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Beta as in let's imagine our illegal gambling ring (let's call it "U Be Screwed" ) is quoted on the stock market?
We can build on the assumption that the vast majority of gambling rings (including UBS) appeal to clients that are lower/working class. We can also assume that UBS rigs the larger events and is thus always profitable, which is priced in since the ipo, and the only significant driver in revenue fluctuations is how much do the costumers gamble.
We can assume our costumers are rational to some degree hence will gamble more when they have more disposable income and feel optimistic about the future, and are also very sensitive to economic downturns since the risk of layoffs, pay cuts, and generic bad weather will affect them more than the average joe. From this we infer that during hard times (that should coincide with a stock market crash) clients will gamble less and UBS revenues will be smaller. It will also take longer to go back to pre-crisis levels of revenue since our working class costumers coming out of a stressful and uncertain period won't be so eager to risk losing the $ they may one day need to feed their families.
We can expect UBS' stock price to have an high positive correaltion with the stock mkt but also to be extra sensitive to downturns and less respondent to upward movements. I would say beta>1 .