Friday, October 8, 2010

Silent Fears in the Hearts of Option Credit Spread Writers : Probabilities of worries, scares, and their bigger sister the probability of an option account blow up

One of the things that strikes fear in the heart of option credit spread writers is the thought that the underlying stock or index might touche or finish above their short strike. There is an even bigger fear which is the thought that the underlying stock finishes above their long strike, which means a maximum loss, and an account blowup if they did not read about this risk in the other posts in this blog--check it up because the devil is in the details in an option credit spread business.

What the probabilities  priced in the options of such events? Let us see how we can compute them.

Assume an  ABC stock (or underlying index)  trading at say 100 (S=100). We have a call option at strike 110 (K=110) which is priced at  $0.50.  We assume we know the delta (denoted D) of the call option at strike 110. Assume  D=0.40 for this example.

One may say that the probability P we are looking for is delta. This is the typical answer you may read about in forum, books, etc. But it is not correct. In fact the value of P is , bless than delta (although not by much by the distinction is important).

Here is how one can compute the probability that the stock would end above strike 110. The quantity ($0.50 + (110- 100)* 0.40)/110 is the difference (D-P). Therefore to get P, we subtract the latter quantity from D. In this case, it is equal to 0.041. This means that the probability of the stock ending above strike 110 is 40% MINUS 4.1%, which is roughly 35.9%. So the answer is not 40%,  but ( a lower number). 35.9%.

Let us ask you a second related question: what is the probability that the stock visits strike 110? (Note that we are asking for the probability that it touches 110, and not the probability that it ends about 110 at option expiration.) We will give the details in a next post.

Now go brag about your new acquired knowledge to friend, and strangers in forums. I give you the bragging rights. :-)

Oh! Before you go. Did you calculate the probability that the stock ends above the strike of the long option in your option credit spread?

Since you are reading down here, may mean you want to know the answer of the touch probability. It is a little bit more than the double of 35.9%.  In this case, you will get scared 72% of the time if you write the 110 call option. A bit more than half will be false alerts, but you do not know in advance which is an alert, and which is the real thing.

Monday, October 4, 2010

Analysis of Trading Systems Outcomes

I was reading a forum post, and a gentleman asked this question: "If one can predict [the] market daily movement 55% of time correctly, for example, SPY movement, how to profit it ?".

In fact, one  should some preliminary questions. A first question whether the abovee method is profitable, because the above quote did not include the loss and gain involved with the 55% probability of success. Let us assume that W is the win amount, L is the loss amount. A prerequisite to profitability is for the quantity  W*.45 + L*0.55  to be positive.

Assuming that the above quantity is positive, one then needs to know the draw down. Let us denote by D, the draw down (for instance D= 24%). To apply proper risk management, one needs to put at work an amount of capital such that at most 2% is lost on a single trade (central limit theorem). To take into consideration the drawdown D, the 2%, and to apply central limit theorem properly,  this means that at most 1/12 of one's capital can be used as the dollar value of a single trade. This implies that the the quantity, W.045+L*0.55 needs to be divided by 12, if it were computed under assumption of full usage of capital. This leads to the amount one may  make on single a trade on average.

Once one does the above calculations, one would get the percentage return on a single trade (projected to the full amount of account size), and since only one trade can be made at any given time and   there can be periods of time when no trades can be placed, the annualized return must be less than the annualized return corresponding to the quantity: (W*.45 + L*0.55)*(D%/2%).

We are not done yet, the trader also needs  to be aware of the probability of ruin, which is always non-zero. The probability of ruin cannot be reduced to zero because the trade outcome is not certain.

One should not forget to reduce the returns to take into account the risk free rate of return, the cost of commissions, and also one's time and other resources devoted to trading. One should also allocate an amount of money to trading mistakes, cost of shorting stocks or using leverage, and the like.

If one runs the numbers one may actually find that the returns are much lower than one may have expected at the beginning.,

Stock Market and currency markets - Some observations

1. After taking a beating over the last 3 weeks against the EUR, the dollar seems firmer today. EUR/USD had gained close to 10% in three weeks, which is huge in  the forex market. EUR/USD is trading at the lows of today, and the next 12 hours will decide on whether this is a retreat in EUR/USD. It has been trading range bound for the last 6 hours (very dull). A head fake is not to be excluded (head fake here means a move up before a real retreat).

We anticipate a possible  down move in EUR/USD that might get under way between 1:30PM and 3:00PM.

