# Allow drift in weights in a risk benchmark?

I am tracking the risk of portfolios using a standard 2-asset benchmark (S&P500 / Agg bond) and I want to throw a flag if the risk of a portfolio goes outside of a certain range relative to that benchmark. I am looking for resources that address whether or not to allow the weights to the risk benchmark to drift over time.

As a sample case, the benchmark is 70% S&P500 / 30% Agg bond

The simplest thing, of course, is to create a series of returns such that the benchmark return in every month = 0.7 * return of S&P500 + 0.3*return of Agg Bond. This amounts to assuming a monthly rebalance of the benchmark.

Alternatively, we can form the 70/30 benchmark and then allow the weights to drift over some extended period, calculate monthly returns of the drifting benchmark, and calculate volatility from that. The period over which you allow the portfolio to drift would most naturally be equal to the length of historical period over which you calculate volatility (but these could be different).

In my experience, people follow the simple solution but I can see some merits to the second. Any suggestions?

Good question. It isn't so common that the volatilities are recalculated based on estimated drifts, it is more about adjusting for those drifts as time goes on. It also depends on how actively you manage your portfolio and how much money is at stake. Portfolios are rebalanced in a few different ways:

Calendar based rebalancing is where the portfolio is rebalanced at regular time intervals to ensure that the same weightings are maintained. Typically, these are done monthly or quarterly, but the time period depends on frictions and rate of drift.

Percentage of portfolio rebalancing or corridor-based rebalancing is where when the actual weights move too far away from the optimal weights, the asset weighting is adjusted based on a tolerance ± x%. The tolerance or corridor is larger when the manager wishes not to sacrifice a potential upside if an asset dramatically increases in price. Once again this depends on the correlation, volatility, risk tolerance, and frictions involved.

Constant proportion portfolio insurance (CPPI) is where when the market is moving up risky assets are allocated a higher weighting, inversely when the market is moving down, more weight is given to less risky assets to reduce the percentage allocated higher volatility assets.

If I understand correctly, if you account for an extra volatility by allowing assets to drift over an extended period, it would mean that your portfolio will end up having a large proportion of high return assets due to them growing faster than low return assets, so your risk will change. So if you attempt to account for this additional change in risk due to drift, your portfolio will be inefficient at the beginning. Thus the case for rebalancing strategies as they attempt to keep the portfolio as efficient as it can for a longer period of time.

In consideration of this, an intelligent investor would note that after a period of time the volatilities of each asset would have also changed, market conditions will have changed, and your risk tolerance would have changed. Not only does one have to adjust their portfolio to keep their weightings consistent, they must adjust their portfolio based on changed market conditions.

Hope this helps.