Investors run the gamut, from fire-and-forget types who buy mutual funds and leave them alone for decades, to fussbudgets who watch their portfolios minute by minute, ready to buy or sell with every up and down.
But is there a golden mean that would allow the investor to act when it will really pay off, while avoiding counterproductive tinkering? Common sense says that this “Goldilocks” zone must exist, but theorists have had a hard time nailing it down, says Wharton finance professor Andrew B. Abel. “It was a mathematical nightmare,” he notes.
Now, Abel and two colleagues — Janice C. Eberly, finance professor at the Kellogg School of Management at Northwestern University, and Stavros Panageas, finance professor at the Booth School of Business at the University of Chicago — say they have come closer to an answer. In a hypothetical case with real-world application, they find, an investor might safely ignore a portfolio for, say, a month, depending on factors like the value of the investor’s time and the size of the broker’s commissions and other transaction costs incurred when assets are bought or sold. The research is described in their paper, “Optimal Inattention to the Stock Market with Information Costs and Transactions Costs.”
Investors can apply this insight to common issues such as how often to buy or sell a security as its price fluctuates, and how often to rebalance a portfolio as it drifts away from the targeted mix of stocks, bonds and cash. If the time and monetary costs of adjusting a portfolio are very large, the researchers conclude, it pays to wait until market conditions make change worthwhile. It would seem, then, that if costs were very low, it would pay to adjust more frequently, fine-tuning to smaller market changes. In fact, the researchers found a surprising insight: Even when costs are small, it makes more sense to act according to a schedule with surprisingly long intervals. Too much fussing, in other words, is counterproductive even if it’s cheap.
This conclusion could also be applied to companies adjusting prices to match changing market conditions, Abel says. Doing it too often just doesn’t pay.
Give and Take
The study assumes the investor has two accounts: The first is an investment account with stocks and bonds that is designed to grow over time. The second is a transactions account containing cash for living expenses. On each “observation date,” the investor studies the accounts and, if necessary, sells enough assets to provide cash to cover expenses until the next observation date. A retiree, for example, might sell mutual fund shares every month to pay the next month’s bills.
Each observation has a cost that can be measured in the value of the investor’s time, plus commissions and other charges that apply to any action taken. An investor who re-examines a portfolio every minute could buy or sell in response to every tiny change in securities prices, keeping the portfolio precisely on its targeted mix of holdings all the time. This kind of hyper-attention might represent the ultimate in investor agility, but it would pay off only if it cost virtually nothing — i.e., if there were no trading costs, and the investor had no other valuable use for his time.
At the other extreme would be an investor who ignored his or her portfolio for years on end. The investor who assessed and readjusted only once a decade, for example, would miss out on the opportunity to adjust his or her consumption and holdings of assets even though there have been large movements in the values of assets held in the investment account. In addition, because the transactions account would be replenished infrequently, it would have to be very large, removing cash from the investment account that pays higher returns.
Somewhere in between is the period of “optimal inattention.” Logic says that the higher the investor’s cost of time and money, the longer this period is. But finding a more precise figure took Abel and his colleagues dozens of pages of calculations.
Finding an Optimal Strategy
In setting an observation strategy, the investor has a choice between being “state-dependent,” reacting to changes in asset prices, or “time-dependent,” making observations at set intervals, Abel explains. The state-dependent approach has more intuitive appeal because it would seem to be more agile, matching asset ownership to market conditions.
“It turns out that notion is wrong — or missing something that we discovered,” he says. Unless costs are very high, the investor who starts with a state-dependent strategy will eventually shift to a time-dependent approach — after discovering that adjusting the portfolio all the time just doesn’t pay off.
One reason is that it turns out that the optimal strategy is to convert a set percentage of the portfolio to cash at every observation — every 34 days in the paper’s example. This would mean withdrawing more when the portfolio is up, and less when it is down, adjusting spending accordingly.
“The need for agility just disappears,” Abel notes. “As it turns out, even if you could do the more agile thing, you would end up taking two-tenths of a percent of your wealth and putting it into your transactions account every 34 days.”
While the mathematical case for this is complex, there is a non-mathematical way to look at it, he adds. To do this, the state of the investor’s holdings is represented by X, or the ratio of cash in the transactions account to the value of holdings in the investment account. Every time the investor observes the account to make adjustments, X will have one of three conditions, each triggering a different action.
If it is high — lots of cash relative to the value of the investments — the investor does not need to sell any investments to pay living costs until the next observation. Instead, he or she can move excess cash back into the investment account. In the event that cash is low, the investor must convert investments to cash to get to the next observation.
If cash is at an intermediate level in between, the investor will do nothing, because the cash level would be close enough. Even if cash is slightly high or slightly low, the investor will refrain from adjusting the holdings because the benefit would be offset by transaction costs.
Going against Intuition
In looking at these scenarios, the only unpredictable factor is the value of the investment portfolio at each observation. If stocks do poorly, X could be high and the investor would not liquidate any investments. On the other hand, if stocks do well, X could be low and the investor could liquidate some holdings to get back to the desired ratio of cash to other assets. But in practice, this wouldn’t make sense because it would incur transaction costs to move more cash than needed to the cash account, taking it out of assets with higher returns.
Therefore, the investor’s best strategy would be to keep just enough cash to get to the next observation. At that date, cash would be zero, X would be infinitely small, and the investor would have no choice but to sell investments to replenish the cash account. Now that the investor knows he or she will do the same thing at every observation — sell assets — the market’s ups and downs in between do not matter, so there’s no need for constant attention to the market, the researchers write.
Intuition suggests that as transaction costs get lower, the costs incurred at each observation get smaller, so it would pay to observe the portfolio — and to sell assets when necessary — more frequently. But Abel says the math shows that very frequent observations — every day, for example — do not pay off even when costs are very low. One reason is that many of the market’s ups and downs are random motion. An investor who adjusted to every price change would waste lots of money simply undoing previous moves.
The research also concludes that the relationship between transaction costs and the optimal observation period is not proportional. Cutting transaction costs to 25% of what they were, for example, might reduce the ideal observation period by only 50%.
Investors who are attracted to online brokerages offering cut-rate trading commissions should take note, Abel points out. “I think the lesson from this is that even if costs are small or modest, very frequent adjustment is unwarranted,” he says. Even with commissions as low as $5 a trade — a level provided by some deep-discount brokerages — it would probably not pay to adjust a portfolio more often than every month or two, he estimates.
“Even a tiny cost like that — $5 — is enough to prevent [any benefit from] continuous, or highly frequent transactions.”