2. EUR/USD and the stock market are generally correlated. The last week, we saw something unusual. The stock market trading weaker/range bound, and the dollar taking a beating. This is not good for American stock market investors.

3. Today the stock market moved lower (probably to reflect the down move in EUR/USD). If EUR/USD weakens, this will be a real test for the stock market. If it goes up while EUR/USD goes down, then that would be a good sign for stock earnings.

4. Conclusion: the next few days are important to ascertain some conclusions on stock market and the US dollar.

5. The stock market is entering the earnings period. This is very important for stock options. We shall come back to this item in future posts (probably the next post).

Stock options Calculators

An internet friend who is training himself in the art and science of options trading has asked for an option calculator. There are a variety of them (some online, some are in excel form). They also vary in what they.
I plan to post here a list of option calculators. To provide immediate help to the friend, here one I have used provided by the CBOE.



http://www.cboe.com/LearnCenter/OptionCalculator.aspx

Saturday, October 2, 2010

High Yield Dividend Stocks --- How to Get The Dividend Before The Dividend Payment Date

High Yield Dividend  Stocks --- How to Get The Dividend Before The Dividend Payment Date


Let us assume  that the dividend is not too high, so that it is not considered a special dividend (Special dividends are dealt with differently). In general, stock investors who  buy it stock on the day before ex-dividend  are eligible for dividend, as their names would appear on the date of record, which is a couple of days after the ex-dividend date  (there is typically a delay between the trade date and the settlement date, which changes from country to country, and can change with changes in rules and regulations). The payment date is usually sometime in the future after the ex-dividend date.

Is there a way to get the dividend earlier than the payment dividend date?

Holding a stock synthetically means buying a call option and selling a put option. If one assumes zero interest rate, prior to the ex-dividend date the price of the at the money  (ATM)  call MINUS the price of the ATM  put should be equal to MINUS the discounted value of the dividend. On the ex-date, the options should be priced without the dividend priced in, and the price of the ATM call minus the ATM put should be  equal assuming there is no other dividend between the ex-dividend date and the option expiration date, and of course assuming zero interest rates. If interest rates are significant, the ATM call minus at the money put should be equal the interest carry cost.

So essentially the synthetic stock appreciates by the amount of the dividend on the ex-dividend date, and therefore capturing the dividend on ex-dividend date before the payment date.

Typically stocks fall by the amount of the dividend on the ex-date, which leads to an interesting question: is it worth to try to capture  the dividend? There might be surprises in the answer to this question.

Friday, October 1, 2010

Hidden Risks In Options Trading

Option traders and investers may sometime be taking risk they not even aware of. These risks appear when the unusual happens in the stock market. I learned about the case I am about to describe back in May 2010, after the flash crash.

 There was a guy who lost his whole account, and even more due to one little "mistake". He had his option positions (spreads with limited risk that are covered), and other non option positions in the same option trading account.

The market moved fast, and he had a margin call, which professional brokers meet in real-time. The robot took some of his option positions off , and that triggered a series of margin calls because the removal of one option position made things worse from a margin point of view. Since the market was moving fast and bid/ask spreads were large, the bid/ask spreads were expensive, and the random manner in which the liquidation was made led to the closure of all positions, and the net effect was that he has lost his whole account, and even may have owned money to the broker. The trading account went from something like +10K to a minus number.

So one should be careful about this part, in case one did not think about it.

Debit Spreads

A friend send me the URL to  website that gives trade recommendations using debit spreads for the QQQQ EFT. He mentioned that the profits were small in dollars, quite consistent,  and have high percentage return. 
The returns range from 40% to minus 45%. The (arithmetic average is 25%). He seemed  impressed, and asked for my opinion.  Their spreads are 2 dollars wide on the QQQQ which trade in the upper 40s. Below Should he be impressed or not? Here is my analysis answer.


1. Their spreads are about $2 wide, which if you project to the QQQQ value, is bout 4%. The leverage is therefore 25. Why is this important? Because if you adjust to leverage, the return is only 0.65% per trade. If you project it for the whole year, and assuming always a trade is on, you get about 3 to 4% annualized. The leverage adjusted return is even lower. Why: check points 2-4.

2. What is shown is arithmetic average of the return, not the geometric average , which is the true return. Geometric return is always less than arithmetic, and if you add the no trade time periods, your return is much less that 3%.

3. Other problems: you have to divide by another factor (which is higher than 1), because the beta of the QQQQ is higher than the beta of the market.

4. No dividend is in there, while you receive it in the QQQQs.

Conclusion, the
return  adjusted for  leverage, risk, dividend is probably around 1.5%.



