Imagine that you are holding $5,000$ shares of stock, currently selling at $$40$ per share. You are ready to sell the shares$$

but would prefer to put off the sale until next year due to tax reasons. If you continue to hold the shares until January, however,

you face the risk that the stock will drop in value before year$-$end. You decide to use a collar to limit downside risk without laying$$

out a good deal of additional funds. January call options with a strike price of $$45$ are selling at $$2,$ and January puts with a strike price of $$35$ are selling at $$3.$

What will be the value of your portfolio in January $($net of the proceeds from the options$)$ if the stock price ends up at $$30,$ $$40,$ $$50?$

What will the value of your portfolio be if you simply continued to hold the shares?