Here’s a Different Way to Think About Stock Diversification
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Here’s a Different Way to Think About Stock Diversification

Everybody knows to spread money across many investments. Fewer think about diversifying over time.

By IAN AYRES
Mon, Oct 10, 2022 9:08amGrey Clock 5 min

Investors often think of diversification as a free lunch—it allows them to maintain returns while reducing risk. But most people only get part of diversification right, and that can hurt them later in life.

With traditional diversification, people spread money around different kinds of investments to mitigate risk. That approach misses a key opportunity: “diversifying” how you invest over time.

Most people start investing with a small amount of money, because that is all they can afford, and ramp it up as their earnings grow. But investing so much later in life unnecessarily puts people at greater risk when they are close to retirement. They end up with far greater exposure to stock-market risk in their 50s and 60s than in their 20s and 30s, even if they are buying diversified mutual funds.

We propose a different method: People ought to borrow money to make their initial investments larger, so that they can invest closer to the same amount every year over their lifetime. Think of investing $2 a decade steadily for three decades, instead of $1 for the first, $2 for the next and $3 for the third.

The overall amount they invest stays the same—$2 of average market exposure—but when it is a steady amount, instead of an increasing one, the market exposure is larger than otherwise earlier on ($2 versus $1) and then smaller than otherwise in later life ($2 versus $3).

Steady dollars

Both choices—investing $2 each decade instead of $1, $2 and $3—provide the same expected return, since they both have $6 accumulated market exposure over time. But risks associated with the two strategies are different: Our time-diversified path brings lower variance in returns than one with increasing investments.

When investment exposure varies over time, the market’s ups and downs don’t balance out as well. With 2/2/2, an up in the first decade balances out with a down in the third, and vice versa. But with 1/2/3, an up in the first decade is dominated by a down in the third, and a down in the first decade is also dominated by an up in the third. Consequently, the 1/2/3 investment pattern leads to larger swings in lifetime accumulations. The 1/2/3 strategy has too little dependence on the first decade’s stock return and too much on the third. By comparison, the 2/2/2 approach is evenly spread out and thus better diversified.

People might think they can’t follow a 2/2/2 type of strategy because they haven’t saved enough when young: They can’t invest $2 because they only have $1. But that’s not true. Using leverage—that is, borrowing money to buy stocks—people can use $1 of capital to borrow another $1 and thereby get $2 of market exposure in their first decade.

Sound risky? Consider that young people do the same thing with housing when they borrow money to buy a house they live in for decades—and there the leverage often involves borrowing $9 for every $1 of equity. We propose borrowing only $1 for each $1 invested. Limiting ourselves to 2:1 leverage means we don’t hit a perfectly even market exposure over time, but gets us closer to that ideal.

The lessons of history

Using an initial 200% allocation—and gradually reducing the allocation to stocks over time, down to 83% at retirement age—is a winning strategy. In a 2010 book, we found that this “leveraged life cycle” approach produced superior retirement accumulation for each and every cohort retiring from 1914 to 2009. We now have more than a dozen years of post-publication returns where we can evaluate how the strategy actually worked in practice. Leveraged life-cycle returns have continued to provide superior retirement accumulation for each and every cohort through mid-2022.

Average investors using our method—assuming they invested 4% of their annual income, which rose during their careers to $100,000 in their final year of work—accumulated $1,255,000, while a traditional target-date fund investment, starting at 90% stocks and going down to 50%, produced only $675,000, and a constant 75% strategy led to $774,000.

Of course, these higher returns are partly due to more stock exposure and not to the diversifying benefits of the leveraged life-cycle strategy. To focus solely on the diversification benefits, we compared the retirement accumulations of a less-aggressive life-cycle strategy, one that again starts with 200% in stock but ramps down to 50% at retirement. We compared this to a constant 75% of savings in stocks and 25% in bonds. We chose this particular 75% allocation because it produces the same average accumulation ($774,000) across the retiring cohorts. Therefore, any difference in the strategies won’t be because one has more lifetime exposure to the stocks, which on average outperform bonds.

Comparing these two strategies shows that the leveraged life-cycle strategy decreases the standard deviation of retirement accumulation across retiring cohorts by an impressive 19%. Our more time-diversified, leveraged strategy produces higher returns for cohorts that experienced the worst stock returns (the 10th-percentile accumulation increases by 10.9% relative to the constant 75% strategy) and lower returns for cohorts that lived through the best stock returns (the 90th-percentile accumulation also decreases by 10.9% relative to the constant 75% strategy).

