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Blog Posts — October 2, 2023

May the odds be ever in your favor: Interpreting active portfolio metrics

We love data. Our clients love data. But when it comes to truly understanding the risk-reward trade-off of an investment strategy, sometimes the devil isn’t in the details. In a whitepaper, “What are the odds?: Getting a better read on portfolio risk-return metrics”, we advocate for spending more time with the portfolio summary metrics as the first port of call, before jumping in headlong into more granular statistics.

In the paper, we outline a step-by-step framework that brings together both the art and science of quantitative portfolio analysis (and probability theory) to help portfolio managers understand and make smarter decisions on:

  • the investment opportunity of a given portfolio
  • the allocation of a risk budget
  • the optimal time for risk-taking over a specific period of time   

We make a few assumptions in order to carry out the analysis – all based on risk reporting in our portfolio construction tool, Axioma Portfolio Optimizer.

The first assumption is that an investor only ‘bets’ when the odds are in their favor. We use ex-ante active risk and projected active returns of an optimal portfolio at the time of construction, to measure those odds.

The second assumption is that the risk and reward metrics to define these odds, represent the mean and standard deviation (or variance) of a distribution which, rightly or wrongly, is assumed to be normal.

The third assumption is that the ex-ante Information Ratio (see definition below) is an acceptable measure of the average risk-reward trade-off to be expected from an optimal portfolio over the long-term.

Using these assumptions as a backdrop, we compare the probability distribution of active returns across two simulated portfolios to derive other statistics and inform decision-making.

Some of the specific ‘screening’ statistics of interest include:

Predicted active risk (or ex-ante active risk): Sometimes called the tracking error for strategies that very closely track an index. This is expressed as an annualized standard deviation of the active return.

Information Ratio (IR): The ratio of annualized expected residual returns to residual risk, a central measurement for active management. A manager’s value add is proportional to the square of the information ratio.

Downside risk: Aggregates the risk from the losses below a minimum threshold that investors may have. Standard deviation measures of risk only look to compute the risk that is under the bulk of the (normal distribution) curve, but investors also need to consider about the negative returns in the left tail.

Upside potential ratio: Like its downside risk counterpart, this measure looks at the size and probability of returns above a certain investment goal. Investors should only choose investments where the upside potential is larger than the downside (i.e. risk-adjusted returns).

Let’s look at an example of these two portfolios side by side:

Source: Axioma Portfolio Optimizer

If you look at the probability of outperforming the benchmark, their average positive and negative active returns, and their average active gains-to-losses ratio, there isn’t much difference between the two hypothetical managers. However, there are two important areas for consideration: Manager B has an IR of 0.32 (putting her in the top 63% of her class) and downside risk is just 7.76% for Portfolio B versus the 13% for Portfolio A.

How do we choose between those two portfolios? Which is the best investment opportunity? The answer is that it depends on what you’re focusing on. If it’s active returns, then clearly you go with Portfolio A, but if you’re after manager skill or minimizing large losses, then you’d go with Portfolio B.

Ultimately, choosing the ‘best’ portfolio is about what the investment goals are. However, summary portfolio statistics can help investors screen the initial portfolios before taking further action to drill down into the details of the additional reports provided by their risk management and portfolio construction tools. Rather than diving right into the depths, it’s best to first spend time above water.

Download the whitepaper and find more information about our portfolio construction tool at