One related conclusion: people use leverage to get high return, when in fact the reverse is probably better. Why? Because if one can get a positive no risk return higher than the borrowing rate, and then one can leverage it. 


One should pay attention to  returns that involve leverage because  leverage can lead to good looking returns which can deceive the eye, when in fact the returns can be less than risk free returns.


Credit Spead Management --- Some Insights

A recent friend ask me a question about his call spreads. He seems to have the right attitude to deal with risk early on in position's life. One of his methods is to roll his credit spreads once the credit spread's value loss has reached   150% the initial value of his spread. 

The question posed are: how often will the adjustments be needed, and how early or late in the life of the position will the adjustment be needed.

Let us consider call spreads on NDX. The distance between the short strike option and the long strike option is 25. points, which represents around 11% of the NDX current value. The option are monthly or less. One starts with a monthly option. When the rolling is ongoing, the option might have less than one month to expire.


The call spread premium is around 1.25, which on a 25 points distance between strikes,  represents 5% of the width of the spread. We consider the 5% as a proxy of the probability of failure, if nothing is done to the credit spread until expiry (if one takes the worse-case loss). The probability that a trade gets beyond the short strike should  be around 10% ( It is the double of 5%). This might may not be intuitive at first, but there is a justification for it from theoretical standpoint.



The probability corresponding to a 150% loss should be higher than 10% (because one wantsthe stock to never get to your short strike). To get an approximation of the 150% loss prob, there are two ways. Here is a first way, which assumes one access to a PL curve of the credit spread as a function of stock price and time.

If your broker gives you a PL for the spread as a function of price and time, you should be able to find the price of the stock where you get the 150% loss on the spread.

Once you get that price, you then run a touch probability calculator. If you do not have it, here is rough approximation that gets the essence of the work.

You get the delta of the call of corresponding to the price of the stock where you will get the 150% loss, and multiple that by 2. That will give you the probability that the 150%  loss would  be reached.

Here is the insight: The probability that one gets the 150% loss is higher at the first day, then it decreases over time if the stock does not move, and of course if the stock moves in one's favor the probability of the 150% loss decreases.

What do we learn from this:  with directional spreads, one is at risk early on in the trade, and adjustment would happen early on in the life of the trade, and they should happen more frequently than one might have thought by looking at the 5% probability of loss if the position is held until expiry.

To your stock and option trading profits!

Saturday, September 25, 2010

Income option credit spreads --- Adjustment of condor credit spreads

Income option credit spreads --- Adjustment  of condor credit spreads

Consider for instance a  80/20 condor credit spread. If one were to put a spread on each and every time period (for instance monthly) for a large number of periods, the percentage of trades  in which the stock price ends is  at or above a short strike represents 20% of all trades. One of the techniques used consists in readjusting the spreads if the stock come close to a short strike, or the loss on the candor spread were to reach a given percentage of the premium received.

Let us refine a problematic trade, and trade in which the stock get dangerously close to the short strike. The question we post in this post is to estimate the percentage of such trades.

Let us consider the call side, and look at rules that trigger a readjustment when if the stock comes close to the short strike without crossing it.  The number of bad trades (at expiry) is 10% (half of 20%). of all trades. The percentage of problematic trades must be greater than or equal to  the percentage of trades that can reach the short strike. Let us then determine the percentage of of trades that reach the short strike.

To determine it we need to find an estimate of the probability that the stock will visit the short call strike, say strike 110 for a stoke trading at 100. We know that a trade that ends above 110 must have visited price 110 on its journey from 100 to a value above 110. We also know that among the visits that the stock will make to strike 110, approximately half of them (in fact it can be less than half) will end up above 110 at expiry.

Therefore the percentage of trades that will visit the short call strike is TWICE the percentage of trades that will end at a price higher than the short call strike. In the case of the 80/20, even if there is only a 10% change that a trade will end up above the short call strike at expiry, at least 20% of the trades will become problematic for the call side.

A similar reasoning can be made for the put side.

Therefore the percentage  of trades that will problematic (need readjustments) is more than the double of the trades that have been legitimate adjustments. In other words, among all the adjustment made more than half of them would have been not needed, and these trades would have been winners.

This is significant because it means that the winner that will need no intervention in an 80/20 condor is actually less than 60% of the trades (probably around 50% or less) depending one where one make the adjustments.

A number of websites and people assume that they would make adjustment 20% of the time, and do nothing during 80% of the time, when in fact it is not true.

