Arbitrage odds

One of the ways I've been evaluating going-private and other arbitrage opportunities is to look at the market's implied probability of success. Like gambling situations and unlike most investment situations, arbitrage is essentially a binary, win-loss event. That makes it relatively easy to apply the Kelly Criterion.

To show how it works, let's take my first going-private transaction, Major Automotive. On October 14, 2005, the company announced plans to implement a reverse split that would pay $1.90 to shareholders of less then 1000 shares. On March 29, 2006, I bought 999 shares at $1.75 a share. After the $19.95 commission charged by my broker at the time, I hoped to make $129.90 when the reverse split was resolved. I guess that there was at least a 95% chance the split would succeed from that point since insiders owned 49.4% of the company. I don't like the idea of assigning higher odds because of Murphy's Law.

If the split failed to happen, what would my position have been worth? The most pessimistic choice would be to assign no value. It isn't unreasonable either, since I'd done basically zero research into the underlying value of the company. In that case, I'd have lost the entire $1,768.20 that the position had cost. The expected payout would be $129.90*0.95 + (0-$1,768.20)*(1-0.95) = $34.995, which isn't half bad for a zero-research investment. A slightly more realistic value would be the price of the shares just before the reverse split was announced. On October 13, 2005, Major Automotive was priced at $1.40 a share. Using that price as a floor, the expected payout was $103.93. If you are following along don't forget to include an extra commission as an added cost of failure.

As it turns out, you can calculate the odds the market is assigning to an arbitrage situation with a little bit of math. This is the equation for expected payout:

S*p + F*(1-p) = E

where:
S = price if split succeeds
F = price if split fails
p = split probablity
E = expected price

If the market is rational, you'd expect the market price to match the expected price. I used the Mathomatic Computer Algebra System to solve for p:

$ mathomatic
Mathomatic version 12.6.10 (www.mathomatic.org)
Copyright (C) 1987-2006 George Gesslein II.
50 equation spaces available, 960KB per equation space.

1-> S*p + F*(1-p) = E

#1: (S*p) + (F*(1 - p)) = E

1-> solve p

        (E - F)
#1: p = -------
        (S - F)

Now if you plug in the values for Major Automotive when I bought it, you get a 70% probability that the split would happen.

Since my probability estimate (95%) was much greater than the market's, my expected payout was correspondingly higher. Given enough of these situations profits would be astronomical for anyone who could identify them. According to the Kelly Criterion, the optimum allocation for even the pessimistic case is 27%. (This can be calculated by taking the expected payout and dividing by the maximum payout or $34.99/$129.90. The more optimistic case calls for a whopping 80% allocation.) Unfortunately, these situations are rare. The only reason reverse splits are so wildly mis-priced is that arbitrage positions are limited to a small number of shares. Unless you have a portfolio of only a few thousand dollars, it's impossible to allocate the optimal amount even under the pessimistic case.

Investment returns redux

I discovered an error with the spreadsheet I used to generate my investment returns. It turns out I hadn't adjusted the S&P 500 index price for some of my purchases. The effect was to make the Benchmark column wrong:

Stock             Opened  Price  Closed   Price Annualized Benchmark
Oracle           6/24/02   8    5/28/03   13.35     67.05%    -9.94%
Major Automotive 2/28/06   1.75 3/29/06    1.90    144.21%   -11.13% 
Oracle           6/24/02   8     4/4/06   13.84     14.99%     6.80%
Canon            12/9/03  45     4/4/06   68.56     19.04%     2.19%
Canon            12/1/04  49.66  4/4/06   68.56     26.38%     5.34%
Select Comfort    2/9/05  19.95  4/4/06   39.80     80.44%     6.60%
Berkshire (B)    1/31/06   2920  4/4/06    3001      8.29%     2.57%

Now I'm 100% both on absolute and relative terms. Obviously this was a pleasant surprize. Even better, I've been tracking my time-weighted internal rate of return and my IRA is earning about 20% annualized. Since I've held a lot of cash earning less than 4% most of that time, I feel pretty confident in my ability to make good investments over time. If anything, I ought to be making more trades.

Investment returns

After selling Major Automotive, I started to wonder how well the other positions in my IRA have faired. After cosidering commissions, my two closed positions are:

Stock            Opened   Price Closed   Price Annualized Benchmark
Oracle           6/24/02  8     5/28/03  13.35  67.05%     -9.94%
Major Automotive 2/28/06  1.75  3/29/06  1.90  144.21%    -59.70% 

And here are the open positions assuming commissions, dividends, and today's closing price:

Stock            Opened   Price Closed   Price Annualized Benchmark
Oracle           6/24/02  8     4/3/06   13.79  14.89%      6.68%
Canon            12/9/03  45    4/3/06   67.41  18.20%      2.00%
Canon            12/1/04  49.66 4/3/06   67.41  24.85%     20.25%
Select Comfort   2/9/05   19.95 4/3/06   39.73  80.41%     24.32%
Berkshire (B)    1/31/06  2920  4/3/06   3012   10.78     332.30%

As you can see, all of my investments are currently in the black and I'm 6 of 7 against the S&P 500. Obviously this won't hold up in the future.

Major Automotive transaction completed

I bought Major Automotive on February 28 for $1.75 a share and received $1.90 a share this morning. After accounting for commission (on the purchase), I made $129.90 in 29 days. If I could make this transaction on a continual basis, I'd earn 144% a year.

Of course, the problem is that there aren't enough of these situations and they aren't big enough to constantly do them on a large scale. Which is just as well for me, since if they were, the opportunities would disappear.

Major Automotive goes private

I'm one step closer to collecting a quick $128 profit according to this 8-K filing.

Why I bought Major Automotive

Today I bought 999 shares of Major Automotive at $1.75 a share. Nearly 100% of the reason may be found in a recent SEC filing. I haven't had many good ideas for long-term investments, so I thought I'd try out an idea for a short-term investment I'd recently read about. The basic idea is to invest in shares that will be cashed out in order for the company to go private.

My hurdle rate for short-term investments is the 4-5% that I will be getting from the money market account my cash will be invested in over the next few months. If I don't expect to earn that rate, I'm better off staying in cash. The Major Automotive proxy says that anyone holding fewer than 1,000 shares will receive $1.90 in cash if the deal is approved. So I stand to receive $1,890.10 for my 999 shares. Including commission ($19.95), I spent $1768.20 to buy my shares, which works out to a $129.90 gain. Obviously, this isn't going to be a huge investment in absolute terms, but it is a little over 7% rate of return.

The one thing I don't know, however, is how long it will be before I get the cash. If the deal is approved at the annual meeting on March 3, and the paperwork takes until the end of the month, I'll be holding the shares for about 1/12 of the year. On an annualized basis, my return (130%) blows away the hurdle rate. Of course, it could take longer than that. But as long as it doesn't become a long-term investment, I'm in good shape.