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- AnarchoCapitalist on Gold and Silver Spread Arbitrage Wouldn't the long term relationship between gol...

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## View Tyler Lewis' Instablogs on:

## How to play Google earnings with option strategies.

I have no idea.

It is in times like these that I turn to a couple of friends of mine- the straddle and the butterfly spread. The combination of earnings announcements and options expiring the same day usually makes for some exciting action.

The first question we have to ask when deciding whether to buy or sell a straddle or butterfly is this: do I think that the underlying security is going to be volatile and have a big move? Or do I think that the stock is going to hang around where it is right now?

When buying a straddle, you are buying an at-the-money call and an at-the-money put. This position basically implies that you don't know which direction the stock is going to move, but you think it is going to move big. Selling a straddle would be the opposite, planning on the stock staying put.

In the case of Google, we can make our decision by looking at the average post-earnings moves over the last five years. By using Bloomberg's ERN (earnings) function, we can pull up a list of all the earning announcements for Google over the last few years. Bloomberg provides us with the expected earnings, actual earnings, % surprise, and % change in the price of the stock after the announcement. It is the "% change in price" column that I am interested in.

Looking at the % Price change of the stock on the day after earnings, I can get an idea of what kind of a move Google usually has on the day following earnings announcements. Because I don't know or care which direction the price is moving, I will average the absolute value of % Price changes for the days after earnings announcements. This will give me an idea of, on average, how much Google moves the day after earnings, whether it be up or down.

So, taking the data from the table, we will use the absolute value of the % Px Change column.

11.9%

6.97%

7.59%

5.66%

3.76%

etc

etc going all the way back to 2005.

After I've got all of these values, I find the simple average, which turns out to be about 6.3%.

Let's recap. What this 6.3% number tells me is that, on average, Google has a positive OR negative move of 6.3% on days following earnings announcements. That's a pretty big move.

So, do I want to buy the straddle or sell it?

Well, by running a P/L analysis, we can find out.

If we were to sell the at-the-money (625) straddle, our breakeven points would be somewhere around 655 and 595. This means that we would make money as long as Google stayed within those bounds. That sounds like a big gap, but those numbers only give us about a 4.8% cushion. If Google moves, on average, 6.3% after earnings, then this straddle would be a bet against the house.

So, why don't we buy the straddle? Running a similar P/L analysis, we see that if we bought the 625 straddle, our breakeven points would still be about 655 and 595. This means that if Google closes outside of these numbers, we make money.

These numbers represent a move of 4.8% in either direction. Given that we assume that Google moves on average 6.3% after earnings, the odds would be in your favor if you bought the straddle. It's risky, though- if Google closes at 625 tomorrow, you stand to lose your whole investment, which would be about $31. But, for every point that Google moves beyond 655 or 595, you make money, and the upside is unlimited.

For the risk averse, may I recommend the Butterfly Spread? The butterfly spread is simlar to the straddle, except that we sell an out of the money put and and an out of the money call to protect ourselves in the event that the trade doesn't work.

The P/L scenario on the butterfly would be an investment of about $19. Should Google close at 625 tomorrow, you stand to lose it all. However, the butterfly gives us less cushion on the breakeven points, so if Google broke outside of 643 or 606, you stand to make money. These breakeven points represent about at 3% move in Google, which is much less than the 4.85% breakeven points given by the straddle.

The butterfly spread limits our risk by making the max amount we can lose $19, vs. the $31 we stand to lose if the straddle doesn't work. What you give up, however, is upside. The straddle has unlimited upside, where the butterfly has about a $6 upside.

Is it guaranteed to work? Heck no. We have the odds in our favor, but that's it. It's a gamble to see where Google ends up at the end of the day tomorrow. Is it worth it to you to put up $19 in hopes of making $6? A chance to make a 33% return over 24 hours doesn't come along often...

These option scenarios are always fun to run when the perfect storm of earnings announcements and options expiration happen on the same day.

Good luck and make good decisions.

## Gold and Silver Spread Arbitrage

Looking for a way to play Gold and Silver? A quick look at the historical spreads between gold and silver may help you make an educated dicision in your arbitrage.

Let's take a look:

Using Bloomberg's HRA (Historical Regression) function, we can easily find the historical correlation between gold and silver. By using the SILV and GOLDS commodity indices, we can get data much further back than we could if we used the GLD and the SLV.

Using a weekly value correlation going back to 1990, we see a tight correlation and a regression line that looks something like this:

It may be a little hard to read, but as you can see, the data points hug pretty close to the regression line over a period of 20 years, giving us a relatively solid R2 coeficcient of .92. I doubt you can see it, but the box in the upper-left hand portion of the graph tells us the linear equation for the correlation- y=.018x.

If you are lost, or have no idea what I'm talking about, I'll explain it a bit more simply: What this all basically means is that we have about 92% confidence that when gold goes up $1, silver will go up somewhere in the range of 1.8 cents. Or, to make it more manageable, when we use the GLD and the SLV, we can say that when the GLD goes up $1, the SLV goes up somewhere around $0.18. This is because the GLD is basically the price of gold divided by 10.

Another way of looking at this would be to say that in order to hedge your GLD position, you would have to sell 5.5555 SLV to achieve a hedged position. We calculate this by dividing 1 by the hedge ratio (.18), which gives us 5.555. What this means is that if SLV moves 18 cents for every dollar that the GLD moves, then if you sold 5.55 of the SLV, against one GLD, the $1 gain in gold would be cancelled out by the $1 loss (.18 x 5.55) in your short SLV position.

Now. Onward to the spread.

When I talk about the spread, I am talking how far out of correlation the two securities are. Here's how we calculate the spread:

The spread = (GLD*Hedge Ratio) - SLV

If silver went up exactly 1.8 cents EVERY SINGLE TIME that gold went up $1, then there would be no spread; GLD*.18 - SLV would always equal zero. However, if one day silver went up 2 cents versus gold's $1, there would be a negative spread. Inversely, if gold decided to go up $2 one day, and silver still only went up 1.8 cents, there would be a positive spread.

(A note: we have to view the spread in terms of which security we are buying and which we are selling. If we are long gold, short silver, then in essence, we are long the gold/silver spread, or we could say we are short the silver spread. If gold goes up more than silver, the spread between gold and silver goes up.

If we are long silver, short gold, then when silver rises more relative to gold, the spread goes up. We would be considered long the silver spread, or short the gold spread. It's all relative to your position.)

Going back to the regression chart from earlier, you can see that the last few data points, located at the top-right end of the regression line, are all above the line. This means that the relative price of silver has risen more than the relative price of gold recently. If we pull up a chart of the spread, calculated as we discussed earlier, you can see that the spread has gone negative, meaning that silver has outperformed gold recently.

You can see from the charts and the bell curve at the bottom right that not only has the spread gone extremely negative, it is the lowest it's been in the last 20 years. Investors looking for an arbitrage would do well to buy the gold.silver spread at these levels...if they think that it's just a minor fluctuation in the spread.

But what if it's not just a short term fluctuation in the spread? What if the correlation between gold and silver has inherently shifted? Anyone working with correlations has to ask this question when spreads and correlations start behaving irregularly. It's not uncommon for correlations to break.

Unfortunately, when working with correlations, only time can tell. Do you invest in the spread, hoping that it is a short term fluctuation, or do you assume that the long-standing relationship between gold and silver have changed?

That's up to you.