A $15-$month futures contract on an equity index is currently trading at R$3763\mathrm{.}52.$ The

underlying index is currently valued at R$3625$ and the continuously compounded risk$-$free

rate is $5\%$ per year. Assuming no transaction costs,

a$)$ What continuously$-$compounded dividend yield is implied by the futures contract

price $?[3]$

b$)$ A trader on the Johannesburg Stock Exchange believes that the continuouslycompounded

dividend yield will be $2\mathrm{.}085\%$ over the next $15$ months.

What is the $15-$month futures contract price induced by the trader

belief $?[2\mathrm{.}5]$

c$)$ Based on the trader belief, is there an arbitrage opportunity $?$ If yes, describe the

appropriate strategy for the trader to take advantage of

this opportunity.