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 per cent 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.
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 – say $5 – is enough to prevent [any benefit from] continuous, or highly frequent transactions.”
This article first appeared at Knowledge@Australian School of Business.
