First, ask: in which possible states of the world might my assets all fall together?
One obvious possibility here is that if the equity market falls a long way, previously uncorrelated shares will rise together; this happened, for example, during the 2008-09 crisis, when most shares fell at the same time and later mostly recovered together.
A less obvious possibility is that whereas some things - such as a rise in risk aversion or worsening in the economic outlook - can cause bonds to rise as equities fall, other things could cause both to fall together such as a debt crisis or rising inflation.
Secondly, don't be fooled by names. You might think that if you own an emerging markets fund, banks and mining stocks that you have diversified. Not necessarily. They are potentially correlated because of a common exposure to a risk factor. If expectations of global growth decline, emerging markets and mining stocks might both fall, as might banks to the extent that they are risky shares and worsening growth prospects deter people from taking risk.
What matters is the risk factors to which assets are exposed, the not the sector or part of the world they operate in.
Thirdly, consider how far your assets will fall if they all fall together. The case for holding defensive stocks or bonds is not so much that they are uncorrelated with other assets. Instead, it is that if everything falls, these would probably fall by less and thus cushion your losses.
Fourthly, keep an eye on the worst-case scenario. One possible scenario is that all shares fall together. A less likely one is that bonds and equities do so. Ask: how would I cope if this happens? If the answer is 'badly', then consider rebalancing your portfolio. Remember that one asset which is largely immune to the risk of correlations all increasing in bad times is cash.
All these recommendations might seem vague. But in a sense, this is the point. There's a common fallacy that numbers are either precise or wrong. This is not so. Thinking imprecisely about correlations can be more helpful than using apparently precise but unreliable numbers. It's better to be roughly right than precisely wrong.
