I will await your later response, but let me deal with this one for now.
Let me just say to begin with that what I wrote shocked me when I first discovered it, and it doesn't surprise me that it strikes many others as counter-intuitive as well. In fact, this very question (whether it's better to use the geometric or arithmetic average of returns as the expected return) is one on which the authors of my college finance textbook were confused. I recall a rather odd scenario from one of my problem sets in college where the question was "should you use the arithmetic or the geometric average?". My TA told the section that I was the only person in the section to get it right. I was quite pleased, until I started to think about it. About halfway through class, I pointed out to my TA that I had in fact gotten the question wrong, and that everyone else had gotten it right. He argued back, and ultimately disagreed (the textbook was no help, as it gave contradictory answers in different chapters). About a week later, he emailed the section to say that in fact I was right in saying that I was wrong, and gave them credit for the answer--although I'm not sure if I got points taken off my problem set. Anyway, while I now believe that both answers are somewhat valid, depending on your attitude towards diversification, this certainly indicates that the question is a tricky one. BTW, that was the last time I went to section.
The use of margin in writing puts incurs no interest payment.
I'm aware of that, which is why I pointed out that interest is just one of the problems inherent in margining your stocks--risk is generally the bigger problem.
The second game here is not quite the same as the first game with 50% down. The first game with 50% down is one in which I give you $0.50 instead of $1.00, and if I win I get $1.50 and if you win I get $0.75. I'll take that bet every time! :)
No... what you're describing is the first game where I pay you 50 cents on the dollar to play it, not where I let you play it with 50 cents on the dollar.
In other words, I say "OK, same bet. If you lose, you lose 25 cents, and if you win, you win 50 cents. This time, I'll let you make the bet using 50 cents as collateral, not $1."
Imagine that instead of a coin toss, this is a put that you're writing (obviously, this is a gross simplification--stocks don't have just two possible outcomes, but it illustrates a point).
XYZ stock is at $11. You write a $15 put for $5. You know that the stock will end up at either $15 or $7.5.
If it's a cash secured put, your initial outlay is $1000 (you also get $500 from the premium, so you've got enough collateral). If the stock ends up at $15, you get $1500 (whether or not it's put to you). If the stock ends up at $7.5, you get $750.
So that's identical to the first bet I described.
Now instead let's say that you can do this with 50% down. You start out with $500. Add to that the $500 from the premiums, and you have $1000 in collateral for the $1500 put.
If the stock goes down to $7.5, you get the stock put to you. This requires more cash than you have, so you borrow $500 (short-term, so you'll pay no interest). You then get 100 shares of stock worth $750, and owe $500, so you end up with $250. On the other hand, if the stock ends up at $15 or higher, you get to keep the whole premium, so you end up with $1000. Maybe you weren't considering the $500 you have to pay back if you lose?
Now to compare the bets, instead of writing one put with $500 down, write two with $1000 down. Now you get $500 if you lose, and $2000 if you win.
This is identical to the second bet I described.
Regardless, in the long run (asymptotically), it appears to me that both games are profitable (assuming we never run out of money with which to place the bet), since the expected returns are positive. This leads me to believe that we are not both talking about the same thing and so we should spend some time clarifying.
It's not that you run out of money with which to make the bet, it's that the losses are so severe that the gains don't make up for it. a 25% loss requires a 33% gain to offset it. a 50% loss requires a 100% gain to offset it. a 75% loss requires a 300% gain to offset it.
The real danger inherent in these games is of losing several times in a row and having $0 with which to make the next bet. In fact, this is expected to happen at some point. For example, if I lose the first 4 tosses in the first game, I am done. In the second game, it only takes losing the first 2 tosses to wipe me out. I think this is what you were getting at?
That's not what I was getting at, but certainly any strategy that you expect to involve losing your entire bankroll maybe ought to be avoided. If you lose the first 4 tosses in the first game, you don't have zero, because you're not betting $1 every time--you can only bet $.75 the second time, etc. After four losing tosses, you have .75^4, or 31 cents. |
