Anyone who has never made a mistake has never tried anything new.
On April 15, I wrote an instablog post on SeekingAlpha. It explained how the forward price of a stock is impacted by its dividend and how to structure an options trade that should benefit from a higher dividend. The article went through scenarios for purchasing a conversion on Apple (AAPL) and the cash flows. As it turns out, Apple did raise its dividend. I’m going to go through the market results so far.
First, let’s review the trade and what happened. I suggested looking at Jan 2014 conversions. Mid-market was $7.03 and I wrote that it would likely cost $7.50 to get into the trade. At the time of the article, AAPL’s dividend was $2.65 per quarter. On their earnings announcement, Apple raised its dividend to $3.05 per quarter. It turned out that was below my “conservative” estimate of $3.60 based on matching the yield of other, similar tech giants. Instead, Apple’s management chose to enhance shareholder return primarily through buybacks.
It is now May 2nd. As I write this, AAPL is $447. It’s next ex-dividend date is May 9. We can reasonably expect two additional dividend payments of $3.05 prior to the Jan 18th 2014 option expiration. Likely dates are August 8th and November 7th (I’m predicting Thursdays). I’ll continue to use a discount rate of 0.5% as I did in the prior post. Had AAPL still had a $2.65 dividend (to be clear, it doesn’t), then the forward would be:
F = $447e(.005)(.715) – $2.65e(.005)(.696) – $2.65e(.005)(.447) – $2.65(.005)(.197) = $440.63
Since AAPL actually did change its dividend, its forward will now be:
F = $447e(.005)(.715) – $3.05e(.005)(.696) – $3.05e (.005)(.447) – $3.05e (.005)(.197) =$439.43
That is a difference of $1.20, which, due to near zero interest rates, is the same as the difference in three dividend payments of 40c each. So far, so good. One expects the conversion to move the same amount, too.
Recall that we valued the forward at $6.17, but that the mid-market price was at the time $7.03. The market appeared to be pricing a move in the dividend. Given the scenarios that I had envisioned, it appeared to be a worthwhile risk to pay $7.50 based on the scenarios in the Expectations section of the post. The current Jan 2014 at-the-money (ATM – meaning those options closest to the forward price of AAPL) conversion is $6.62-$7.56, with a mid-market of $7.09. Putting things together, our forward calculations moved from $6.17 to $7.57 ($447 – $439.43). Note that is a difference of $1.40, not $1.20. Those extra 20c are the interest costs that already were paid for holding the trade since April 15th.
Where is the difference between the forward and the current conversion price from? From the early exercise provision of American style options. This is where the quote from Einstein comes in. As it turns out, it is the quote for the chapter “Options on Stocks that Pay Discrete Dividends” from Espen Haug’s excellent The Complete Guide to Option Pricing Formulas book. I’ve no idea what motivated him to put that quote with that chapter, but it fits well with my situation. Perhaps he, too, made a mistake in a dividend exercise situation. Or perhaps he was referring to the Roll-Geske-Whaley model which had been used to price options with dividends but turns out to be incorrect. At any rate, my problem is that in addition to putting this trade on with options expiring Jan 2014, I also put it on with options expiring May 17, 2013 (in 2 weeks). It will make a nice illustration of dividend driven early exercise risks.
Starting with the 2014 conversion, if one gets an appropriate option model that can properly handle discrete dividends (hence my dive back into Haug’s book), the theoretical price of the Jan 2014 440 conversion when AAPL is $447 is $7.31; note for European style options it is $7.58 – matching our forward. The early exercise makes a difference, albeit only a 27c difference. Why should early exercise matter? Because should Apple rebound, the extrinsic value of the call can become less than the dividend to be earned. Another way of looking at this is to compare the deep call with its analogue put. If the extrinsic value for the corresponding put is less than the dividend, one exercises the call to own the stock just prior to the ex-dividend date. For options expiring in 2014 with 3 dividends and a lot of extrinsic premium, it doesn’t matter much.
But for the May 17, 2013 options, it matters a lot. Consider that I purchased the May 400 conversion for $2. Now that AAPL is $447, those May 400 puts are not worth much. Right now they are trading around 74c. 74c is considerably lower than the dividend of $3.05. Why do I care about the puts? We are talking about the calls. A position of long 1 call and short 100 shares is (most of the time) equivalent to one put. This is called a synthetic and it requires explaining on its own, but stick with me. If a trader has a position of long call and short stock, it pays to exercise the calls to collect the dividend. The trader can replicate the same risk profile by purchasing the puts for 74c in the open market. Think about that for a moment. He exercises the call which is equivalent to selling it, receives shares that pay him/her $3.05 and then creates the same risk position by buying puts for $0.74.
That was my mistake. I was technically short AAPL and didn’t realize it. I had paid $2 for the conversion thinking I would collect my dividend. But since AAPL rallied 10% those puts are not worth much at all. I’m probably going to get my shares called away from me so that some other guy will get the $3.05. D’oh.