Naked put

The usual way to protect a portfolio from a fall is to buy a put option. Because there is something to protect, that trade is called a protective put. The put pays off as the market drops, which offsets what the holdings lose.

Now take the same option away from the portfolio. Someone buys the put purely as a trade, with no shares behind it. The workbook calls that a naked put.

The word naked simply means there is nothing underneath. The option is not insuring anything. It is a view on the price falling.

The pay-off arithmetic is the same option either way. What changes is the rest of the picture. A protective put sits beside a loss it is cancelling. A naked put stands alone, so its gain is a gain and its loss is a loss.

The workbook's own wording (section 18.13). The most common protection against loss on an existing portfolio is buying a put option, known as a protective put given that there is a portfolio to be protected. The other form of put option is the naked put, where the put option is taken for either trading or speculation without any portfolio to be protected.

The workbook's protective-put figures. A portfolio manager has bought 100 shares of Reliance Industries at Rs 2,000 a share and buys a one-month put with a strike price of Rs 2,000 for a premium of Rs 25.

That is how a put locks the downside to the extent of the premium paid.

Strip out the portfolio and the same put becomes naked. Using the workbook's own numbers, a buyer holding no Reliance shares:

• price falls to Rs 1,900 — the put is worth Rs 100, less the Rs 25 premium, a gain of Rs 75 a share, with no offsetting portfolio loss;
• price rises to Rs 2,100 — the put expires worthless and the whole Rs 25 premium is lost, with no offsetting portfolio gain.

The option's cash flows never changed. What changed is that they are no longer cancelling anything.

Section 18.13 gives no figure for the naked case — it defines it in a single clause and moves on. The Rs 2,000 strike, Rs 25 premium and Rs 1,900/Rs 2,100 scenarios above are the workbook's protective-put illustration; the naked column is the same arithmetic with the shares removed.

Working the workbook's own numbers on 100 shares, at a Rs 2,000 strike and a Rs 25 premium.

Case 1 — a protective put. Mrs Deshpande owns 100 shares bought at Rs 2,000, worth Rs 2,00,000. She pays Rs 2,500 for the put.

Price falls to Rs 1,900. Her shares are worth Rs 1,90,000, a loss of Rs 10,000. The put is exercisable for Rs 10,000, of which Rs 2,500 was the premium, so Rs 7,500 net. Net loss Rs 2,500 — the premium, and nothing more.

Case 2 — a naked put. Mr Kulkarni owns no Reliance shares. He buys the identical put for Rs 2,500 because he expects the stock to fall.

Price falls to Rs 1,900. He collects Rs 10,000 less the Rs 2,500 premium = a gain of Rs 7,500, a return of 300% on the Rs 2,500 he risked.

Price rises to Rs 2,100 instead. Mrs Deshpande is up Rs 7,500 overall: Rs 10,000 on the shares less her Rs 2,500 premium. Mr Kulkarni is down the whole Rs 2,500, because he had no shares to gain on.

Same option, same premium, same market. One is insurance; the other is a bet.

Chapter 18, section 18.13 (Protecting Portfolios with Put Options), introduces naked put in a single parenthesis while defining the protective put, and the chapter's caselet works a portfolio protection question — a Rs 200 Mn portfolio falling 10% is matched by a European put option, Rs 15 Mn gain against a Rs 20 Mn portfolio loss.

Expect the distinction to be tested rather than the pricing: which form of put option is taken without any portfolio to protect (the naked put), and what the protective put's maximum cost is (the premium).

• Answer from the workbook's definition. Section 18.13 uses naked put for a put taken with no portfolio behind it. Some texts use the same phrase for writing an uncovered put, which is a very different risk profile. In this paper, take the workbook's sense.
• A naked put is not a naked position in the derivatives paper's sense — that is a futures position with no holding in the underlying and no offsetting contract. Related idea, different definition and different chapter.
• The buyer's loss is capped at the premium. Buying any option, naked or protective, cannot lose more than what was paid for it.
• A protective put does not remove the loss, it caps it. The workbook's own figures leave a Rs 25 per share net loss — the premium.
• Protection costs money every time. The premium is spent whether or not the market falls, which is the whole Rs 25 in the workbook's rising-price scenario.