Buy High or Buy Low? Perold and Sharpe on What Rebalancing Really Does

Here is a question that sounds trivial and is not. Your portfolio was 60 percent stocks. Stocks have fallen sharply, so now it is 50 percent stocks.

Do you buy more stocks to get back to 60, or do you sell stocks because things are going badly?

Both answers have respectable-sounding justifications. Rebalancing back to 60 is the standard advice: buy low, sell high, maintain your target risk. Cutting exposure as things fall is the logic of stop-losses, portfolio insurance, and trend-following: protect the downside.

Perold and Sharpe's 1988 paper is the definitive treatment of this question, and its great contribution is to show that these are not merely different tactics, they are opposite bets on the character of markets, with mirror-image payoff profiles, and neither one is free.

The problem: rebalancing rules were treated as housekeeping

Investors and advisers treated rebalancing as an operational chore, something you do quarterly to keep the portfolio tidy. Perold and Sharpe pointed out that a rebalancing rule is not housekeeping. It is an investment strategy in its own right, and it fundamentally reshapes the distribution of your outcomes. Two investors with the same starting mix and the same underlying assets can end up with completely different return profiles purely because of how they respond to price moves.

To see the structure, they laid out and compared the main families of dynamic strategy.

The key idea via analogy: the shape of your payoff

The trick is to stop thinking about what you do each quarter and start looking at the final payoff curve: your portfolio's value plotted against the stock market's value. That curve's shape tells you everything.

Buy and hold: a straight line. You buy 60 percent stocks and never touch it. As stocks rise, your stock share drifts up. As they fall, it drifts down. Your payoff is a straight line, and your downside is floored by the value of your bond holding. No trading, no drama.

Constant mix (rebalancing to a fixed target): a concave curve. To hold your stock percentage fixed you must sell stocks as they rise and buy stocks as they fall. You are systematically a contrarian, buying the dips and trimming the rallies.

Now, what does that do to your payoff? It concaves it. You underperform in a sustained bull market, because you kept selling on the way up. You underperform in a sustained bear market, because you kept buying on the way down. But you do very well in a choppy, oscillating market that goes nowhere, because you were mechanically buying low and selling high the whole time and harvesting each swing.

Rebalancing is a short-volatility strategy. You are, in effect, selling insurance to the market. You collect a premium when markets oscillate, and you pay out when markets trend hard in one direction. Very few investors who rebalance quarterly realize this is the position they hold.

Portfolio insurance (including constant proportion portfolio insurance, CPPI): a convex curve. Now do the opposite: buy stocks as they rise, sell stocks as they fall. As your cushion above your floor grows, you take more risk. As it shrinks, you de-risk toward the floor.

This convexes your payoff. You do well in sustained trends in either direction, because you are always adding to the winning side and cutting the losing one. You are protected on the downside, because you keep selling as you approach your floor. But you get whipsawed to death in an oscillating market, buying every rally just before it reverses and selling every dip just before it recovers.

Portfolio insurance is a long-volatility strategy. You are buying insurance, and you pay a premium for it in the form of whipsaw losses in choppy markets. Trend-following has exactly this shape, which is why trend followers describe their returns as looking like a long straddle.

The insight that ties it together

Here is the elegant part. Concave and convex strategies are mirror images, and they need each other.

The person who rebalances is selling stocks into a rally to someone. The person running portfolio insurance is buying stocks in a rally from someone. They are each other's counterparties. For the market to clear, both types must exist. Not everyone can be a portfolio insurer, because there would be nobody to sell them stocks as prices rise. Not everyone can rebalance either.

Perold and Sharpe make the point that buy and hold is the market-neutral middle: it is what everyone does in aggregate, since in aggregate the market's holdings are simply the market. Any dynamic strategy is a deviation from that, and every deviation requires someone taking the other side.

So the choice between them is not a question of which is smarter. It is a question of what kind of market you expect, and what shape of payoff you want to own.

• Expect choppy, mean-reverting markets? Rebalance. You are paid to supply liquidity into the oscillations.
• Expect big sustained trends, or simply want protection from disasters? Insure. You will pay for it in quiet markets.
• No view and no strong preference about shape? Buy and hold costs nothing and requires nothing.

There is no dominant answer, and pretending there is one is the mistake the paper exists to prevent.

Why it mattered

• It turned rebalancing from an operational habit into a deliberate investment decision. Anyone who rebalances mechanically without knowing they are running a short-volatility strategy is taking a risk they have not thought about. This paper is why sophisticated allocators now discuss rebalancing policy explicitly.
• It explained trend-following before trend-following was fashionable. The convex payoff of a strategy that adds to winners and cuts losers is exactly the crisis-alpha profile that managed futures funds sell. Perold and Sharpe describe the mechanics of why it looks like a long option position, and why it bleeds in range-bound markets.
• It framed the aggregation constraint, which is a genuinely deep point. Not everyone can pursue the same dynamic strategy. Strategies that require you to trade in a particular direction as prices move need someone willing to trade the other way. This was a warning that would look prescient a year later.
• It gave a common language for a huge range of practices. Stop-losses, volatility targeting, CPPI, glide paths, and rebalancing bands are all points on the concave-convex spectrum this paper maps.

The honest limitations

• Costs are treated lightly. Every dynamic strategy trades, and trading is expensive. In practice, the whipsaw cost of a convex strategy in a choppy market is dominated by transaction costs, and the rebalancing benefit of a concave strategy can be eaten by them too. The stylized payoff curves assume you can trade smoothly.
• The market can gap, and floors can break. Portfolio insurance depends on being able to sell as prices fall. If the market gaps down overnight, you cannot. The 1987 crash, which happened the year before this paper appeared, demonstrated this brutally: portfolio insurance strategies could not execute their selling fast enough, and the very act of them all trying to sell at once contributed to the crash. The paper's own point about aggregation, that everyone cannot insure at the same time, was validated in the most expensive way possible.
• It assumes you know your risk tolerance and it is stable. The choice between concave and convex ultimately rests on how your appetite for risk changes as your wealth changes, which is a preference most investors have never articulated and which tends to change under stress.
• It says nothing about which market environment is coming. The framework tells you the payoff shape of each strategy. It has no view on whether the next decade will be trending or choppy, which is the one thing you would need to choose correctly.

The one-line takeaway

Perold and Sharpe showed that a rebalancing rule is an investment strategy, not a chore: rebalancing to a fixed mix means selling into rallies and buying dips, which is a short-volatility bet that pays off in choppy markets, while portfolio insurance means the opposite, a long-volatility bet that pays off in trends, and since the two are each other's counterparties, no one shape can be right for everyone.