Asian markets were down 5% on the news but the S&P 500 futures were down 24 on Globex over Thanksginving, but today the damage was 19 points. So it looks like the market considers it contained.

Minnesota Mining & Manufacturing

A steady conglomerate paying steady dividends. So 29th October I thought it would pay its dividend around the 19th of November, like last year. So I bought some stock at 75.24 and sold the Nov 75 call for 1.8 giving about 2.4% of downside protection. The beta of MMM is 0.8 so you could say that we have about 3% downside protection on the S&P 500.

There was 0.24 of intrinsic value and the rest, 1.56 time value in the call.

Usually MMM announces the dividend eight to nine days before the ex-dividend date and it hasn’t announced yet.

Today, MMM was trading near 78.75 and the call at 3.9, 3.75 in the money. My return would be 1.41, so I took off the trade. My reasoning was, if the ex-date is before November options expiration, and the stock is called, I would earn another fifteen cents, but I would have to wait about nine days. If MMM dropped enough so that it wouldn’t be called, I would get the 51 cents dividend if the ex-date is before expiration.

Didn’t seem worth waiting for. What do you think? Comment below.

PUT

The CBOE has created several interesting indices. The buy-write index, BXM, sells the first out of the money SPX call every month and owns the index. The put-write index, PUT, sells the at the money SPX put every month and holds one month and three month T bills as collateral. It is a mirror strategy to BXM since a covered call is equivalent to a short put. The difference is that BXM sells the first out of the money call and PUT sells the at the money put.

The way I am trying to capture the dividend is by selling the at the money call, or first in the money call, so that there is some time premium left in the call. That way, if the stock is called away, I’ve earned the time premium. If not, I get the dividend.

Return Comparison

Here is an interesting table of monthly data covering the period 30 June 1986 to 31 October 2008 from a paper on the CBOE micro-site PUT:

In strongly positive return months, almost half the time, the S&P 500 returns an average of 4% and the Put-Write index lags, returning a little more than half that, 2%.

In relatively unchanged months, about 22% of the months, PUT outperforms the SPX returning 1.67% compared to a -0.8%. In these two states of the market, the correlation of SPX and PUT is 0.5.

In strongly down months, the SPX loses an average of 5% and PUT does better, losing 3%. The correlation here is almost 1, perfectly correlated.

So far we have the correlation of PUT with SPX, but we are trading individual names, not the index. How do we get the correlation of a buy-write of IBM, say, with SPX?

Implied Correlation Indicator

CBOE to the rescue again. They have developed an indicator that extracts the average correlation of the fifty largest SPX components with the index. They publish two of these average correlations, ICJ and JCJ.

ICJ will expire with November options, because it looks at the implied correlation by extracting implied volatilities of the December 2009 SPX options and January 2010 options for the fifty individual names. On the next Monday KCJ will be calculated using January 2012 options.

The index implied volatility can increase in two ways, one is if the implied volatility of the individual constituents increases. The other way is if the correlation in the volatility increases. In the tails, when the market rises fast and especially when it falls fast, the correlations go to one. Everything is moving together in the same direction and vol goes through the roof. Look at KCJ, the yellow line, right between the two VIX spikes last fall. It spikes above 100 which is because the calculation isn’t perfect, but it shows that everything was moving down together. (Click on the chart to enlarge.)

Looking to the right, we see the the implied correlation is around 50%. So a basket of the fifty largest stocks has an average correlation of 50% with the index.

Correlation of ‘IBM’ with PUT

Can we put these two correlations together to extract the correlation of the average large stock in SPX, what I am calling in the header ‘IBM’, with PUT?

Here is a geometric way to look at correlation. It is the cosine of the angle between the return vectors of SPX and PUT. So if you hold up two pencils and join them at the bottom, when the tops are touching they are pointing in the same direction and the correlation (cosine of the angle between them) is one. As you move the tops apart the angle between the pencils gets larger and the cosine gets smaller and so does the correlation.

So hold the two pencils apart and think of them as SPX and PUT. Now take a third pencil and that will be ‘IBM’. We know the angle ‘IBM’ makes with SPX. What does that tell us about the angle it makes with PUT? Nothing, because ‘IBM’ can spin around SPX in a circle with a fixed angle between them and its angle with PUT varies from 0 when it bumps into PUT to 120 degrees (cos (120) = -1/2) where the correlation is -0.5.

