RISK is linked to reward; it is virtually the first lesson one learns about finance. Safe assets pay low returns; if you want higher returns, you have to risk your capital. Academics have been examining these issues for decades, and have come up with such insights as the capital asset pricing model (CAPM) and the efficient market hypothesis. In turn, investors have applied their insights to the market. The techniques they have adopted may have changed the nature of the market. Risk and reward may not be as securely linked as they used to be. Two papers in the spring Journal of Portfolio Management bring these issues to light. The first—“Risk Neglect in Equity Markets” by Malcolm Baker of the Harvard Business School—looks at an obvious flaw in the CAPM. The model suggests that stocks which are more volatile than the overall market (high beta in the jargon) should display higher returns while stocks that are more stable (low beta) should deliver lower returns. More risk means more reward.

But that is not what has happened. Mr Baker assembles two portfolios from 1967; one consists of the 30% of US stocks with the lowest beta; another of the 30% with the highest beta (the portfolios are adjusted as betas change). By the end of the period, $1 in the low-beta portfolio had grown to $190, while the high-beta portfolio rose to just $18. The difference in compound returns is huge—5.5% a year. The low-beta portfolio is a lot less volatile and the maximum drawdown (peak-to-trough loss) is 35% compared with 75% for the high-beta portfolio.

Think about that; low risk meant higher reward. It was the equivalent of finding $20 notes lying on the street.

When you move to the world of asset classes, however, the traditional rule held; over the entire period, equities returned 10.9% a year while safe Treasury bills paid just 5%. Investors did get paid for owning risk.

Was this a fluke? Mr Baker is not the first to notice the anomaly. One of finance’s best-known academics, Fisher Black, wrote up the low-beta anomaly in 1993. That means the period since his paper was published is “out of sample” and thus a good test of the hypothesis. Sure enough, low-beta stocks have outperformed since then, despite a period in the late 1990s when, thanks to the dotcom bubble, high-beta stocks were all the rage.

Why might this be? Veteran readers might recall a column from 2012 which explained the outperformance in terms of low beta. AQR, a fund management group, explained the low-beta effect in terms of institutional constraints. Fund managers want to beat the market and deliver higher than average returns; so they buy high-beta stocks, as academic theory suggests. This makes high-beta stocks too pricey and drives down their returns. The answer should be to buy low-beta stocks and combine them with leverage. But investors are generally constrained from using borrowed money. So the anomaly persists.

Mr Baker thinks part of the reason that private equity has been successful is down to this strategy; the likes of Blackstone and KKR are buying less volatile (cash-generating) businesses with borrowed money.

The second paper ("Index-Linked Investing—A Curse for the Stability of Financial Markets around the Globe?" by Lidia Bolla, Alexander Kohler and Hagen Wittig) deals with tracker funds, a product your blogger has enthusiasm for. Tracker funds have been around for 40 years but took their time to gain market share despite the obvious attractions of their low costs; in recent years, exchange traded funds (ETFs) have surged in popularity, taking the tracker share of the market market to more than a third. The efficient market hypothesis suggests that it is very hard for active managers (those who pick stocks) to beat the market after costs because all the information is already reflected in market prices; what will move prices in future is “news” which, by definition, cannot be known in advance.

Some have worried, however, that tracker funds dilute the purpose of the stockmarket, which is to allocate capital to the most attractive companies. Trackers just buy shares in proportion to their market weight. The paper looks at the potential for the rise of index funds to cause herding. As people pile in and out of index ETFs, all shares will move together as those who run the index funds either buy, or sell, all the component stocks of the benchmark. Sure enough, that is what the paper did discover:

We found a substantial increase in the co-movement of stocks with respect to trading patterns, price returns and liquidity risks within all markets analysed. Furthermore, we investigated whether the increase in risk commonalities can be attributed to the growth in index-linked investing, and we found statistically significant and economically relevant evidence that the growth in index-linked investing is related to the substantial increase in risk commonalities.

The irony here is that a shift by investors to reduce their individual risk (that they pick an underperforming fund manager) might end up increasing risk in aggregate. Does this diminish your blogger’s enthusiasm for trackers? No. First, the figures still show that active managers do not beat the markets over the long term. One can always find some that have in the past, but they cannot be relied upon to do so in future. Second, the charges levied by active managers have a corrosive effect over the longer term that is a much greater risk to investors’ wealth than occasional bouts of herd-driven volatility.

Some people in the finance industry have a sniffy attitude towards academics. (My favourite, probably apocryphal, exchange is as follows. Hedge fund manager to academic: “If you’re so smart, why aren’t you rich?” Academic to fund manager: “If you’re so rich, why aren’t you smart?”) But academics play a vital role; they are a generally unbiased check on the pretensions of financial practitioners, with enough technical knowledge to cut through the jargon with which Wall Street can confuse the investing public. Academic views will change over time; of course they will. But we should be glad they are around.