How do you define investment risk?

Principles of a good risk metric

A good risk measure should be meaningful to investors. We believe it should be:

• forward-looking;
• long-term; and
• focused on outcomes – in other words on the destination, not the journey.

 

Oxford Risk's definition of investment risk

Historical volatility may be ubiquitous in the investment industry, but it’s hardly relevant to most people.

Worse, short-term volatility is unstable, so that the same portfolio ends up with a different risk rating over time, sometimes within months!

We therefore define investment risk as the annualised standard deviation of ex-ante (i.e. forward-looking) long-term returns. By 'long-term' we mean 10 years, and we present the figure annualised. Our definition of risk is most easily understood by looking at the chart below which is taken from Investor Compass. 

The risk model projects forward many thousands of future paths based on 30 years of real market data. We use 9 asset classes as standard and the indices can be found here. We then measure the spread of returns at 10 years (i.e. the standard deviation) and we annualise this number.

This definition of risk means that we have to project many possible future outcomes, rather than rely on a single set of historical returns.  

Standard deviations of outcomes, not during a period of time

While volatility – standard deviation of returns along a period of time – is very strongly related to the uncertainty of future outcomes, it is not quite the same thing.

By risk, we mean the chance of both good and bad outcomes – variability in destination, not the bumpiness of the journey.

We therefore use the standard deviation of such outcomes, because as a statistic it succinctly does the job of capturing the essence of that 'unknowableness' of the future.

 

Why use ex-ante (forward-looking) returns?

Relying on historical returns is not acceptable for several reasons, most notably:

• it assumes that the future will be a repeat of the past; and
• there is not enough history to measure long-term returns (without overlapping periods to an egregious extent).

Instead, we choose to project many simulated return paths, and measure risk as the standard deviation of outcomes across these simulations.

We therefore define investment risk as the standard deviation of projected long-term
returns. By “long-term” we mean 10 years, and we present the figure annualised.

In making those projections we cannot simply copy and paste the past. Recent history
offers a guide to the future in some respects, yet we have only limited realised long-
term outcomes - inadequate to fully sketch out their shape.

Instead, we simulate myriads of possible futures. This can be done by first describing an
investment portfolio in terms of its allocation to broad asset classes, each represented
by generic, diversified market indices.

Then, we generate a great many return paths for these asset classes, by remixing
historical index data in such a way as to preserve important features such as cross-
correlations and momentum.

As for multi-asset portfolios, we assume quarterly rebalancing.

Finally, we calculate the annualised standard deviation of these ex-ante 10-year returns,
our measure of portfolio risk.

 

Why long-term?

Investing in multi-asset portfolios should really only ever be about the long-term.

In the short-term, there is so much noise to contend with – only over a full economic cycle does the stock market turn from a 'voting machine' into a 'weighing machine', to borrow from Benjamin Graham's famous metaphor.

We should therefore measure risk over an appropriately long time horizon. While it is hard to define what is precisely 'long', we say that 10 years is adequately long enough.

Why annualised?

We present the figure annualised to render it independent of the time horizon under consideration.

It also enables a straightforward interpretation of the risk metric as the amount by which we would expect annual returns to deviate from their anticipated trajectory (plus or minus), two-thirds of the time.

Quantifying the projected outcomes

The future is profoundly uncertain, so it is impossible to be precise about the returns
you will get. However, how various investments have performed in the past provides
some guide to the range of returns you might expect over different time horizons.

To obtain the very good/average/very poor projections, we use the simulated paths as
described above. The very good outcome refers to the 95'" percentile, the average
outcome refers to the 50" percentile (median) and the very poor outcome refers to the
5" percentile of the ending values of the simulated paths.

Quantifying the downside

Probability of loss: the chance of ending up with less than the initial investment amount.

Possible drawdown: the maximum amount the portfolio’s value may fall from peak to
trough over a bad 1 year time horizon, measured as the worst 5% of maximum
drawdowns of each simulated path in the first rolling year of the projections.