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FBI: A little faith goes a long way

Some belief is needed in factors other than market exposure to justify choosing a multi-factor strategy over a market-cap weighted one. But how much belief?

Let’s start with a thought experiment to test your spatial intuition. Imagine you are 100 metres south of a destination (say your favourite pub) but you step one metre east (perhaps because this wasn't your first pub of the night?). How much further are you now from your destination? The answer may surprise you – it's just five millimetres. In other words, despite your blunder, the total distance from your destination has increased by just 0.5% of the distance you have moved. This isn't so bad, particularly if there is some potential upside such as (literally) bumping into an old friend.

What has this got to do with factor-based investing (FBI)? Well, a similar phenomenon occurs in investing but instead of distances we are talking risks. On introducing an uncorrelated risk – effectively orthogonal to other risks (like east versus south) – the incremental increase in overall risk is very small, at least to start with. Introducing ‘additional’ factor exposures (i.e. factors other than market exposure) only has a marginal impact on risk, yet may significantly increase return. This can mean that you only need to have a relatively small amount of faith that such factors will continue to perform for it to make sense to include them in your portfolio.

In a recent blog Poker and FBI and also this paper, we considered multi-factor exposure across the five main factors (value, momentum, quality, low volatility and size) that has been neutralised to broad market movements by shorting the market. We estimated that it has a Sharpe ratio (excess return per unit volatility) of around 0.4. When combined in a long-only factor-based portfolio (i.e. including market risk) we estimated it would outperform the market index by about 1% per annum (before costs and fees) and with slightly less volatility*.

This is all very well, you may think, but what if you’re more sceptical than us? What if you think there is a significant risk such strategies lose their shine? The question arises – to what extent do you need to believe in factors for a long-only FBI portfolio to 'beat' a market portfolio? We sought to understand this from the perspective of an objective-driven investor that judges risk in absolute terms (typically volatility) as opposed to relative to the market (typically tracking error). The FBI portfolio 'beats' the market if its Sharpe ratio is higher.

It turns out that, ignoring any additional costs for now, you only need to believe a Sharpe ratio of around 0.13 on the multi-factor exposure for the risk efficiency of the overall portfolio to beat that of the market. This is much lower than our best-estimate of 0.4 and far lower than that observed historically. This is shown in the chart below:

The reason for this is that the five main factors commonly in use are generally uncorrelated with the market. There is a strong diversification effect from combining these factor risks with market exposure. The upshot is that there could be even greater reductions in factor efficiency in the future than what we assume and still the FBI portfolio could remain attractive for our objective-driven investor.

The diagram above does not allow for costs. If FBI costs more than market cap the table below shows how the belief required is greater, to overcome any additional costs:

Extra cost of FBI

'Belief' Sharpe ratio required


0.13 (as above)








But even allowing for significant costs and fees, the belief required is much lower than our paper’s estimate of 0.4. Some degree of belief is needed but the above suggests you have to take quite a sceptical view of factors to not expect them to generate return in a more risk efficient way than the market portfolio. Stepping sideways might not be a blunder after all.


* The lower volatility arises because the overall beta of the multi-factor portfolio is less than one.

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