The constant level of risk argument implicitly assumes that stocks and bonds have constant risk levels, or at least constant relative risk levels. I can't find any good theoretical basis for this view. The main support I find is that rebalancing to fixed percentages is easy.
I just saw an interview with William Sharpe that includes his take on this infrequently discussed subject:
http://www.stanford.edu/~wfsharpe/art/apinterview.pdf (thanks fundtalker123 for posting the link).The argument against a constant mix strategy is that if, for example, you set a target of 60% equities and 40% bonds, and the prices of equities rise (and the prices of bonds don’t), then you have to sell stocks and buy bonds. If everyone had a constant mix strategy they would all try to follow that pattern, and there would be a lack of buyers and sellers on the other side of the trades. Not everyone can follow that strategy, and sell what has risen while buying what has fallen. Thus it involves betting against the market. The same argument also applies to target date and life cycle funds. If the market moves sharply, they will have to sell the relative winner and buy the relative loser.
I believe there is a better way. If you are an average investor, invest in market average proportions, and live with the changes in the markets. If you are affected more by changes in wealth than the average investor you may want to decrease your stock position after stocks outpace bonds, and do some rebalancing, trading with someone who should be rebalancing in the other direction. More generally, you should always look at the market value of securities. Market values reflect a consensus of opinions regarding value. Without a sense of the value of asset classes you are throwing away critical pieces of information. At Financial Engines we look at the values of major asset classes every single month and incorporate this information when we analyze investor portfolios. The result is that we don’t advocate a lot of trading. This kind of a coherent system leads to advice and management that is closer to a buy and hold behavior than a constant mix strategy.
Of course bonds have maturities and calls, new shares are issued by corporations and companies sometimes buy back shares. Over the longer run these actions tend to cause market proportions to come back to something like a 60/40 stock/bond mix. The message is that investors should not be slavishly rebalancing over time. There is a better way, which is to invest taking into account current market values. This will also save a lot in transaction costs.
This is not to say don't rebalance. Rather it's saying rebalance based on market proportion changes (which often means doing nothing), not constant percentages.