April 2015: Richard 'Jerry' Haworth - The Linear Delusion

We are fairly convinced, in our own minds at least, that there are four important variables in portfolio management. Like the instruments in an aeroplane cockpit, they need to be constantly monitored.  Of these variables, one is extremely well known and understood: return, one is extremely well known but misunderstood: risk, one is somewhat known but also generally misunderstood: correlation. Finally, one is generally unknown and not understood: convexity.

What is also generally not known and therefore not well understood is that these parameters are not stable and more importantly, not linear. It is an error which is often fatal, yet continues to go unrecognised!

Let me explain.

Many investors and portfolio managers cannibalise the fact that end investors do not know that risk and correlation are not stable. They trade off higher and higher levels of risk, correlation and convexity to produce higher and higher returns, or in the case of this low interest rate environment, just to maintain a level of returns where investors can live off the income.

This will work until it doesn’t – and the resulting capital losses can be huge. In any event, the portfolio managers will merely blame the market because everyone else made the same mistake as well.

Volatility is mistakenly used as a proxy for risk, so when volatility is low ergo risk is low. If returns are to be had and volatility is low, look no further. It’s safe to swim when the waves are small, even if there are black fins breaking the water surface. Non-correlation is unstable, especially when you need it but hey, if a portfolio of collateralised mortgage obligations give us higher yields in an apparently uncorrelated portfolio, let’s do it. And convexity, well the concept doesn’t even exist outside of bonds so let’s ignore it! 

And so the market waits until everybody has cannibalised risk, correlation and convexity and then it catches everyone unawares. 

Convexity is basically how non-linear your parameters are in relation to each other. For simplicity we assume most modern portfolio theory assumes linearity. This alone renders the models about as useful as an ashtray on a motorbike.

Imagine you are doing a bike race. One of your variables is the “volatility” of the track. If you assume you are in the velodrome then you assume linearity (no accelerating change in the environment) and narrow ranges (no big jumps or change of altitude) i.e. low or at least constant volatility. You would gear up for this type of track and get a racing cycle, which is very light (read fragile) with no brakes and very thin tyres.

Most of the time, assuming the landscape is flat or at least benign seems to work fairly well. It’s when you start picking up speed to the downside that things start to go awry, in life, cycling and in portfolios. 

Firstly, we lose our rational decision making capability as things get faster and faster and our ability to deal with the subtle-but-quick changes necessary to stay upright get harder and harder. The risks accumulate and magnify. The potential for huge losses loom large. Suddenly, you discover you are in the Utah desert doing the Red Bull Challenge (YouTube it!). The landscape is concave, it gets steeper and steeper and you are going faster and faster, and next thing you know there is a chasm to be jumped over. Your bike, designed for track racing, has no brakes and is set up for speed.  The inevitable happens… 

Fortunately we can assume life is non-linear and adjust our strategy accordingly. The only curious problem is that we don’t! We insist in modelling life as a linear, constant variable because we are irrationally biased to hope and be optimistic. Thus we are continually corralled into various abattoirs every few years by smart salesmen who tell us that the road to riches lies in assuming linear, constant worlds.

Another truism: Life seems to take seriously ‘For whoever has, to him more shall be given’ and the corollary ‘but whoever does not have, even what he has shall be taken away from him’. That’s convexity and concavity. 

Convexity is the former, it is like knowing there is a trampoline underneath you to soften the blow, or that the next part of the roller coaster ride will be up and will be slowing the coaster down. In portfolio terms it is the knowledge that the portfolio is robust and the more extreme the downdraft, the more insured against further losses the portfolio will become. 

But when we are on a flat, benign landscape and we can see right the way to the horizon, we assume a flat benign landscape is OVER the horizon. We don’t see the need for protection against what we cannot yet see.

Therein lies the rub.

Bottom line?

Portfolio insurance doesn’t have a chance with most investors which, in turn, is why most investors will get seriously hurt by most systemic crises.

It is like experience. It is what you want (or get) just AFTER you need it!