So please comment and let me know if we have another constraint that I missed that will help us to combine the two correlations.

Wednesday, the owner of the calls exercised and called away my stock so that he will be owner of record and receive the dividend. The Nov 25 put closed at 0.35 bid 0.5 offered, so it makes sense that the stock was called. What does the put have to do with it?

Conversion

An arbitrageur would look at the conversion to decide whether to do this trade. In the conversion, you own the stock at 26 and sold the Nov 25 call at 1 for a net outlay of 25.

To make the position risk free, you could buy the Nov 25 put.

You will receive 0.5 in a few days from the dividend and it will cost 25 *2% * (number of days to Nov expiration) to carry the position.

So how much would you be willing to spend on the put to make this worthwhile?

At expiration, if the stock stays above 25, the call will be exercised and your account receives a credit of 25. So that is a scratch.

So to do this profitably, the put has cost less than the dividend received minus the interest cost to finance the buy-write.

So that is the condition: d – i > p.

Here is another way to look at it:

Market Maker’s Trade

Here is Stan Freifeld’s derivation for those of you, like me, that feel deriving helps make the connections to understanding. The derivation is based on what market makers might do to get the dividend since their costs are so low. They might buy deep in the money calls and sell the next call up for $5 if that is how far apart they are. Then they exercise the call on the cum date (day before ex-dividend date). Now they have long stock and the short calls that they started with. Of course, the owners of the short calls will exercise too. If they are left with five or ten percent of the position they started with, they have made money if the dividend is large enough.

So we are starting out C1 – C2 > 0 in order to have a profitable position.

We exercise C1 so we have S + d -i -C2 > 0. That is, we have stock, S, the dividend, d, and we have to pay the interest, i, for financing the stock.

S – C2 = -P2 since a buy-write is equivalent to a short put. Put that in our equation, d – i -P2 > 0. Add P2 to both sides and we have our condition for exercise:

d – i > P2

For BWP d = 0.495 i is negligible and P2 was 0.35 So the condition was satisfied.

Tomorrow, Abbott Labs (ABT) goes ex-dividend, paying $0.40; Mid America Apartment Communities (MAA) goes ex- paying $0.615; and Watsco Inc (WSO) goes ex- paying $0.48.

Nothing interesting in ABT or MAA, but WSO puzzled me. The stock was trading at $53.60 and the Oct 55 puts expiring Saturday, were 2.25 bid, 2.75 offered. One way to think about the value of the put is to add up its intrinsic value and the dollar amount of time decay to expiration. In this case, the intrinsic value of the put was 55 – 53.6 = 1.4. Theta is 0.041 per day, so with five days left, that is 0.205 in time decay “value”. Adding it up, we get 1.605 not 2.25.

So one could sell the put and sell stock to hedge. That way, at expiration, the in the money put is exercised and stock is put to me, flattening out my position.

Here is what the return graph looks like (click on the image to enlarge):

So if WSO stays below 55.88, this trade is a winner. Since I am short the stock, I have to pay the dividend which reduces the return. Instead of 2.25 – 1.4 = 0.85, the return is 0.85 – 0.48 = 0.37 minus transaction costs.

Note: This is equivalent to selling the Oct 55 call against cash and letting it expire, if worthless, at the end of the week.

We’ll see if this reasoning holds up.

Owning $100 of the Nasdaq 100 ETF from April 1999 to May 2009 would result in this roller coaster ride (Click on the image to enlarge):

Passive Collar

We want to compare this to the collar strategy in each of the sub-periods outlined in the graph. The title on this graph in incorrect, we are comparing one month, three month, and six month puts. (Click on the graph to enlarge.)

Here is how the passive collar strategy does:

• The dark green line is the return for the strategy of owning QQQQ and selling at the money one month calls and buying at the money one month puts. It has a steady bond-like return where $100 grows to about $140 in ten years. That is a 3.4% compounded return.
• The purple line is the return for the strategy of owning QQQQ and selling at the money one month calls and buying at the money three month puts. Here, most of the increase is in the early period, from March 1999 to March 2003. Starting with $100, it grows to about $180 in this period and then in the next six years, increases to about $190. This is a 6.6% compounded return over the ten years.
• Similarly, the turquoise line, which is the return for the strategy of owning QQQQ and selling at the money one month calls and buying at the money six month puts, rises to $275 by September 2003 and then treads water until March 2009. This is a very respectable 10.6% compounded return over the ten years.