Producing the same average return with less risk is compelling evidence of how a leveraged life-cycle strategy can diversify market risk. Of course, ramping down to 50% instead of 83% in stocks at retirement has less market exposure and therefore lower average returns. The investor can choose: the same returns as a constant 75% exposure strategy with less risk, or the same risk but with higher expected return. Time diversification makes either possible.

Avoiding trouble

Our strategy works in theory and in practice. But there are possible objections that might hold people back.

For one, people might say that it is expensive to invest on margin. But competitive margin loans are cheaper than home mortgages (though you may need to consider online brokerages).

A second objection is that leverage is risky. But when you are more evenly exposed to market risk across time, you have less risk. Using leverage to go from 1/2/3 to 2/4/6 would be adding risk and market exposure. But a 2/2/2 strategy doesn’t.

When markets drop, those investors near retirement who have followed 1/2/3 are in trouble. If stocks fall by 25% in their last decade of investing, they would lose 25% of their $3 investment—while a 2/2/2 investor would lose just 25% of $2. That is a 50% greater loss on the $3 investment.

One objection that does have some merit is that our approach requires discipline. Some people can’t bring themselves to borrow money to buy stock or would bail out at the first downturn in the market. We would like to see target-date funds make things easier for investors by automating the process, borrowing at low cost and automatically adjusting a portfolio. People could put in money each month and forget about it.

Meantime, young investors can move to 100% equities. That isn’t 200%, but it is a step in the right direction and doesn’t require the psychological or logistical burdens of borrowing to buy. And even if this advice is coming a bit late for readers in their 50s and 60s, this is advice to pass along to the next generation. They don’t have to repeat our mistakes.

Dr. Ayres is the William Townsend professor at Yale Law School, and Dr. Nalebuff is the Milton Steinbach professor at the Yale School of Management. Together, they are the authors of “Lifecycle Investing.”



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The personal wardrobe of the late fashion designer Vivienne Westwood, who is credited for introducing punk to fashion and further developing the style, is headed to auction in June.

Christie’s will hold the live sale in London on June 25, while some of the pieces will be available in an online auction from June 14-28, according to a news release from the auction house on Monday.

Andreas Kronthaler, Westwood’s husband and the creative director for her eponymous fashion company, selected the clothing, jewellery, and accessories for the sale, and the auction will benefit charitable organisations The Vivienne Foundation, Amnesty International, and Médecins Sans Frontières.

The more than 200 lots span four decades of Westwood’s fashion, dating to Autumn/Winter 1983-84, which was one of Westwood’s earliest collections. Titled “Witches,” the collection was inspired by witchcraft as well as Keith Haring’s “graphic code of magic symbols,” and the earliest piece being offered from it is a two-piece ensemble made of navy blue serge, according to the release.

“Vivienne Westwood’s sense of activism, art and style is embedded in each and every piece that she created,” said Adrian Hume-Sayer, the head of sale and director of Private & Iconic Collections at Christie’s.

A corset gown of taupe silk taffeta from “Dressed to Scale,” Autumn/Winter 1998-99, will also be included in the sale. The collection “referenced the fashions that were documented by the 18th century satirist James Gillray and were intended to attract as well as provoke thought and debate,” according to Christie’s.

Additionally, a dress with a blue and white striped blouse and a printed propaganda modesty panel and apron is a part of the wardrobe collection. The dress was a part of “Propaganda,” Autumn/Winter 2005-06, Westwood’s “most overtly political show” at the time. It referenced both her punk era and Aldous Huxley’s essay “Propaganda in a Democratic Society,” according to Christie’s.

The wardrobe collection will be publicly exhibited at Christie’s London from June 14-24.

“The pre-sale exhibition and auctions at Christie’s will celebrate her extraordinary vision with a selection of looks that mark significant moments not only in her career, but also in her personal life,” Hume-Sayer said. “This will be a unique opportunity for audiences to encounter both the public and the private world of the great Dame Vivienne Westwood and to raise funds for the causes in which she so ardently believed.”

Westwood died in December 2022 in London at the age of 81.

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