What has AAPL done recently when earnings are announced? Here is the move from the close before earnings to the open the next day.

The average move is 2.39%, but there are a lot of large moves. There are three times when the close to open move is less than 1.5%, one -3%, six times around 6%, once an 8% move, once greater than 12%, and two moves down greater than 10%.

To try to center the returns around 140 and 165, we can try a dual calendar spread, selling the 140 Aug put and buying the 140 Sep put and selling the 165 Aug call and buying the 165 Sep call. Here is what the return looks like. The dark line is expiration, which we aren’t waiting for, so lets look at the blue and red lines.

If the August options’ implied volatility drops to the Sep values, this is what tomorrow’s return looks like:

So a big part of the return is the drop in volatility. Apple August options volatility should drop to the out month value once the uncertainty of the earnings are digested.

Case-Shiller Housing Index Through April 2009

There is great variability between the cities.  Here are the results for each city in the index:

It would be great to hedge the value of your house so that further declines would be made up by an increase in a security. Well, MacroShares launched two Exchange Traded Trusts on 30th of June that track the ten city composite.

Or do they?

MacroShares Major Metro Housing Up (UMM) and Major Metro Housing Down (DMM) return three times the index and minus three times the index. But not month to month. They are designed to return the given multiple of the index in November 2014. Until then, they will fluctuate depending on investor sentiment.

Another interesting feature is that they transfer money between themselves based on the relative price. As more money comes into the funds, they buy Treasuries that they transfer depending which Trust is higher.

If they had launched in 2006, DMM would already be shut down, because the 10 city composite peaked at 225 and now it is at 150.  A 1/3 drop wipes out the Trust.

Because the trusts move to plus and minus three times the Case-Shiller index in five years, they can be used as a five year hedge for your house value.  If you sell your house before then, there is no guarnatee that the Trusts will reflect the change in housing prices.  They act like a warrant, trading on what investors expect housing prices to be on 31st August 2014, payable in November 2014.

This is the table he published:

One feature of this portfolio is that a large move down, 50% or greater, will wipe out the BGU part of the portfolio, leaving the cash.  But now, the portfolio is all cash, so it doesn’t participate in the market anymore.

The table is correct if you make the move in one step. If you get there in two steps the second portfolio lags to the upside and does better to the downside, if the two steps in the downward move are both down. If one step is up and the other down, then the BGU / cash portfolio lags. The following table illustrates the point for a net 20% down move.

The first column is a one step move down 20%. The second column is a step down 10% and then another step down 11.1% which is a total loss of 20%. The third column is a step up of 7%, then a step down of 25.23%.  Why does the BGU portfolio have this seemingly erratic behavior?

It has to do with compounding.  The reason compounding grows faster than an arithmentic growth is the multiplying of terms.  So the IWM portfolio grows in two steps to

$100 * (1 + r1) * (1 + r2) = $100 * [1 + (r1 + r2) + r1 * r2]

The first term is the principal, $100.  The second term is the arithmetic return, r1 + r2, and the third term is what compounds the returns, r1 * r2.  Usually, r1*r2 is small.  If they are both one percent, multiplying them gives one hundredth of one percent, tiny.  If both returns are ten percent, then r1*r2 is one percent.  Now, it is beginning to matter.  In the BGU portfolio, this term is multiplied by 3.  So two ten percent moves will contribute 3% to the overall return.

It is this term, and all higher order terms, that is different between the two portfolios.  When there are several big moves, these terms are large because they have the powers of 3 multiplying them.

Yesterday the VIX closed at 28.27, its lowest close since the VIX ended the day at the 25.66 level on September 12, 2008 – the Friday before the Lehman Brothers bankruptcy filing.

In addition to the new lows in the VIX, a number of measures of historical volatility (HV) in the S&P 500 index are also at levels not seen since the week of the Lehman Brothers bankruptcy. These include 20 day HV (24.65), 30 day HV (25.50) and 50 day HV (28.57). Further, while the 10 day HV has not yet fallen below recent May and January lows, at 21.54, this is the type of number that makes the 30+ VIX advocates more than a little nervous.

The culprit is recent range-bound trading in which yesterday’s 3.29 point gain in the SPX is actually the largest daily change in the past three trading days. For the last six sessions, the SPX has hardly moved at all, which has driven historical volatility – also known as realized volatility – dramatically lower.

The chart below shows the trends in the VIX and historical volatility in the SPX since last September. Note that since the March lows the VIX has been falling in conjunction with the highlighted 10 day and 50 day historical volatility measures. Note also that the last three times 10 day HV got significantly ahead of the VIX (1/5, 2/5 and 5/6) each time this was a precursor to topping action in the SPX. As the 10 day historical volatility in the SPX gets ahead of the VIX once again, it is reasonable to ask whether this pattern will continue and we will see another topping pattern in the next few days.

[graphic: VIXandMore]

Here is a visual way to see that.

The return for any ETF or stock is S * (1 + ret1) * (1 + ret2) ….. after two days returns of ret1 on day 1 and ret2 on day 2. Where S is the stock price at the open of day 1. For FAS the return would look like:

FAS * (1 + 3 * ret1) * (1 + 3 * ret2)

If we look only at (1 + ret1) * (1 + ret2) and the same term for FAS, we can think of it as an area. If we had three terms it would be a volume. If we had more terms it would be a hypervolume. The point is, you maximize the area or volume when the terms are the same. That is, a square has a greater area than a rectangle with one side longer than the square and one side the same amount shorter than the square.

FAS goes to zero because when the financials drop, one gets a term (1 + 3* ret) that is much smaller than one, squashing the “volume” that gives the current price.

Since the market was between two strikes, I put on a spread ratio trade. I bought the 79 strike call and sold three times as many 80 strike calls, for a small credit. If the market stays between 787 and 803 I will have a profit. If it wanders out of that range, I will take the trade off. The best possible outcome is if the market closes at 800. Then the 79 calls that I am long, have their maximum value and the 80 calls that I am short are worthless.

1:45 PM the S&P has moved up to 803 which is touching my breakeven point. If it gets to 805 I will sell out the position to avoid large losses.

2:45 PM The S&P has moved to 810. I have bought back the short calls and left the long calls on.

3:45 PM Now the market has turned over so that I have losses from the short calls and the long calls are losing value. It is the worst possible scenario, but I was trying to recoup my losses on the short calls by keeping the long calls on. That was a big mistake. If I kept the trade on to closing, it would have made money according to plan, but the move to 810 was too large to keep the trade on safely