This widget should be used to visualize the risk concentrations of a portfolio under normal conditions (the stress test widget isolates behavior on “stressed” conditions).

The aim of risk attribution is to specify the contribution of each security to the overall portfolio’s risk. Simply summing the risk of each individual security will not equate the portfolio’s risk because it does not account for the role of correlation. Securities that are highly correlated with the portfolio are riskier than ones that are negatively correlated. In the former case, the security tends to co-move with the rest of the portfolio, thus offering little diversification. A negative correlation, by contrast, actually reduces risk, since it acts as a hedge for the rest of the portfolio

We use a measure called Marginal Contribution to Total Risk (MCTR) for risk attribution. It takes into account three characteristics to determine the riskier positions, namely:

- Larger allocations
- Higher individual volatilities
- More correlation to the rest of the portfolio

Conversely the less risky positions have opposite properties:

- Smaller allocations
- Lower individual volatilities
- Less correlation (preferably negative) to the rest of the portfolio

The mathematical formulation is complex and involves finding the resulting change in portfolio risk from an incremental change in the allocation of a single security (with all others kept constant). A nice property of MCTR is that they add to the total portfolio risk.

The risk attribution widget has 2 components:

- A visualization with stacked bars.
- A number in the upper right corner with volatility statistics.

Let’s describe each component separately:

**1. Visualization Area:**

The graph represents the marginal contribution to portfolio total risk (MCTR). The x-axis holds different bars, each representing a source of risk in the portfolio. Bars can represent underlying positions, sectors, market capitalization, country of risk, liquidity or user-defined baskets, depending on the desired aggregation level.

The size of the bars (y-axis) is proportional to their marginal contribution to portfolio risk: red bars stack up and represent correlated sources of risk, whereas blue bars stack down and represent uncorrelated risks. The absolute value of bars are sorted left to right.

Move the mouse over the visualization area and a popup menu will automatically display the following information:

- MCTR: this is the marginal contribution to annualized portfolio risk (volatility) from the position.
- Cumulative Volatility: the cumulative measure of the above. The cumulative MCTR of the rightmost bar corresponds to total portfolio risk.
- Percent: the ratio of that position’s MCTR to total portfolio risk.
- Cumulative Percentage: the cumulative measure of the above. The cumulative percentage of the rightmost bar corresponds to 100%.

An example with a short position in Haliburton is shown below:

It can be seen that Halliburton is shown as a blue bar stacking down. That means that incrementally adding to HAL position, will help decrease the portfolio risk.

**2. Summary Statistics:**

On the upper right portion of the widget there is a number indicating the forecasted, **annualized** volatility of the portfolio. The main visualization also displays that volatility as a blue horizontal line. By design, the rightmost stacked bar should touch that line.