# Risk Budgeting (RB)

Risk budgeting is a relatively new method to construct and manage investment portfolios. Unlike traditional asset allocation, risk budgeting does not allocate capital based on dollar allocations the way traditional capital budgeting does.

Instead, a risk budgeting asset allocation approach starts from the riskiness (i.e. volatility and correlations) of the different asset classes under consideration. Thus, rather than allocating different amount of money to different assets, we buy assets such that the total risk of the different assets in the portfolio contribute in a certain way to the overall riskiness of the portfolio. Some of the most important contributions in the field on RB are those made by Thierry Roncalli.

On this page, we discuss the basics of the risk budgeting portfolio construction approach. The mathematics of the approach are quite involved can be found in the work of Roncalli.

## Risk budgeting definition

Risk budgeting is an asset allocation approach were we first decide on the risk budgets for each asset class. Once these are set, a portfolio optimization is executed which sets the total risk contributions of the assets equal to the desired risk contributions.

RB is closely related to risk parity or equal-contribution-to-risk. However, whereas risk parity will set each asset’s contribution equal to 1/n, risk-budgeting allows investors to set the risk contribution of each of the investments to a specific value.

## Risk budgeting framework explained

There are three steps to implementing a risk budgeting approach.

1. First, determine the overall amount of risk we want to take (“target risk) and how we want to allocate that risk over the different asset classes (the “risk budgets”).
2. Implement a risk-budgeting approach to select the portfolio weights that meet the risk weights. This is done using a risk-budgeting portfolio optimization using e.g. Python, MATLAB,… . It is important to note that it is not to solve a risk budgeting problem using an Excel spreadsheet. For those who are limited to the use of Excel, an equal-volatility weighting scheme is a good option.
3. Periodically rebalance the portfolio to the target weights.

Note that we do not look at expected returns. This is different from traditional mean-variance optimization, where we do consider expected returns. The advantage of not relying on expected returns is that we do not have to try and forecast future stock prices, which is notoriously difficult.

## Summary

We explained the basics of portfolio construction using a risk budgeting approach. It is a portfolio optimization approach that does not consider expected returns but that distributes risk over the different securities. RB is a new approach to investing that looks at where we are allocating risk, rather than our money.