# Once And For All - Naked Put = CC



## wayneL (6 October 2010)

I am starting this thread as a reference for the next time someone says something like Covered Call good, Naked Put bad.

Why? Because they are the same thing, they are synthetic equivalents. If the naked put is horrible and risky, then so is the covered call. If the covered call is conservative and good, then, so is the naked put. Once again because they are the same thing.

Firstly, for those with a more advanced grasp of options:

Supposing we have two traders, one who has a covered call, the other a naked put of the same strike and expiry.

The question is how do you get flat with one trade?

For the naked put it is easy, simply buy a put of the same strike and expiry, ergo closing out the trade.

What about the covered call? How do you get flat with one trade? It is the same, you simply buy a put of the same strike and expiry, making the position a "conversion" which is a flat position.

If you understand options, this should be enough conclusive proof that they are the same, but if still not convinced, lets do a bit of arithmetic....


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## wayneL (6 October 2010)

...suppose we have the same two traders, one with a naked put, one with a CC of same strike and expiration.

With the stock @ $50.00 let's suppose the CC guy wrote the at-the-money call for $3.00 credit.

The naked put guy also receives (for ease of calculation and presumes no cost of carry) $3.00 credit.

What happens if the stock is at $50 at expiry?

Both traders end up with $3.00 profit by the options expiring worthless. Equal result.

What happens if the stock is say $56 at expiry?

The CC guy will have his stock assigned at $50 so no profit from the stock, but he still keeps the $3.00 premium from the call sale, so $3.00 profit.

The NP guy's put expires worthless so keeps the $3.00 premium.

Again same result, both traders profit by $3.00


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## wayneL (6 October 2010)

What if the stock goes down? Let's say the stock goes to $40 at expiry.

The CC guy loses $10 on the stock, but the call expires worthless and he gets to keep  the $3.00. Net loss $7.00

The NP guy will be assigned and will be forced to buy $40 shares for $50, a loss of $10, but keeps the $3.00 premium from writing the put. Net loss $7.00

Once again same result.


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## wayneL (6 October 2010)

What if the stock goes to zero?

The CC guy loses $50 on the stock, but the call expires worthless and he gets to keep the $3.00. Net loss $47.00

The NP guy will be assigned and will be forced to buy worthless shares for $50, a loss of $50, but keeps the $3.00 premium from writing the put. Net loss $47.00

Once again same result.

This is the maximum loss from either position - $47

So which is more risky again? Yep, the risk is the same and in this case appears NOT to be "unlimited".

Cheers, questions welcome. 

P.S. All the above ignores transaction costs.


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## mazzatelli (6 October 2010)

Excuse me sir, 

I have heard from questionable sources, that with covered calls you receive dividends, thus it is not the same as a naked put :...


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## BradK (6 October 2010)

Hi, 

Just to spoil another covered call thread... 

My name is Brad and I have just began renting shares. I get 8% return per month and my question is: Can I use a credit card to finance my trades? I got a letter in the post from GE Money the other day giving money away real cheap on a cash advance. A friend of mine does this and I can't go wrong. In fact, I am about to quit my job as a school teacher to do this full time. 

I do not want to write naked puts... they are far too risky! I would much prefer the conservative safety of the covered call. 

Thanks in advance for your kind help Wayne and Mazz


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## hmmm (6 October 2010)

BradK said:


> Hi,
> 
> Just to spoil another covered call thread...
> 
> ...




Hi im 12 and new around here and what is this... so is what you're saying

Disregard naked puts
acquire covered calls
????????
Profit


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## village idiot (7 October 2010)

omg imagine if someone just bought a bunch of the stock??? according to the figures above he would be risking $50 a share, and whats more would make a big fat zero if the stock was unchanged at expiry. 

Now that does sound like a risky strategy...


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## wayneL (7 October 2010)

BradK said:


> Hi,
> 
> Just to spoil another covered call thread...




LOL 



mazzatelli said:


> Excuse me sir,
> 
> I have heard from questionable sources, that with covered calls you receive dividends, thus it is not the same as a naked put :...




Ah yes, the last line of defence for the CC muppets. Thanks for the vicarious objection :

Although Messrs Black and Scholes made some erroneous assumptions when they first devised their option pricing model, they weren't so silly as to ignore dividends.

