Friday, December 5, 2008

A Heuristic Approach for Rolling-Up-and-Out Covered Calls

A prior post (link) described the decision-making process used by the Covered Calls Advisor to determine if an existing covered calls position should be rolled-up (in the same expiration month) to a higher strike price. Alternatively, this post explains a heuristic method used to analyze whether an existing position should be rolled-up-and-out (i.e. rolled 'up' to a higher strike price and simultaneously 'out' to the next expiration month).

First, the term 'heuristic' is defined in Webster's dictionary as "involving or serving as an aid to learning, discovery, or problem-solving by experimental and especially trial-and-error methods." So by definition, the criteria developed to determine whether or not to 'roll-up-and-out' a particular covered call will not be a scientifically derived optimal solution, but rather this advisor's best estimate, based on experience with covered calls (especially options premium pricing and options time decay rates) as to what the decision-making rule should be at this time. Over time, it is expected that the decision criteria will be modified as additional information (i.e. feedback) is received that provides additional insights into this question. This continual feedback loop process is consistent with and is a normal feature of the heuristic method.

To determine what the roll-up-and-out policy should be, let's consider an existing covered calls position in the Covered Calls Advisor Portfolio. The existing position was:
Owned 600 shares Fluor(FLR) at a price this afternoon of $44.56.
Had 6 Dec08 $35 calls written (i.e. a short positon) at a price this afternoon of $10.10
Question: Should the existing covered calls be rolled-up-and-out to the Jan09 $45 strike?
(Note: the Jan09 $45 option was priced at the same time this afternoon at $5.30)

In answering this question, it is important to understand two key concepts:
(1) Notice that there is no mention above of when the existing FLR covered calls were established or the prices of the stock and calls when this covered calls position was originally established. It is only natural for us to want to know what our initial cost basis is in the existing position. However, including this historical information in our decision-making thought process actually distorts that process. What was paid initially and how much profit (or loss) has been achieved so far is irrelevant for us today when analyzing whether to roll-up-and-out or to simply maintain our existing position. The concept of disregarding past transactions and price changes that occur prior to today is a concept referred to by economists as a ‘sunk cost’. A sunk cost is simply a cost that has already been incurred. It’s past. It’s history. In short, it's irrelevant when trying to answer the question today as to whether to simply retain the existing position or whether to roll-up-and-out to another position.
(2) The second key concept used to aid in answering this question is what is referred to as 'average daily rate-of-decay', which is a short phrase that describes the average daily decline in the remaining time value of the call options assuming the existing covered calls position are retained until the options expiration date. For example, as of today there are exactly 15 calendar days until Dec08 options expiration. For the existing FLR Dec08 $35 call, the 'average daily rate-of-decay' of the short call option position is $.036 [total time value of $.54 ($10.10-($44.56-$35.00)) divided by 15 days remaining until Dec08 expiration]. This $.036 per day [which alternatively can be thought of as $3.60 per day per option contract written(since each contract represents 100 shares of stock)] represents the average daily income that will be squeezed out of the remaining time value of the option between today and the option expiration date. This $.036 per day from retaining the existing position is then compared against the 'average daily rate-of-decay' for a new Jan08 $45 strike alternative position. In this case, the 'avg daily rate-of-decay' is $.123 ($5.30 divided by 43 days remaining until Jan09 expiration). This roll-up-and-out alternative has a 241.7% greater average daily rate-of-decay than the existing position if it were to be retained until expiration. This +241.7% increase in the average daily rate-of-decay is a very substantial increase -- so the decision was made today to close out the initial covered calls and simultaneously roll-up-and-out to the Jan09 $45s.

As implied above, the heuristic approach is an ongoing work in progress. As time progresses and additional information and roll-up-and-out alternatives are considered, it is expected that the Covered Calls Advisor will develop a specific threshold that will dictate precisely when to keep the existing position and when it is preferable to roll-up-and-out. For now, a threshold of +200% will be used. That is, a roll-up-and-out transaction will be done if the average daily rate-of-decay is more than 200% higher than that for retaining the existing position.

