RichardGibbons

The host will always open at least 98 of the doors that don't have goats. Therefore, the probability of the car begin behind the other door is 1 - P(it's behind the door you pick). In other words, when you start, there's a 1/100 chance that it's behind your door, so there's 99/100 chance that it's behind one of the other doors. After the other doors are opened (and the host will always open 98 other doors with goats), there's still a 99% chance that it's behind one of the other doors. The only other door left is door 57, so there's a 99% chance that it's behind that door. Richard

In that case, Biaggio, I'll propose a great deal for you then. We'll play the game with a random number generator and 100 doors, 99 goats and 1 car. The computer can hide the goat, and you can pick a door. Then we'll have the computer open 98 of the other doors that contain goats. At that point, you stick with your original pick, and I'll take the unopened door. If I have the car, then you pay me $10. If you have the car, I'll pay you $20. If it's 50-50, then this should be a pretty lucrative game for you. I propose that we both commit to playing this game 100 times, to attempt remove the effects of bad luck. If the odds are 50-50, your expected return is $500. If the stakes aren't big enough to make it worth your time, I'll commit to playing this game with up to 5,000 times, with you expecting to gain $25,000. (My wife wouldn't be happy with me gambling more than $100,000.) Just let me know. Maybe Sanjeev would be willing to act as a intermediary to hold the cash for 5% of the winner's profits. It could help pay for the website. :) Richard

Partner, there is a beneft to switching. You can try it and see what the results are. However, an intuitive "proof" that might help is if you take the same problem to 100 doors. Suppose instead there's 100 doors, 1 car and 99 goats. Suppose you choose door 1. Then the host opens doors 2, 3, 4 ... 56, 58, 59, ... 100. So there's exactly 2 doors closed, door 1, which you picked, and door 57, which the host decided not to open for some strange reason. Would you still claim that there's no benefit of switching from door 1 to door 57, that it's still 50/50? I think it's the same question, just reframed. Richard

The cigar butt in question was First Industrial Realty (NYSE:FR).

Yes, it is a covered call. If your broker doesn't recognize it, you can always move the shares from a Canadian-denominated account to a US-denominated account. I think I've done this in the past.

Options are very different than long stock, though LEAPs are much closer to long stock than shorter term options. With short term options, a 5% move in a stock can effectively wipe out 100% of your investment. I think options can be used to hedge, but are also effective as a speculation. There are a variety of strategies, on both the long and short side. When you start combining multiple option and stock positions, it can get confusing. You should understand how different positions combine and what your equivalent long/short position is. For example, possibly the most common options position is a covered call -- buying shares and selling calls against those shares, then waiting for the sold options to expire. A surprising number of people seem to believe that in this situation, the best result is for the stock to stay flat or fall a bit, so that the options expire. However, this position is equivalent to being short a put, so truly the optimal result is the stock to skyrocket instantly, so that the position can be closed out the next day at a high annualized return. Generally, I'd say that there are two strategies, hitting singles by selling options and pocketing the premium when the options expire (like the covered call strategy), or going for homeruns by buying options. When selling options, a key thing to understand is that one big loss can wipe out a lot of gains. e.g. suppose you'd been selling AIG covered calls a year or two ago when the stock was at $60. You might have got $2 premium for a short term call. Maybe you did this 3 times, making $6. Then the stock fell to $2. Then, you've basically lost $52 (and also can't sell more calls at a reasonable price with the stock at $2). One interesting way around this problem is to sell longer term options. Then you bring in a lot of premium, protecting the downside, but the annualized return isn't as great. But returns can still be good, particularly if the stock moves up quickly and you can close out the position early. The first thing to understand about long options is that it isn't uncommon to lose 100%. Even if you say that you're going to sell after a certain time period -- before hitting the worst of the time decay -- if the position moves against you, you can lose money quickly. So, the strategy you chose should be robust enough to handle a string of huge losses. Thus, the key to long options (and maybe short options too) is money management. You want to invest far less in an options position than in an equivalent stock position. It would be very stupid to have 50% of your portfolio in call options, because the market could go down for 2 years, and you'd lose that 50%. One reasonable way to play long options is with 90% cash, 10% in options, with a rule that you can only lose 10% in one year. I think generally, one should aim for 400%+ returns on long options. Then, if you win once for every two losses, you're still doing well. You might be able to get away with smaller returns on LEAPs, since your winning percentage might go up. But generally, I think the right strategy with long options is to try to win big.

Plus, black swans are not necessarily unusually bad events, even if the most recent example in the market was unusually bad. You can have unusually good events too. (e.g. Harry Potter, Bill Gates, maybe oil going from $10 to $143). I don't think exclusively playing the downside is a requirement of the theory. Richard

Hi Philip, Yeah, for me, the main goal is to maximize happiness, not maximize money, so I can't argue with your decision to stay in your place. It is a lovely house. My parents live in Qualicum, near Parksville. If Parksville's demographics are anything like Qualicum's I could see that the stock market drop and low interest rates could have more of an effect on rents there than other cities. If a large chunk of that market is retirees whose primary source of incomes was investments, that could have a significant impact on rents. I'd agree with you on the mortgage rates having a bigger impact than unemployment. The interesting thing is that I've been looking at this stuff for a 3 or 4 years, and historically there was much higher correlation between unemployment and prices than there was between interest rates and prices. But I think that may no longer be true, since housing is priced so highly that it's only feasible for a large segment of the population to buy when rates are extraordinarily low. This time it's different. ;) (The other fun real estate-related stat I saw a couple years ago was that something close to 100% of Vancouver's employment gains during the last boom were jobs in real estate.) Richard

Nodnub, I'd agree with most of what you said. The Vancouver housing market is in a bubble, and will almost certainly correct significantly in real terms. The typical ratio between median household incomes and median housing prices is about 3. Even if you consider Vancouver attractive enough to warrant twice that ratio, Vancouver at the peak was somewhere areound 9. So, that would imply a 33-35% correction. The price to rent ratio is out of whack too. Not so much as it used to be because of falling rates, but if you're buying, you probably shouldn't get a 30-year amortization mortgage on the assumption that mortgage rates will remain at multi-generational lows for the next few decades. If you assume reasonable long term interest rates, the price to rent ratio is insane. (When I looked at it last summer, the typical family would have had to spend 70% of their gross income to buy the average house with 25% down.) The correction is extremely likely to happen in real prices falling rather than rents rising, because rents are constrained by rationality more than prices. If you earn 60K, you really won't rent something that takes 50% of your gross income, whereas if you're buying, you can do that, because someone will lend you the money even if you're unlikely to be able to afford it. So, I think the most likely scenario is falling prices in Vancouver. (That said, I'm talking my book since I'm someone in Vancouver who could afford to buy, but is renting.)

Barring a conflicting commitment, I would attend.