# Prepaid variable forwards (PVF)

Reading 13 - Page 350, 4.3.2.3 Prepaid Variable Forwards

It says if an investor holds shares currently trading @ \$100, a PVF would consist of a collar (long put with \$95 strike and short call with \$110 strike) and \$88 from the dealer up front. At maturity, if share price is between \$95 and \$110, the investor must deliver \$95 worth of shares. If the price of shares is above \$110, the investor must deliver \$95 worth of shares plus the value of shares above \$110.

Can someone please explain why the investor would have to deliver \$95 worth of shares in both of the above cases? I understand why he would be liable for anything above \$110, but where did the \$95 come from? Much appreciated.

Think of the transaction in terms of total money, and it’ll become clearer. Not sure what you mean by “the investor would have to deliver \$95 worth of shares in both of the above cases.”

Floor is \$95 because of the long put. At \$95 you must deliver 100% of the shares to the other party because the only way to settle the trade at \$95 is to get rid of your entire stock position. At

Ceiling is \$110 because of the short call. At >= 110, you must deliver the number of shares that will equal \$95. Since there’s one unit of stock in this example, you’d deliver \$95/\$110 = 0.86 units of stock to settle the trade. This is the variable in the the name PVF.

If you’re anywhere between \$95 and \$110, again, you’d deliver the number of shares that will equal \$95. So let’s say the closing shae price is \$100. You’d deliver \$95/\$100 = 0.95 units of stock to settle the position. Again, this is the variable in the the name PVF.

Note that the original cash advance was \$88, and it is not used anywhere in the calculations. \$95 - \$88 = \$7 was the spread (assuming stock is at least \$95 at expiration) you paid the dealer for the convenience of receiving the cash advance ahead of time. Also, tax liability is not due until the contract is settled.

Hope this helps. Not completely proof read the numbers, so sorry for typos.

ahh… okay. i see. Thank you for the detailed explanation. gd luck studying!

Aether - seeking a small clarification here. When you say must deliver \$95 worth of shares - if the price is \$100 - shouldn’t the amount of delivery be 95/100 = 0.95 and if the price became 109.99 -> 95/109.99?

so he delivers 1 share if price is 95 and progressively goes down to below a share at any price between 95 and 110?

Or is 110 the denominator always?

Nice catch cpk. Closing price is always the denominator, not the ceiling. Of course, this rule applies only when you’re between the floor and the ceiling. When you’re less than the floor (\$95) or greater than the ceiling (\$110), the floor or the ceiling becomes the denominator, respectively. Have updated my original post to reflect the correction. Sorry if the typo confused… typed up the explanation without proof reading. Always good to have other people verifying the numbers.

Guys, to make it short, if the price is above \$110 you deliver \$95 / (MARKET PRICE) of stock. If the price is below \$95 you deliver MARKET PRICE/\$95 price of stock. Thus, the maximum you deliver is 100% of you stock?

I don’t think this is to be correct. From what I understood from the books, if the price is above \$110, you deliver [\$95 + (Market Price - \$110)]/ Market Price, which makes sense because you are short the call.