How to calculate the 'right amount' of investment risk

Your finances are personal, especially when it comes to investing. Setting objectives, timeframes and risk levels depend on age, lifestyle, circumstances and personality. There’s no one-size-fits-all, so investors should judge performance against their own goals and risk tolerance.

The idea of personalised risk management and targets is a postmodern portfolio theory (PMPT) innovation, which builds on the earlier work we’ve examined in this series. At its heart is the idea of maximising an investor’s utility from investing, based on how risk averse they are and what rate of return they need.

Maximum utility investing

Firstly, investors must understand where they sit on the risk spectrum. This is hard to do. For example, when we review IC Portfolio Clinic submissions, there is often a disconnect between the risk investors are taking and their stated risk tolerance. For example, someone with a portfolio made up of 70 or 80 per cent equities will state they wouldn’t be prepared to lose more than 15 or 20 per cent in a given year.

But consider that the MSCI World fell 54 per cent during the 2008 financial crisis, and by almost half after the dotcom bust. Any portfolio with 70–80 per cent in equities would suffer mark-to-market losses far higher than 15 per cent in events of a magnitude similar to the dotcom crash or the financial crisis.

In short, investors ought to sense-check assumptions made about themselves and the markets to ensure they decide on the right strategy, which should be multi-asset to some extent.

To help do this, portfolio managers often assign clients a risk rating. In some of the technical models this becomes a coefficient, ‘theta’, that can be used to generate a maximum utility allocation. Higher thetas indicate those who are more perturbed by drops in portfolio value when market undulations get rough.

In our Investors’ Chronicle Alpha asset allocation models, we model using data going back to the 1970s (thus taking in a number of economic and market shocks). We adjust the risk-reward metric for a series of assets, allowing for the fact asset returns don’t follow a normal distribution (most daily observed returns are positive, but there is a ‘fat’ left-tail of high-magnitude negative days that occur more often than a symmetrical bell curve frequency distribution would predict).

We then run an optimiser to suggest the asset allocations (the mix of shares, bonds, gold, real estate and other commodities) that should give investors greatest satisfaction depending on their theta coefficient. For a cautious investor – more cautious than most IC readers – with a theta of six, the model returns a strategic asset allocation of roughly 51 per cent bonds (a mix of US government Treasuries and UK government gilts), 44 per cent shares (global large company stocks and UK all-cap stocks), and 5 per cent gold. That would have made a 6.4 per cent annualised real (ie ahead of inflation) rate of return between 1980 and today.

The worst peak-to-trough drawdown such a strategy would have suffered is a 15.1 per cent fall during the equities bear market that followed the dotcom bust. Its next worst performance was a drop of 12 per cent in 2021-22, when equities and bonds fell in unison as higher interest rates popped a cross-asset bubble stoked by years of loose monetary policy.

In short, investors who consider 15 per cent drops in portfolio value as their maximum threshold for risk may find their strategy is bolder than they thought. Our optimiser doesn’t recommend an 80 per cent shares allocation until we drop the theta coefficient to 2.5 and the maximum drawdown for this, our adventurous category, is more like a third of the portfolio value. That’s pretty uncomfortable, but still significantly better than the falls a shares-only strategy would have suffered. The payback is a smoothed-out rate of return of 8.2 per cent a year ahead of inflation. If you’re in a position to plan without being forced to sell in a downturn, and can remain unflustered as such sell-offs unfurl, this may be a worthwhile trade-off.

Past performance isn’t a guarantee of the future, but at least these models provide a framework for considering what might happen in a really bad situation, and help to weigh up if the real returns feasibly on offer are a fair inducement to take the risk. No-one should be put off investing altogether, however: doing nothing guarantees you lose or at best stand still. In the same 40-year period during which our adventurous strategy would have made a real return of 8.2 per cent a year, Barclays’ Equity Gilt Study shows cash in a building society account would have made an inflation-adjusted 0.4 per cent a year.

Cash savings are always sensible, but the opportunity cost of not investing at all, especially in periods of structurally higher inflation, is significant. Just remember, you don’t have to be gung-ho if your objectives are modest. If they can be achieved with 6 per cent annualised real returns and you really don’t like taking risk, then even a cautious strategy could limit peak-to-trough drawdowns to a more palatable level.

Whatever option best suits you, post-modern portfolio theory techniques that help mitigate the risk of missing your target rate can offer some useful control mechanisms. We’ll discuss them next time.