Interesting takeover situation for me. (long)
Going from memory here, some facts (dates/amounts) may not be exactly right, but close enough for this discussion.
Couple weeks back I came across a buyout offer to close roughly three weeks hence. Stock selling for $21.65 with offer of $22.00 cash/sh.
Question: Would you buy the stock at that time in anticipation of receiving the cash offer? Just talking to a few of my acquaintances/relatives their answer was invariably no. Not for 35 cents/sh. profit. Plus, they say, there's no sure thing in the market. (Stockholders hadn't approved the deal at that time.)
There are several other ways to look at the problem though. One way is to calculate the return on investment for tying up each $21.65 share. See if the roi meets one criterion for an investment in the time frame. Another way is to look at the expected outcome and see if it's positive and by how much. This would be, imo, the (probability of the gain x the gain amount) minus (the probability of the loss x the loss amount). The gain amount is .35 cents. I guesstimate the loss amount is $2 sh. if the deal were to be delayed, and maybe $5 share if the deal collapsed (Stock dropping back to pre-offer price of about $22.65-$5.00 = $16.65. Now for the probabilities. I figured the deal had a 98-99% chance of being completed and so just a .01 or .02 probability of loss. This works out to a positive expectation. Would you make the buy at $22.65? Bluntly and maybe wrongly said, you are still risking $5/sh to make 35 cents/sh.
One way of looking at it is that if you're a value investor and you make buys based on some sort of positive expected outcomes, then this buy must be one of many made previously and to be made in future. You know that if you lose here ---and are out $5 even though the odds are in your favor---, you will continue to make such bets, and over time, you can expect to have an overall positive outcome. Looking at it something like this: if the numbers work, you always want to make the bet.
I shall make the bet. The question then becomes ---and this is now the general issue, HOW MUCH of the the portfolio do you wager? Would it just be a bother to tie up $2165 to maybe make $35 before expenses? And before possible short-term cap. gain taxes. How about $21,650 for $350? Maybe $216,500 for $3500? Numbers I show above work okay for a positive expectation even if you use margin (assuming you get a good margin rate from your broker). In this latter case, if you have a million dollar portfolio, you tie up 20% of your portfolio for a few weeks. You gain - if you had such a portfolio - if you gain - about $3000 (roughly) but could lose (small chance though) as much as $5/sh x 10,000sh = $50,000 or about 5% of the portfolio. 5% of portfolio doesn't seem that big, but a loss of $50k seems very big. Well it would be to me anyway, even if I had that size portfolio.
What is the optimum bet size when odds are in one's favor?
To me it's clear that if ...IF...there is 100% certainty of gain and decent gain over the calculated time period, then that's the limit and at the limit, one might/should/could/ wager 100% of one's portfolio. It's not really a wager if there's 100% certainty of the payoff. But for anything less, how should one optimally wager one's portfolio?
I researched something called the Kelly Criterion, which originally was for gambling games apparently, but which may or does have practical application in the stock market. Here's Thorp's take on it:
bjmath.com
Very technical. I couldn't really make heads or tails of it -gg(pun)-.
Here's a possibly decent note about Kelly Criterion as applied to the stock market:
ezinearticles.com
Another reference is Poundstone's "Fortune's Formula"
amazon.com
On SI, one person who has considered the Kelly Criterion carefully is E. Charters. Here are a couple of his posts which I found illuminating:
Message 22552561
Message 22552561
Dale Baker also reposted an interesting article about using Kelly:
Message 23647774
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What I did, and what happened:
I decided to wager 20% of my after-tax portfolios on the deal.
What I found was in an analytical sense, there was no support for my assumption of the probabilities I estimated. That is, events -- the Bear Stearns fund debacle putting a damper on funding/structure of loans for upcoming deals made many people believe those deals could be delayed or could falter. Therefore, fewer players willing to commit to holding the stock through to completion of buyout. (So stock price down.) The stock fluctuating quite a bit as rumors/changes in other concurrent buyouts hit the media. I decided that since my ruling reason for the purchase was not as assured as I predicted, it was not worth jeopardizing so much money for so little gain. I cut back holdings to under 2% of portfolio.
Looks like deal will be completed as scheduled, with some changes in loan structure. As stockholder, I'll come out positive. Not much money there, but for me, a good story. |
