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Tuesday, 24 March 2009

The problem with the US rescue package.

Suppose the government approaches you to buy a lottery ticket. "Go on", they say, "you might win big".

"OK, you reply", being a rational person, "This is all about statistics and probability. There are no brownie points for good management or smart selection. Let me work out the likely payoff on a $1 ticket. Hmm, it looks like that would be about 35 cents."

"So how much are you prepared to invest per ticket?".

"Invest? Oh, OK. No more than 35 cents per ticket, probably less because I want to make money. But I'll buy 100 to spread my risk."

"Oh", they reply disappointedly, but they are desperate, so they say "OK but we would like you to buy more than that. Here's an idea. If you buy 200 tickets, we will match your investment and we can share in the risk. Does that make it look better?"

"Not really", you reply, "At 100 tickets I felt my risk was pretty much covered. What you are saying is that if I invest twice as much I can get a 50% interest in 400 tickets, which in my world view is not much different than having a 100% interest in 200 tickets. The payoff has a different profile but my expected profit is the same."

"Oh, OK", says the government, "If you do our matching scheme, then for every dollar you invest of your own money, we will lend you two more, so you can buy three times as many tickets and have a 50% interest in 1200 tickets, leveraged 2:1".

"Who takes the first loss?", you ask.


"Who gets paid out first. You are lending me the money I am putting in the equity", you explain.

"Oh, I see. We do".

"So the deal is that I take the 50% of the first loss on 1200 tickets and you get paid out first because you are a lender. I only get a share of anything when you have been paid out in full on the price of the first 800 tickets and I get paid out 50 % thereafter?"

"Yeah, but you get all the upside on 50% of the whole 1200. So isn't that worth more per ticket?"

"No the payoff is still 35 cents per ticket, so the price hasn't changed."

"Oh, OK. So are you going to invest?"

"Look my position is no different than if I had bought 200 before you came along. If the tickets were worth 35 cents each and I could have bought them it for less, I would have done it already. Your participation doesn't make any difference to my appraisal of value and risk. I can raise my own leverage if I have reasonable assets. 2:1 gearing is not hard to find."

"Oh, OK", say the government people, "but you have to admit we look pretty smart!"

"How do you figure that?", you reply.

"Well we get to buy at the same price as the market."

"You put up 5 times as much money as me at whatever price I told you was good. That sounds pretty dumb to me."

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