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Updated on July 26, 2022 7:53 am
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Updated on July 26, 2022 7:53 am
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Updated on July 26, 2022 7:53 am

On Investment Objectives and Risks, Clear Communication Is Key, Part 3

Adapted by Lisa M. Laird, CFA, from “Communicating Clearly about Investment Objectives and Risks” by Karyn Williams, PhD, and Harvey D. Shapiro, originally published in the July/August 2021 issue of Investments & Wealth Monitor.1

Earlier in this series, we discussed the need for clear communications at the initial stage of the investment process and pointed out the communication challenges that accompany traditional investment decision frameworks and risk concepts. Here, we present a holistic approach that directly connects objectives and risks to new decision metrics, namely Portfolio Pi and Portfolio Eta, which were developed by Jakša Cvitanić, a scientific advisor to Hightree Advisors, and Karyn Williams, PhD.

These metrics enable decision makers to make direct trade-offs among competing objectives. We show that using shared language that is meaningful for investors can help assure that the chosen investment strategy best serves its purpose.

Portfolio Pi is a weighted average of the probabilities of attaining desired investment objectives, which includes avoiding specific losses, over an investment horizon. Applied in context, the Hightree Pi Score summarizes an investment portfolio’s potential to achieve objectives and avoid losses.
Portfolio Eta is the economic value that an investor potentially stands to gain or lose between portfolios with different Pi Scores. Portfolio Eta fully summarizes, in dollar or percentage terms, the differences between portfolios’ returns, risks, and costs.

Risks That Matter, Attainable Objectives

Being precise about what we want our investments to deliver — target returns, for example — says nothing about whether what we want is attainable. Investment committees must recognize this explicitly. What does attainable mean? It means having a high probability of meeting target-return objectives, given the amount of risk we can spend. And if standard deviation is not a meaningful and useful measure of risk, as we saw in our previous article, then we need a measure that is.

There are several ways to estimate risk capacity. One approach is to determine the available financial resources that the investment portfolio can lose without impairing the institution’s purpose.

Next, the investor needs to assess the potential impact of pursuing its target investment returns on its available financial resources. Suppose a $100 million private foundation has a target return of 8.04% and has estimated its risk capacity at $25 million. That is, the most it can lose without impairing its ability to serve its purpose is 25% of its portfolio’s value. This risk-capacity information facilitates the evaluation of an investment strategy simply by asking, “What is the average of the probabilities that the portfolio will hit our target-return objective annually and not lose 25% over the next five years?”

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The following chart shows the probabilities that the 8.04% target return and the 25% horizon loss limit will be achieved under each distribution assumption for three investment portfolios the foundation is evaluating. These include the current portfolio, a lower-equity portfolio, and a higher-equity portfolio. The lower-equity portfolio is 25% US equities, 25% non-US equities, 40% fixed income, and 10% broadly diversified hedge funds. The higher-equity portfolio is 35% US equities, 35% non-US equities, 20% fixed income, and 10% broadly diversified hedge funds. For simplicity, all analyses use indexes and all figures and results assume a non-normal distribution of portfolio returns.

Probabilities of Success: Investment Objectives and Risks That Matter

Chart showing Probabilities of Success: Investment Objectives and Risks That Matter

Under normal distribution assumptions, the probabilities of success are generally higher. If the loss limit is an important consideration, the results based on a non-normal distribution of outcomes provide critical information for the decision makers about risks that matter.

Regardless of the distribution assumption, all of the portfolios shown above have low probabilities of achieving the target-return objective. This is because the private foundation is required to spend 5% annually, real yields are expected to be negative, and asset premia are insufficient to cover the gap. This is an essential piece of information: The foundation may not get what it wants, even if it raises its equity allocation all the way to 100%.

These results are easily communicated and highlight necessary trade-offs. How can the foundation choose among these three portfolios?

If the foundation weighs the relative importance of its target-return objective versus its loss limit, it can measure its potential for success as an average of the probabilities. This average — its Pi Score — helps the foundation determine whether the objectives are attainable and which investment strategy is best.

The graphic below shows Pi Scores for each portfolio, where weights have been applied to the target return and the loss limit probabilities, representing the relative importance of each to the decision makers. If the investor equally weights the importance of achieving the target return and the loss limit, corresponding to the vertical line in the middle of the chart, the higher-equity portfolio has the highest Pi Score at 48%, slightly above the current portfolio’s, which is 47%. This is determined by equally weighting the target return and loss limit objectives: Pi Score of 48% = 50% weight × 32% chance of success in achieving return target + 50% weight × 63% chance of success in not violating loss limit.

