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.
Friday, October 8, 2010
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.,
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).
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
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.
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.
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.
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!
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!
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