Important nuances of good risk budgeting and portfolio construction.

The equation below decomposes a portfolio’s risk into long-term, short-term and diversification risks.

This is a typical perspective for either strategic and tactical asset allocation or benchmark-relative portfolios.

The key insight is that there is a trade-off between the short-term risk and how diversifying it is relative to the long-term risk.

If the short-term exposures are very diversifying, we can increase their standalone risk without increasing the risk of the overall portfolio.

So, it is desirable to have diversification in both the long-term and short-term exposures as well as between the two.

This helps protect against simultaneous losses in both parts of the portfolio. Hence, good portfolio construction takes this interaction into account.

If you have a benchmark-relative portfolio and underperform significantly over one year, this indicates there is an issue with your risk budgeting or model.

If your relative performance tends to go up and down with the benchmark, this indicates that you have poor diversification between the long-term and short-term risks.

To eliminate the above issues, you can perform benchmark-relative optimization as presented in Section 6.3 of the Portfolio Construction and Risk Management book: