\documentclass[a4paper,12pt]{article}
\begin{document}
\parindent=0pt
QUESTION
Today's date is $16^{th}$ March 2008. You are interested in
investing in a company called Globaldom whose current stock price
is \$10. There will be a US presidential election in the first
week of November 2008. Depending on who wins, you believe the
stock price of Globaldom will rise or fall by approximately 10\%.
Call or put options are available with expiry dates in June,
September and/or December with strike prices of \$9,\$10 and \$11.
Assuming your estimates of the likely rise and fall are accurate,
construct a portfolio of options which will do well under both
outcomes. (Ignore initial costs).
ANSWER
If shares are equally likely to rise or fall, then hold options
equally in calls and puts. Try a portfolio with expiry dates in
December.
Long one call with strike $k_2=\$7$
Long one put with strike $k_1=\$11$
Then payoff
is$=\max(11-S,0)+\max(S-9,0)=\left\{\begin{array}{cc}11-S&0\leq
S\leq 9\\2&9\leq S\leq 11\\S-9&11\leq S\end{array}\right.$
Graphically
\setlength{\unitlength}{0.5in}
\begin{picture}(7,5)
\put(0,1){\vector(1,0){7}}
\put(1,0){\vector(0,1){5}}
\put(0.8,0.7){0}
\put(7,1){$S$}
\put(0,4){Payoff}
\put(.7,2){2}
\put(.7,3){11}
\put(3,.7){9}
\put(4,.7){10}
\put(5,.7){11}
\put(1,3){\line(2,-1){2}}
\put(3,2){\line(1,0){2}}
\put(5,2){\line(2,1){2}}
\put(1.8,2){$11-S$}
\put(4,2.5){2}
\put(6,2.2){$S-9$}
\end{picture}
Other possibilities exist.
\end{document}