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Let's say we have a set of investments, a target allocation to those investments, and commit to rebalancing at some particular frequency. In the worst-case scenario, if one of the classes catastrophically goes to zero, wouldn't that (if rebalanced mechanically) cause our entire portfolio to go to zero? Consider in the limit where class A drops, so we shift more funds in, then drops again, etc.

This is obviously a systems-collapse type scenario. But are there theoretically situations where one class could go to zero while another is still viable? Is there a lesson here that in extreme circumstances we should monitor and possibly abandon one class instead of rebalancing?

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This is a valid criticism of a simple (static-weight) rebalancing strategy. It can reduce portfolio volatility but also reduce expected return. A realistic case would be allocating by country where one country's government permanently collapses (gradually enough for you to keep averaging down on soon-to-be-worthless securities).

The real issue is where the target weights come from. They should be based in some way on historical risk and return of each asset. So if one asset declines badly enough, its history would look worse and you would presumably reduce its target weight before it takes your portfolio all the way to zero. Also, rebalancing works particularly well during the accumulation phase of the life cycle, where inflows remove the risk of permanently going bust.

A contrasting example is an "unmanaged" portfolio (where you simply hold a fixed number of shares of each asset, e.g., market-cap weight), which is optimal according to some theories. You can split between two assets and know that you'll always be within a factor of 2 of the better-performing one, which can be a powerful guarantee in the long term.

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The prior exercise to rebalancing is checking whether you still want to hold each share.

If you don’t, sell it before the rebalancing exercise.

If you do and it’s cheap, that’s a buying opportunity. If the price drops again, too bad. You’ve already followed your convictions and discipline - it happens.

If it’s no longer trading (eg dropped to zero), you can’t trade it anyway. It doesn’t even enter the rebalancing exercise.

Disclaimer: I am not a qualified financial advisor and the above is not to be taken as financial advice. Seek professional advice prior to an actual trade.

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