Saver return tickets?

Is there any reliable research on the return on investment from buying lottery tickets vs. "high yield" ETF's in an equal amount?

• I often joke that if you can buy lottery tickets on the street, why not junk bonds? Maybe you win, maybe you lose. But behind that joke is a real question. Over a long term, say 1-5 years, what would bring a better return on investment, buying lottery tickets, or investing an equal amount in the high-yield market, say a high yield bond ETF? What would the variation be if you purchased "numbers" tickets, which are drawn every day, or sometimes twice a day, offering lower payouts but better odds of winning, or a game with a higher prize like a semi-weekly "Lotto" or PowerBall/ MegaMillions, which have a lower winning percentage? Does anyone know if there was a serious statistical study done on lottery vs. high yield?

• Answer:

  Most liquid financial instruments are going to have similar risk adjusted expected return, where the risk / return tradeoff is whatever the market prices it at right now (you may be more or less risk averse than the market, and the market may be more or less risk averse at any given time). The reason for this is that if any instruments are cheap (high return relative to risk) they will be bought up until the price rises until the expected return is back in line. If any instruments are expensive (low expected return relative to risk) they will be sold or shorted and better assets purchased. I'd be surprised to see any liquid stocks, bonds or ETFs that aren't within a factor of two of the general market risk / return tradeoff. That said, there are some financial instruments that exist almost purely for hedging or other non-investment activity. For example, someone with lots of investments in Europe may want to simultaneously buy some derivative that pays off if the Euro declines. This separates out the performance of his investments from the currency they're priced in. An exchange rate swap has zero expected return, though. Inverse or Short ETFs have a negative expected return over any time period, but they're useful to people who make bets on individual stocks (buying GOOG and an inverse Nasdaq ETF gives you a combination that makes money proportional to how Google performs relative to other tech companies). These financial instruments are useful because they can be combined with other instruments to reduce the overall risk of the portfolio, and if you are willing to take 2 units of risk, and you find a trick to reduce your risk by half, you can now get the same return as if you were willing to take 4 units of risk. The lottery almost always has a negative expected value, and it isn't useful as a hedge in any way. This isn't about the risk, it's purely about the expected return even ignoring risk. I expect to win back maybe $0.60 of every dollar I gamble. Negative expected returns are worth accepting if they give you something else. But the lottery doesn't give you anything else that you would want in your portfolio. If the lottery had a positive expected return, or occasionally had a positive expected return, this might be useful when combine with other investments, but lotteries almost never get to positive expected returns. That is, if $1 wins me $5M one time in four million, that's an expected payoff of $1.25 for every dollar. If I managed a $100M fund, and I can logistically make the bet, I'd probably be happy to put $2M down for a 50/50 chance of winning $5M.