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John mcgahern’s novel, “That They May Face the Rising Sun”, is set in a remote corner of Ireland. There is a lake, a church, two bars and not much else. Gossip is prized but in short supply. Much of it is concerns John Quinn, a womaniser who has buried two wives and is looking for a third. His quest takes him to Knock, a shrine to the Virgin Mary, which has become a place to find a partner. Like many pilgrims, John Quinn is outwardly pious. But his mind is fixed on earthly matters.

The masking of intent may also be true of visitors to the temple of private equity. On the surface, investors in such funds might hope to harvest a reward—an “illiquidity premium”—for locking up their money for five to ten years. That allows private-equity funds time to turn sluggish businesses into world-beaters. The pitch is seductive. Capital has flooded in as readily as pilgrims flock to the shrine at Knock.

Perhaps, though, private equity’s pilgrims are really after something else. These institutional investors may face limitations on how much they can borrow. Private equity offers a way round such constraints: it is liberal in its use of debt to juice up returns. And that is not all. The value of privately held assets are not assessed all that often. That is a plus for those who, for ignoble reasons, would like not to be told how volatile their investments are.

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This is a conclusion of a new paper from aqrCapital Management. Its authors look at the returns on private-equity purchases (“buy-outs”) of American businesses. They find that, after fees, private equity outperformed the s&p500 index of large companies by an average of 2.3% a year between 1986 and 2017. That is quite the winning margin. But on closer examination, it looks less impressive. Buy-out targets tend to be small firms that are going cheap—that is, they have a low purchase price relative to their underlying earnings. An investor would have achieved higher returns from a basket of small-capitalisation “value” stocks than by putting his money in private equity.

The edge that private equity had over large listed stocks seems also to have dulled. In the past decade returns have been no better than the s&p500. This may be because more capital is chasing buy-out targets. Private-equity funds once purchased businesses that were much cheaper than s&p500 firms, says aqr. But the gap in valuations has closed.

Why are pension funds still so keen to push money into private equity? A tenet of textbook finance is that investors can build a portfolio that fits their preferences by choosing the right mix of equities, the risky asset, and cash, the risk-free asset. Nervous types might keep most of their assets in cash. At the other extreme, a risk-loving investor may wish to borrow (ie, have a negative cash holding) so that stockholdings exceed 100% of his capital. An investor with a limited ability to borrow can instead turn to private equity. Its funds take on $1-2 of debt for every $1 of equity.

The aqr authors point to another appeal. Illiquid assets, such as private-equity holdings, are not revalued in line with the price of publicly traded companies—“marked to market”—all that often. A common practice is to rely on self-appraisals. These tend not to reflect the day-to-day fluctuations in the price of listed firms. All this makes for artificially smooth returns.

Such smoothing has several advantages. When stock prices fall, the value of private-equity funds appears to fall less sharply. A mixed portfolio of public and private equity will look less volatile than a pure portfolio of listed stocks. The true riskiness of private equity would only become apparent in a prolonged bear market. Otherwise, it appears to offer diversification, albeit of a specious kind.

Some investors are forced to sell stocks (to “de-risk”) when prices fall, to comply with solvency rules. In such cases a bit of returns-smoothing is helpful, as a rigid marking to market would oblige investors to sell stocks at rock-bottom prices. That said, capital tends to flood into private equity when markets are booming. A lot of buy-outs will then be at peak prices.

The best private-equity funds are skilful investors. But the discretion they all have over how they report returns makes it hard for investors to judge who the best are. One study finds that half of funds claimed to be in the top quartile. Still, smoothed returns and leverage may be what investors are really after. Like lovelorn pilgrims to Knock, they will treat any other reward as a bonus.

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