$-$term bonds and we thought rates might increase back then too. They ended up increasing

but we didn$$t lose much money at all. So I$$m not worried, and you shouldn$$t be either.$$

Question X$\mathrm{.}1$: $(20$ points$)$

Assume for simplicity that your boss is remembering the beginning of $1980$ correctly. Short$-$term interest

rates did go up before they came back down. Is his explanation to you convincing? Why or why not?

$2$