The transactions history to date for the Fluor covered calls position is as follows:
11/24/08 Initial Stock Purchase Transaction -- Bought 600 FLR @ $35.35
11/24/08 Initial Calls Sold Transaction -- Sold 6 FLR Dec08 $35 Calls @ $3.50
12/03/08 Ex-Dividend of $75.00 ($.125*600 shares)
12/05/08 Roll-Up-And-Out Transaction:
Bought to Close 6 FLR Dec08 $35 Calls @ $10.10
Sold to Open 6 FLR Jan09 $45 Calls @ $5.30

Including the roll-up-and-out transactions today for the Fluor covered calls, the overall performance results(including commissions) through the Jan09 expiration would be as follows:

Stock Purchase Cost: $21,218.95
($35.35*600+$8.95 commission)

Net Profit:
(a) Options Income: -$820.35 (600*($3.50-$10.10+$5.30) - 3*$13.45 commissions)
(b) Dividend Income: +$75.00 ($.125*600 shares)
(c) Capital Appreciation (If stock price unchanged): +$5,508.10
= ($44.56-$35.35)*600 - 2*$8.95 commissions
(d) Capital Appreciation (If exercised): +$5,772.10
= ($45.00-$35.35)*600 - 2*$8.95 commissions

Total Net Profit(If stock price unchanged at $44.56): +$4,762.75
= (-$820.35 +$75.00 +$5,508.10)
Total Net Profit(If stock price exercised at $45.00): +$5,026.75
= (-$820.35 +$75.00 +$5,772.10)

Annualized Return If Unchanged (ARIU): +141.3%
(+$4,762.75/$21,218.95)*(365/54 days)

Annualized Return If Exercised (ARIE) +160.1%
(+$5,026.75/$21,218.95)*(365/54 days)

For comparison, an ARIE of +129.9% would be achieved if the roll-up-and-out transactions had not been made today, and instead the original position had simply been held until Dec08 expiration.

Finally, further analysis will be done in the near future to develop criteria to help determine the trade-offs involved at any given time as to whether an existing covered calls positions should be: (1) retained as is; (2) rolled-up (to a higher strike price in the same expiration month); or (3) rolled-up-and-out (simultaneously to both a higher strike price and a future expiration month). In addition, future posts on this blog will address the decision-making processes needed when the stock price declines and the possibilities of rolling-down or rolling-down-and-out become a consideration.

3 comments:

  1. Hi, great site! I really appreciate hearing what others are thinking as they wrestle through real time trading decisions.

    I am curious about your thoughts on the risk in this transaction. It looks like you had a net loss on the first covered call position ($6.60 ex transaction costs) that was offset by writing the new calls at 5.30. The risk, as I see it, is that the stock falls back to 35 or below. Then you are out the 1.30 difference and transaction costs.

    All told, the up-and-out strategy seems best suited to following a sustained bull move. Of course, imagine that you ran the up-and-out for twelve months running, to the same effect as above, and then the stock plummeted to your original purchase price. You would be out (1.30*12)--a bad trade in my book.

    Given this risk, I usually like to rollover at the same strike price in this type of market environment (choppy and overbought). You lose some of the rate-of-decay benefits, but have better protection for any downside.

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  2. Great Example and it begs a few questions for us to all deal with: When to roll and when to let something be exercised.

    My question is:
    Why did you buy FLR at 35.35 and write calls at $35? Wouldn't you do a call at a higher strike price than you bought at?

    You wrote:
    "Had 6 Dec08 $35 calls written (i.e. a short positon) at a price this afternoon of $10.10"

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  3. Good questions. I will soon be completing an update on my rolling criteria and plan to make a post to my blog on that topic in the very near future. Stay tuned.

    Jeff

    ReplyDelete