Average Probability of Success, Varied by Relative Importance of Target Return and Loss Limit, Assuming a Non-Normal Distribution of Outcomes

Chart showing Average Probability of Success, Varied by Relative Importance of Target Return and Loss Limit, Assuming a Non-Normal Distribution of Outcomes

Alternatively, the foundation might choose to weigh its target return and loss limit other than equally. In fact, decision makers might want to evaluate a broad array of weightings and results. There is no one right answer. But, with the metrics described here, the dialogue moves beyond vague generalities about “a lot,” “a little,” or “somewhat” to more precise statements of probabilities relative to targets, especially risks, that matter to the institution using a common language and the agreed-upon preferences of those involved.

A complementary way to help judge whether one portfolio is preferable to another is to translate differences in potential outcomes into dollar terms. The foundation board can ask, “How much money would we have to add to our current portfolio in order to achieve the higher Pi Score of the higher-equity portfolio?”

The chart below illustrates the dollar-value (and percentage return) differences — i.e., Portfolio Eta — between the current portfolio and the lower- and higher-equity portfolios when the foundation board puts an 80% weight on the target return and a 20% weight on the loss limit.

Economic Value Differences between Portfolios: 80% Target Return Objective, 20% Risk Limit Weighting

Chart showing Economic Value Differences between Portfolios: 80% Target Return Objective, 20% Risk Limit Weighting

The preceding chart shows that given the foundation’s target-return objective, loss limit, and weightings, the higher-equity portfolio is “worth” about $2.2 million more than the current portfolio over the five-year investment horizon. This is equivalent to 0.44% in additional return per year — return that is left on the table with the current portfolio. This is no small sum for the foundation, and a value that is hard to attain through manager alpha.

Still, the foundation board may not feel satisfied with a low probability of hitting its return target or safe enough with the drawdown risks. Using these metrics to help trade off what it wants with risks that matter, the foundation might revisit its target-return objective and consider changes to its portfolio’s construction, active vs. passive managers, risk management activities, and other investment lifecycle attributes.

Alas, these metrics do not provide absolute, definitive, unassailable answers. Rather, they contextualize investment concepts, particularly the concept of investment risk, so that everyone involved is speaking the same language and understands the potential impact of their choices.

Tile of Defined Contribution Plans


Every fiduciary, regardless of their role or experience, can communicate clearly about investment objectives and risks that matter. Direct measures of the probabilities that fundamental targets and limits can be achieved, weighted by agreed-upon preferences and coupled with comprehensive comparisons of portfolio strategies in dollar terms, provide a more accessible and disciplined decision framework for all stakeholders. Even newcomers to the investment world can feel more confident that they understand their choices and are doing their best to protect and sustain the purpose of the investment assets.

1. Investments & Wealth Monitor is published by the Investments & Wealth Institute®. The full original article can be found here: “Communicating Clearly About Investment Objectives and Risks”.

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All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.

Image credit: ©Getty Images / skynesher

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Lisa M. Laird, CFA

Lisa M. Laird, CFA, is a principal and senior adviser at Hightree Advisors, LLC. She is a foundation trustee and is a former chief investment officer, investment committee member, board member, and investment consultant. Contact her at

Karyn Williams, PhD

Karyn Williams, PhD, is the founder of Hightree Advisors, LLC, an independently owned provider of investment decision tools, success metrics, and risk information. She is a chief investment officer, foundation trustee, independent public company director, and a former investment consultant. She earned a BS in economics and a PhD in finance, both from Arizona State University. Contact her at

Harvey D. Shapiro

Harvey D. Shapiro is senior advisor at Institutional Investor, Inc., where he has been senior contributing editor of Institutional Investor magazine as well as an advisor and moderator for numerous Institutional Investor conferences. A former adjunct professor and a Walter Bagehot Fellow at Columbia University, he has been a consultant to several foundations and other institutional investors. He earned degrees from the University of Wisconsin, Princeton University, and the University of Chicago. Contact him at

On Investment Objectives and Risks, Clear Communication Is Key, Part 3 is written by Lisa M. Laird, CFA for


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