How volatility risk explains a trading anomaly

New research offers a solution to the equities premium puzzle

Economists puzzle over why, if you invested $1 conservatively in US government guaranteed bonds in 1890, you would have $300 today. Yet if you had put a dollar in stocks and shares, you would be sitting on $1.3 million. It is hard to believe there is such a huge difference.

Nervous investors certainly demand higher returns from shares, because they are not as safe as bonds – but surely not by that much.

US investors got an average 7.67% p.a. from equities during the past century compared with 1.31% from bonds. The difference of 6.36%, the premium US investors demand for buying equities instead of bonds, is even greater in Australia where it's about 8.5%.

A premium of 1% should be more than sufficient to compensate for equities' risk, according to theoretical mathematical modelling. So why don't bond investors rush into equities? That would boost demand for shares and reduce the discrepancy.

Figures of 8% seem implausible because they suggest investors are more nervous and risk averse than markets warrant. And this equities' premium does not seem to fit other economic principles, either.

There has been a flood of suggested solutions to this equity premium puzzle, but none are generally accepted. Now Peter Swan, a professor in the school of banking and finance at UNSW Business School, has joined the debate.

In the paper Is Liquidity Largely Unpriced While Market Volatility is Systematically Priced? Swan argues that the premium is justified by the magnitude of the volatility risk.

‘Share trading cannot eliminate or even reduce the aggregate risk in the economy due to fundamental uncertainty’ 


 Buyer and seller interaction

The puzzle arises from either ignoring trading altogether (the representative investor) or only taking the point of view of the stock or bond buyer, in isolation from the seller.

The puzzle disappears if framed as the interaction of the buyer and seller, who are trying to get the best deal they can in the circumstances. They are sharing the market risks and the midpoint price they settle on prices market volatility.

While any impediments to trade such as illiquidity may be irrelevant to this price they are vital when it comes to trade volume and turnover.

Since the puzzle was posed in 1985, suggested solutions range from denial – that the premium does not exist but is some form of statistical illusion – to agreement that equities are indeed risky, given that another Great Depression or a Third World War could occur.

The US stockmarket lost 90% of its value in the first three years of the Depression, industrial production halved, personal consumption fell by 20% and it took a decade to recover.

This 'rare disaster' explanation of the premium puzzle states that we live in extraordinary times – there has been a 60-year run-up of markets without such a market crash. The chance of such good fortune is a million to one – a wall of worry for investors, which tempers the demand for shares.

"Share trading cannot eliminate or even reduce the aggregate risk in the economy due to fundamental uncertainty about technology and largely unpredictable movements in individual preferences for goods and services," says Swan.

"Since the relatively well-to-do seem more willing to bear these risks, stock trading is effective in mitigating some of this risk by sharing it across a sizeable portion of society."

A counter explanation revolves around the great advantage of US treasury bonds – they are readily convertible into cash, quickly and cheaply. Equities can become illiquid in a crisis, when the owner really needs the money. While there was a downward spiral of liquidity during the global financial crisis this was largely for subprime mortgages and collateralised debt obligations (CDOs).

‘Our model provides a motive for trading based on the mutual sharing of volatility risk between the counter-parties’ 


Public investment

The equities premium puzzle is not just theoretical. If you get so much higher returns from shares, without equivalent risk, shouldn't governments be investing more of its money in the sharemarket?

Shouldn't it be borrowing more money in bonds for infrastructure if bond interest rates are comparatively discounted to the future market returns from such infrastructure?

Economist John Quiggin, a professor at the University of Queensland, has argued the equity premium suggests there is a strong case for public investment in long-term projects and corporations.

The premium is also a factor in determining the worth of government assets in private hands, where returns are higher – especially if the proceeds of privatisations are used to pay down government debt.

Swan says that even government-sponsored national projects such as Australia's Ord River Scheme have turned out to be largely "white elephants".

"[The market] leaves profit-focused firms to make investment decisions – not governments. And dramatic interventions by governments can destroy gains from trade; think of the tariff wars that destroyed the global economy at the time of the Great Crash," he says.

Swan argues the equity premium puzzle comes from so-called neoclassical growth models, where neither the equity buyer nor seller has a motive to trade. In fact, the proper framework is a dynamic trading model which takes into account the mutual sharing of volatility risk.

He compares it to the pioneering economist David Ricardo's discovery of the mutual gains from free trade. If you look at the buyer and seller separately, in isolation, it is a zero sum game, where one nation exports and one imports, one earns and another pays out.

Ricardo showed with simple numerical models that international trade encourages industry specialisation that always produces positive results for both sides. This is so counter-intuitive to the uninitiated it is still being argued in the present US election over the fear that growing free trade agreements are sending jobs offshore and to Mexico.

Sharing volatility risk

As Swan says, it takes two to tango. The interests of both the buyer and seller have to be considered simultaneously. A purely buyer focus is only one-half of the transaction. If the preferences of buyer-seller counter-parties are met simultaneously then the equity premium puzzle is solved when markets settle on price.

"The buyer and seller have quite different perspectives for trading," says Swan.

"Our model provides a motive for trading based on the mutual sharing of volatility risk between the counter-parties. We show that, when investors trade two related assets to share volatility risk, both the buyer and seller compare 'apples with apples' based on different units of account."

The buyer's unit of account is cash. Since he forgoes a dollar in cash by buying at the higher ask-price, he must compare this with the cash dividend he receives in the next period plus the net bid-price of the unit of stock which is the cash value he could sell it for.

By contrast, the would-be seller's unit of account is the stock itself, not cash. He owns the stock and realises the lower bid-price if he sells. Hence he must compare this with the foregone dividend, plus the higher ask-price, which is what it would cost him to replenish the unit of stock and represents its continuing value in the absence of future transactions, if he retains the unit of stock.

Consequently, the buyer with his cash values the stock at the net-of-transaction-cost price, while the seller with his stock values the stock at his gross-of-transaction-cost price with the trade impediment netting out in the determination of price.

The investors might win in some trades and lose in some other trades, depending on how informed they are about the worth of the stock.

One important implication is that the gains from sharing volatility risk are diminished by high spread costs, making it important to ensure that these costs are kept to a minimum in an efficient and cost-effective market. 


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