The passive strategy is most sensitive to the put expiration. So we look at 2% out of the money puts written six months out and see how the return varies with how far out of the money the one month calls are written.

This is for the whole ten year period:

• The passive collar strategy cut the standard deviation of return by two thirds from 30% to 10%. This is a very substantial improvement.
• Of course, it also turned a losing strategy, owning the Nasdaq, to a nine to ten percent per year winner.
• The maximum drawdown for owning the QQQ was 80%, nearly impossible to recover from. The collar had a maximum drawdown of 21% for the loosest collar.
• The correlation with the underlying increases as we loosen the collar by increasing the amount that the call is out of the money.

Active Collar

(Click on the graph to enlarge.)

The upper turquoise line is the short term active strategy. It turns $100 into $300 in ten years, which is an 11.6% compounded return. All the return was made by September 2003, the strategy treads water after that.

Tomorrow, we’ll look at what it all means.

Australia: -1.99% today.

Nikkei 225 (Japan): -2.47% today.

Europe at mid-morning:

FTSE 100 (UK): -0.85% at 12:00 PM.

DAX (Germany): -0.68% at 1:00 PM

CAC 40 (France): -1.18% at 1:00 PM

SPY pre market open: -0.1% at 102.87 at 7:00 AM EST

QQQQ pre market open: -0.0% at 7:00 AM

Economic Indicators: The unemployment rate for September is expected to rise slightly to 9.8% when announced at 8:29 AM EST.  The non-farm payrolls is expected to show a drop of 175K in September.  Important for consumer spending, the average work week is expected to be flat at 33.1 hours in September,  but hourly earnings are expected to show a rise of 0.2%.  More money in workers’ pockets.

Factory orders, announced at 9:59 AM, are expected to be flat for August.  They are down 25% from a year ago.

Earnings Announcements: None.

I ran a few Monte Carlos to see if it mattered if you sold the near month versus the far and to get a feel for how often you would have to adjust given where you choose to play. These are for the Russell 2000 index, RUT.

So here, this close in, it doesn’t matter if we trade the near month, October or November. We’d have to adjust all the time, though it would close past one of the strikes between 60% and 65% of the time.

What happens if we move farther out?

This is much more manageable. One has to adjust about 25 – 30% of the time, though the market closes past one of the strikes less than 20% of the time.

Next question is, what happens if you don’t adjust? Take your lumps when the market closes past your short strike but sit with it and make the return when the market turns back around. Is that a good strategy or poor one?

Stay tuned.

Here is the closing price data from Thinkorswim:

On Tuesday 15th September, Phillip Morris declared what the dividend would be. That takes most of the uncertainty out of the payment on 9th October. To make any money we have to take on some risk. So putting on the position on Monday the day before, we could buy shares and sell in the money calls. Since the stock was at 47, I picked the 46 call to sell.

To make the trade delta neutral, one would have to sell 13 calls for every 1,000 shares bought. That is probably the right way to do it. Unless one can show that there is interest in a stock when it is about to pay a dividend and there is an upward bias to the price. If that were true, then one can sell calls one for one and have a positive delta.

By the end of the week, 18th September, the time premium has disappeared in the Oct 46 call bid. That means that the call will be exercised next week, the day before the ex-dividend date, 24th Sept. In that case, one can close out the position, there is no more to be gained.

The return after paying the bid ask spread is $130 for the delta neutral position, a return of 0.28% for the week, and $220 for the straight buy write, 0.48% return. The dividend would have been $580.

Another possibility is to try this as a calendar spread. I will come back to this tomorrow.

Most of the in the money October calls were exercised or sold, as we expected.  But as discussed yesterday, they had no time value and a very low implied volatility, 14, right where the historical volatility is.

I sold the Nov 46 calls and bought the stock.  Actually, I jumped the gun and did the buy / write day before yesterday.  Today when I went to unwind the position, I came out flat.

Generally, if you are taking no risk, you can only expect to earn the risk free rate, which is very low. That is what is going on here. I have to figure out which risks I can take on with this strategy to make a decent return.

Back to the drawing board.