As we know, dividends are one of the six inputs to any option pricing model used for stocks. Therefore, pricing must surely account for this somehow... in fact it does, torpedoing the CCs for dividends nonsense.

Firstly, many people think dividend magically appear from nowhere; they don't, they are drawn from the earnings and/or capital reserves of the company. This is why the stock generally drops by the grossed up amount of the dividend when it goes ex-div.

For the shareholder, this means the dividend payout is equity neutral; the stock drops, but you have the cash.

Option pricing accounts for this: When a stock is cum-dividend, put prices will be higher and call prices will be cheaper.

This means that if the stock is cum-divi, the CC trader will recieve less premium for the written call, whereas the naked put trader will receive a greater premium, with a correction in the option prices when the stock goes ex-dividend... depending on the moneyness of the options, this will be of a magnitude that reflects the grossed up dividend.

So if you write a naked put, you still effectively receive the dividend via the greater premium, just like with the CC.

Still equivalent.


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## Mofra (11 October 2010)

mazzatelli said:


> Excuse me sir,
> 
> I have heard from questionable sources, that with covered calls you receive dividends, thus it is not the same as a naked put :...



Is this also the time to be a smart-**** and mention that with naked puts you reduce transaction costs (no acquisition of the physical as in CCs) and earn interest on the funds you didn't use to acquire the underlying security? :


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## wayneL (11 October 2010)

Mofra said:


> Is this also the time to be a smart-**** and mention that with naked puts you reduce transaction costs (no acquisition of the physical as in CCs)




Yes



> and earn interest on the funds you didn't use to acquire the underlying security? :




Yes you do, but as interest rates are an input into the option pricing model, the net result is equal. IOW cost of carry is priced into the option premium.

Where the underlying is an asset, you get just a little bit more premium for calls and just a little bit less premium for puts.

More here ==> http://sigmaoptions.blogspot.com/2008/05/effect-of-interest-rates.html


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## alex21 (11 October 2010)

You are absolutely right. The naked put is almost equivalent to the covered calls. The difference is - the naked puts give a significantly larger leverage. So the trader with short puts might receive a margin call and potentially can lose ALL his money. When the trader is using good money management then the "naked puts" are cheaper (in the sense of commissions and margin requirements) and more flexible than covered calls. However there exists a "seduction" of higher leverage and consequently the higher risks. (IMHO)


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## wayneL (11 October 2010)

alex21 said:


> You are absolutely right. The naked put is almost equivalent to the covered calls. The difference is - the naked puts give a significantly larger leverage. So the trader with short puts might receive a margin call and potentially can lose ALL his money. When the trader is using good money management then the "naked puts" are cheaper (in the sense of commissions and margin requirements) and more flexible than covered calls. However there exists a "seduction" of higher leverage and consequently the higher risks. (IMHO)




Well that depends.

Those on portfolio margin can lever themselves as much with CCs as naked puts.



> e.g.
> 
> Position
> Long 500 IBM @ $91.25
> ...




Same thing with trading CCs with stocks on a traditional margin loan.

On the other hand, some people are in a position of having to cash cover their naked puts.

Margin requirement or the decision to use maximum leverage is one of money management and nothing whatever to do with synthetic equivalency.


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## mazzatelli (11 October 2010)

However sir, 

I understand the positions are equivalent in payoff, but doesn't the market have a tendency to crash more than it gains?
This would make the naked puts more likely to lose money doesn't it :....?


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## cutz (11 October 2010)

mazzatelli said:


> However sir,
> 
> I understand the positions are equivalent in payoff, but doesn't the market have a tendency to crash more than it gains?
> This would make the naked puts more likely to lose money doesn't it :....?




Geez,

This grinding rally has made me forget what a crash skew looks like.


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## colion (12 October 2010)

mazzatelli said:


> However sir,
> 
> I understand the positions are equivalent in payoff, but doesn't the market have a tendency to crash more than it gains?
> This would make the naked puts more likely to lose money doesn't it :....?




http://www.futuresmag.com/Issues/2010/May-2010/Pages/Naked-put-vs-covered-call-Whats-riskier.aspx


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