To recap, our definition of investment risk is the standard deviation of projected 10-year returns. For this, we need to project the performance of a given investment.

We do this using the asset allocation of the portfolio under consideration (where it’s reasonably stable over time). We then use our risk engine to simulate thousands of future return paths for each asset class, and assume quarterly rebalancing.

Our model is realistic enough to give an accurate risk estimate, but not so complex that it’s vulnerable to calibration errors.

## Four market phenomena every model should reflect

**Bolts from the blue**: too many models assume that returns conveniently follow a normal distribution. If that were true, the stock market would lose 30% on average only two years each century. But it’s happened four times since 1990! We insist that it’s vital to model the risks of 'fat tails' in a distribution.**Dynamic correlations**: almost every investment model assumes that correlations remain static. But this is palpably untrue: the five-year rolling correlation between developed stocks and government bonds has flipped from +0.5 to -0.5 and back into positive territory. Models must be as dynamic as the markets they’re aiming to reflect.**Momentum**: the nadir of the 2008 financial crisis came after month upon month of snowballing anxiety. Simulations generated by a model with short-term memory loss can severely underestimate how bad things can get.**Mean-reversion**: it’s an empirical fact that risk changes with the time horizon under consideration – even accounting for annualisation. Returns over 5 to 10 years are considerably less dispersed than their component annual returns would otherwise suggest. Markets typically recover from crashes, and models should mirror this.

## The Oxford Risk model: remixing history

We don’t make assumptions about the shape of every asset’s distribution and correlation. Instead, we remix the historical returns themselves.

Each simulated path is generated by picking random months from history, and appending the returns for every asset class in each month as we go along. This captures a lot of the desired behaviour, but not all.

So, to capture momentum and mean-reversion, we set a pre-defined chance of using the very next month in sequence. In this way, we preserve the unique characteristics of each asset class, and the phenomena described above. The paths are consistent with observed history, yet uniquely different.

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