# 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.

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