The Behaviour of the Spot and Forward Markets

In a recent working paper, we examined the link between these two markets under both the classical economics approach and under a behavioural lens. The economic theory of ‘rational expectations’ says that rational and risk-neutral investors will set a forward price that is an unbiased predictor of the future spot rate; not a perfect predictor but one whose errors sum to zero over time. But we rarely find this to be the case for any asset examined.

We tested whether this holds for gold, using data from 1989 to mid-2013. First, we looked for, and found, a long-run equilibrium relationship between the spot and forward prices using co- integration analysis. But it is not in the form of a one-for-one relationship as it should be, one eventually equal to the other. Strike one against Rational Expectations.

We also assessed whether changes in spot and forward prices are equal over time. At longer horizons (12 and six months), the theory again fails, but once we move to the shorter term, the answer begins to change. The three-month forward rate is a marginal case, but we can be fairly confident that at a one-month maturity, the forward market is an unbiased predictor of the expected future spot price using this method. The gold market seems to be able to predict the near-term level of the spot market with forwards but not much out beyond a quarter.

So there is some evidence that the gold market may be irrational. This finding is not unusual, mirroring the results of studies on other asset classes such as equities and foreign exchange. A significant portion of the research on this issue from the Foreign Exchange market finds that instead of a perfect positive correlation between the two, a strong negative correlation exists. Rational expectations ignores both the market’s ability to act irrationally and the influence of risk adverse speculators. These can cause forward prices to be above the expected future spot price if they take mostly short futures positions, while end users are mostly long. Speculators can then sell the asset for more than the spot price, giving them a return from bearing the risk of the forward contract.

Our work is mainly concerned with looking at the behavioural explanations of the failure of rational expectations to hold. Specifically, we ask: Is the market optimistic or pessimistic in its forecasts? Do investors over or under-react to news? We try to answer these questions by looking at the way news is incorporated into the forward premium, the market’s forecast errors, and the revisions made to forecasted spot prices as they come to maturity. We allow for investors to be risk averse in all of our findings below.

Irrationality can be observed in a number of ways. If investors put more weight on ‘private’ information over public information, they consistently underreact to all types of publicly available news, as has been found to be the case in the equity market. The market’s mood can also be dependent on the type of news it receives, as shown in the table below. If the market overreacts to good news and underreacts to bad news, it is optimistic; if it underreacts to good news and overreacts to bad, it is pessimistic.

We find that the gold forward premium is optimistic; overreacting to large positive changes in the spot rate (good news) and underreacting to large negative changes (bad news). Indeed, forecast errors react in the same way to all news, overreacting to good and bad news alike. Revisions to the market’s forecasted spot price overreact to the forecast errors it has just made. To see whether the gold market’s mood has been stable over time, we rerun the same tests but do so on an ever-increasing sample, starting at four years of data and gradually increasing the sample size until we use the full sample again.

The forward premium and the markets forecast errors suffer from mood swings throughout the sample, sometimes being optimistic, then pessimistic. We show this for the 12-month forward premium in Figure 1, using changes in the spot price as news. If there were no behavioural biases and markets were rational, the two lines would be at 0 all the time. If the Good News line is positive, the market is underreacting to large positive spot price changes and overreacting if it is negative. By the end of the period, the market is optimistic as stated above, but we can see that there are times (e.g. the mid 2000s) when the opposite is true. At the beginning of the sample, the market is consistently overreacting to all news. The market’s revisions to forecasts are consistent over the sample, overreacting to its past errors almost all of the time.

So, the gold market’s behaviour does seem to be better explained by behavioural factors than by assuming investors are all and always rational. Its mood and reaction to new information tends to evolve over time. But over the full period under examination, the market’s predicted spot price was optimistic, and its errors and revisions overreacted to news.