$2 billion is nothing though.
All prop trading is struggling recently. Many banks downsized their prop trading desks. In my opinion, investment opportunities ebb and flow, like a wave. (Are you familiar with that expression? It's an American expression.)
So, for example, when prop trading is very profitable, many firms rush to increase their prop trading desks. When there are more firms prop trading, the opportunities are more difficult to find. There is no easy money left. When there is high volatility and financial difficulty (huge problem with volatility in US Equities in 2011, which lead to many banks closing their prop trading desks), the prop traders suffer. After many banks stop prop trading, and financial situations improve, and volatility decreases, there become a lot more opportunities for prop traders, because nobody is taking advantage of it. Then banks rush to increase their prop trading divisions again. It's a cycle, like regular business cycle, or a wave.
Anyway though, $2b is not a lot of money. I think the US public becomes easily astounded by these large numbers, because they compare it to their own bank account.
The problem with restricting banks investment options is that is takes a very narrow perspective. It is like moving back to the Prudent Man Rule instead of the Prudent Investor Rule.
Prudent Man Rule says, every single investment in a portfolio must be safe. This rule was established way before mathematics studied portfolio theory. It's almost impossible to have high returns with this rule. It's only possible to stay above inflation.
Prudent Investor Rule says, the entire portfolio should be well diversified so that it can be safe. This rule can have decent returns, and still low risk, if the individual assets in the portfolio have low correlation (therefore, the portfolio as a whole is still not risky).
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Here's a link from US Government that talks about these two rules.
Prudent Man Rule sounds like the way you describe Japanese banks ability to choose investments.
Prudent Investor Rule uses
Modern Portfolio Theory discoveries by Nobel Prize winner Harry Markowitz.