is there any value in including lottery tickets to an investment portfolio?

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dvictr's picture

as a binary instrument it appears to have positive qualities to improve the efficient frontier, tail risk exposure..

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bchad's picture

binary option?  What’s the underlying asset?

Hedge tail risk??  Only if a lottery ticket is negatively correlated with whatever tail event you are hedging.  But a fair lottery ticket’s returns should be uncorrelated to pretty much everything by definition.

For profit lottery ticket companies can be good to add to a portfolio, though.

Lottery tickets have negative expected returns.  You never want to add something with a negative expected return to a portfolio, unless its presence nullifies (hedges) risk for another asset that has a positive expected return *and* the portfolio still has a positive expected return after adding it.  Even tail risk hedges ought to have positive expected returns, in the sense that the payoff in a tail event should be large enough to compensate for a long stream of non-tail event losses.

You want a quote?  Haven’t I written enough already???

dvictr's picture

bchadwick wrote:

Lottery tickets have negative expected returns.  You never want to add something with a negative expected return to a portfolio, unless its presence nullifies (hedges) risk for another asset that has a positive expected return *and* the portfolio still has a positive expected return after adding it.  Even tail risk hedges ought to have positive expected returns, in the sense that the payoff in a tail event should be large enough to compensate for a long stream of non-tail event losses.

i guess i skipped that chapter on PM :/ 

i think there is value in terms of using it as a marketing gimmick.. a fund manager could buy 10k in lottery tickets and include it as a footnote in the executive summary. some investors might be looking for that exposure. in the event of a win bloomberg news would have a field day

bchad's picture

I never thought the CFA curriculum emphasized that point much, although when I taught for Stalla, I often included it.  It’s 100% true for diversification purposes… you never want to add an asset with negative expected excess return for “diversification” reasons, even if it is negatively correlated.  There is a formula that does cover that, which says that you should add something to a portfolio if its Sharpe ratio is larger than the existing portfolio’s Sharpe Ratio times its correlation coefficient to the existing portfolio, but it’s not always an obvious implication until you stop to think about it.

For hedging purposes, it’s more complicated.  If you want to make your portfolio market neutral, because you aren’t supposed to have market risk, or because you think the short term forward looking sharpe ratio is negative, you might want to short a future to get rid of the market beta.  >ong term, that future will have a negative expected return.  However, the portfolio *with the future in it* still needs to have a positive expected return and a higher sharpe ratio, which it can have if you have expected alpha in the portfolio.

For options that pay off in extreme tail risks, you still need a long term positive expectation.  Nassim Taleb’s strategy of investing in deep OTM options that pay off in black swan situations but which constantly lose until the swans come in isn’t going to be a help if you are down 50% from 5 years of normalstan, and up only 105% from a moment in extremistan.  Taleb’s strategy requires payouts that are on the order of 10x or 100x in a black swan event before it is useful as a hedging strategy, because most likely you are not going to have 100% of your investment in a portfolio that is losing money 99% of the time.

Lotteries are by definition uncorrelated to other stuff, so it would seem to be a natural addition to a portfolio, butit has a negative expected (pot size * winning probability < cost of ticket), so there is no diversification argument.

For hedging purposes, if you had a correlation between bad returns elsewhere and a large payout, it could arguably increase the sharpe ratio by reducing the size of risk, but only if it reduces risk faster than it reduces return, which typically requires high magnitude correlations.

So yes, maybe I misspoke… you never want a negative expected return asset in your portfolio for diversification purposes.  For hedging, it’s more complicated, but if you are hedging, you will need a high correlation magnitude, and usually some implicit leverage (like an option or future).

You want a quote?  Haven’t I written enough already???

krazykanuck's picture

dvictr wrote:

i think there is value in terms of using it as a marketing gimmick.. a fund manager could buy 10k in lottery tickets and include it as a footnote in the executive summary. some investors might be looking for that exposure. in the event of a win bloomberg news would have a field day

I’d think a fund manager was off his rocker and the gimmick would backfire if he started spending money on lottery tickets to include in a portfolio.

newsuper's picture

I like the idea of UK Premium Bonds.

Like playing the lottery but with guaranteed return on and of your capital. Invest your cash in a AAA rated investment, earn a relatively modest return and hope you win the monthly 1 million pound prize.

ohai's picture

Lottery tickets are:

1) Negative expected return

2) Uncorrelated with your portfolio

So, the CAPM efficient frontier just shifts downwards. That is, the portfolio with no lottery tickets dominates the portfolio with lottery tickets. 

If you want to get a lottery-like payoff, buy a bunch of OTM options or penny stocks. 

“I’m a CPA! I got money b***h!”

FrankArabia's picture

this question can’t be serious…what is even more crazy is how many ppl responded to this stupid question including myself….

bchad's picture

I responded mostly because it forced me to think through stuff again, sometimes useful insights come from answering what seem to be dumb questions.  And sometimes questions that seem silly on the surface can be driven by unusual circumstances that force you to go there.

I agree that the question is from someone who is either inexperienced in portfolio construction or from someone who just enjoys screwing with us.

You want a quote?  Haven’t I written enough already???

FrankArabia's picture

i got implicite rejection yesterday by this hot babe in the elevator…she gave me the body language to let me know I could never get her…..

former trader's picture

Maybe we can add lottery bonds to the portfolio:

http://www.bloomberg.com/news/2012-04-16/lottery-securities-beating-aaa-provide-winning-bet-muni-credit.html

Want to win the Oregon (STOOR1) or Florida lottery? Don’t purchase tickets. Buy their bonds instead.

Oregon’s AAA rated bonds, whose historic default risk is near zero, are backed by lottery revenue and compare with odds of one in 176 million to win the multistate Mega Millions jackpot. Since November, yields on the debt have dropped almost seven times as much as those on top-rated municipal securities as interest rates in the $3.7 trillion market have fallen to lows not seen since the 1960s.

Florida (STFLA1) and Oregon are among four U.S. states that have sold $5.5 billion in bonds backed by cash from games of chance, mostly to fund school construction, said Natalie Cohen, a senior analyst at Wells Fargo & Co. who wrote a report on lottery revenue this month. Mega Millions, played in 42 states and theDistrict of Columbia, awarded a record $640 million jackpot after a March 30 drawing.

“In economic good times and bad times, people want to play the lottery,” said Terry O’Grady, senior vice president of muni trading at FMS Bonds Inc. in North Miami Beach, Florida.“Lottery revenues, while they are discretionary, are not going to be that volatile.”

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