In an 80/20 condor one should expect to be busy with adjustment at least almost  once in  every other trade.

If You Have Two 5 Years Condor Spread Trading Records From Two Advisory Services, Could One Of Them be Reliable?

If You Have Two 5 Years Condor Spread Trading Records  Each, Could One Of Them be Reliable? You guessed it right: the answer is the classical expression "It depends". Let us check what it depends on, and how to make a determination.

In the previous post, we explained why a minimum of 10 years are needed to make a judgment on an 80/20 condor spreads trading record.  Suppose that when you visit the web, you find a number of advisory services that provide five year record. Could some of these trading records be useful? It depends on the probs assumed in the spread, and the duration of the spread, which we shall assume is 1 month.

We mentioned the expression of a "bad trade", but we did not define it. For the purpose of this analysis at least, a bad trade where the stock price is at or above the short strike at expiration. Please make sure you do not confuse this definition, with another definition that may be in your mind such as  a trade in which the stock reaches a short strike during the life of the trade, which is probably the one you may have in mind, or an even worse definition of a bad trade. The latter definitions of a bad trade lead to larger percentage of bad trades than implied in the numbers attached to the condor spread. In the next post, we are going to address this issue in more depth. So do not go away as they say on CNN-- we will be right back.

Now we are back to our analysis. If we take the 80/20 condor spread, a bad trade (for the purposes of this post) is a trade that finishes at or above a short strike. There are 20% of them on average, and we explained in the previous post why one needs 10 years. Let us call a advisory service that offer these spreads as advisory A. 5 years in not enough for advisory A. Let us say a second advisory, denoted advisory B, follows  (more aggressive spreads) 60/40 monthly condor spreads . In this case, a 5 year period would generate 24 bad trades for advisory B, and therefore the 5 years meet the minimum requirement for advisory B, but not for advisory  A.

The lesson: A smart condor spread trader should then ask not only for the duration of a spread, and the length of the trading record, but should also ask about the nature of the spread, and make sure that it was kept consistent---For instance, you do not want to have in the same record 80/20 spreads in certain months, and 60/40 in another  months, etc. You then use the rules as discussed above.

While asking your questions to the advisory guys, if the guys do not seem to understand what you are asking for and why you asking for the information, then you have an indication about the intellectual strength of the intellectual strength of the advisory service---Edges can take a conceptual form.

Before I leave you, I have a question: Could we have a 50/50 condor spread ? If yes, could you apply the analysis above?

Answers:  I will wait before I give it to allow you time to think about it. Make sure you visit in a few days. It will be here. You can also post your answer in the comments section below.

Option Condor Spread Writers -- How Long Should A Trading Record Be?

 Short answer: a reliable track record needs at least 10 years! We explain why below, but first some introductory remarks.

One should not confuse a high probability trading strategy with a trading strategy that has an edge. A well known example of high probability strategies is the option condor strategy, in which  one sells one put and one call, and hedge them by buying a put and a call  that are respectively at higher  and  lower strikes, when compared to strikes of  the call and the put that were sold. This leads to "impressive" annualized yields because of  lower margin requirements (which are the difference between strikes adjusted by the net premium), and condors can be designed to achieve a high probability of success in one trade.


For instance, it is not unusual to write these condor spreads so that the probability of the stock ending between the two sold strikes is 80% (with a yield on margin that impresses the eye). When option beginners look at these numbers they are typically  impressed, and .do not think in sufficient depth about the risks.  

The  typical  condor writer makes a series of successful trades, and then one day a non successful trade can come along, and wipes all profits. It may even lead to the loss of  the whole capital, if all of it was used as margin, and the bad trade involves gap well  beyond the long protective strikes.

One can find a number of option advisory services that  provide condor spread signals. People can be easily impressed by the numbers. An advisory service typically posts a track record, and they in different length, from  6 months to 6 years/etc. 

What is an acceptable track record in terms of length of time, and why?


This is a core issue with all trading strategies with high prob of success on one trade. If the prob of success is say 80% on one trade, it would mean that one would need 10 years to generate 24 trades that are bad. A sample size of around 25 is needed to form a scientific conclusion, via the application of the Central Limit Theorem/Law of "large numbers".

Therefore a reliable track record needs at least 10 years!





Interestingly, some of the well known times when option writers took major hits were separated by 10 years: crash of '87, crisis of '98, and the credit crunch crisis ten years later.

There is an alternative to track records based on observed numbers and time:  one needs to prove theoretically (using mathematics) that a high prob strategy has a positive edge.