Risk Mapping Projections

Projected measures

Measuring the risk of investments

A good risk measure is meaningful, and relevant to investors’ goals. We believe it
should be:

• Forward-looking
• Long-term
• Focused on outcomes (i.e. the destination, not the journey)

Historic volatility may be ubiquitous in the investments 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 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.

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.