Earlier on this series, we discussed the necessity for clear communication within the early stages of the investment process and highlighted the communication challenges related to traditional investment decision frameworks and risk concepts. Here we present a holistic approach that directly links goals and risks to latest decision metrics, viz Portfolio Pi and Portfolio Eta, developed by Jakša Cvitanić, a scientific advisor at Hightree Advisors, and Karyn Williams, PhD.
These metrics allow decision makers to make direct trade-offs between competing goals. We show that using a typical language that’s meaningful to investors will help make sure that the chosen investment strategy best serves its purpose.
| Portfolio Pi is a weighted average of the chances of , including , over an investment horizon. Applied in context, the Hightree Pi Score summarizes an investment portfolio’s potential to realize goals and avoid losses. |
| portfolio and is the economic value that an investor can potentially gain or lose between portfolios with different Pi scores. Portfolio Eta summarizes the differences between portfolios’ returns, risks and costs entirely in dollars or percentages. |
Important risks, achievable goals
If we are saying exactly what we wish to realize with our investments – for instance goal returns – that claims nothing about whether what we wish is achievable. Investment committees must explicitly recognize this. What does attainable mean? This implies that given the danger we will invest, we’ve got a high probability of achieving the goal return objectives. And if standard deviation will not be a meaningful and useful measure of risk, as we saw in our previous article, then we want such a measure.
There are various ways to estimate risk capability. One approach is to discover the available funds that the investment portfolio can lose without compromising the aim of the ability.
Next, the investor must assess the potential impact of pursuing his targeted investment returns on his available financial resources. Assume a $100 million private foundation has a goal return of 8.04% and estimates its risk capability at $25 million. This means it may well lose at most 25% of the portfolio value without affecting its ability to satisfy its purpose. This risk-capacity information makes it easier to judge an investment strategy by simply asking, “What is the average probability that the portfolio will achieve our target return objective annually and not lose 25% over the next five years?”
The following graphic shows the chances of achieving the goal return of 8.04% and the horizon loss limit of 25% under each distribution assumption for 3 investment portfolios evaluated by the Foundation. These include the present portfolio, a portfolio with a lower equity share and a portfolio with a better equity share. The lower equity portfolio consists of 25% US stocks, 25% non-US stocks, 40% fixed income and 10% broadly diversified hedge funds. The higher equity portfolio consists of 35% US stocks, 35% non-US stocks, 20% fixed income and 10% broadly diversified hedge funds. For simplicity, all analyzes use indices and all numbers and results assume a non-normal distribution of portfolio returns.
Probabilities of Success: Investment objectives and risks which might be vital
Under normal distribution assumptions, the chances of success are generally higher. When the loss limit is a very important consideration, the outcomes based on a non-normal distribution of results provide decision makers with vital details about vital risks.
Regardless of the distribution assumption, all the portfolios presented above have low probabilities of achieving the goal return objective. This is since the private foundation has to spend 5% annually, real returns are expected to be negative, and asset premiums usually are not enough to cover the gap. This is crucial information: the muse may not get what it wants even when it increases its equity ratio as much as 100%.
These results are easy to speak and highlight needed compromises. How can the muse choose from these three portfolios?
If the muse weighs the relative importance of its goal return goal against its loss limit, it may well measure its potential for achievement as a mean of the chances. This average – the Pi rating – helps the muse determine whether the goals are achievable and which investment strategy is best.
The chart below shows Pi scores for every portfolio, with weights applied to the goal return and loss limit probabilities for example the relative importance of every to decision makers. If the investor equally weights the importance of achieving the goal return and the loss limit, corresponding to the vertical line in the course of the chart, the portfolio with higher stock value has the very best Pi rating of 48%, barely higher than the present portfolio’s 47% . This is set by equal weighting of the goal return and loss limit targets: Pi rating of 48% = 50% weighting × 32% probability of success in achieving the return goal + 50% weighting × 63% probability of success in not violating the loss limit.
Average probability of success, varies depending on the relative importance of the goal return and the loss limit, assuming a non-normal final result distribution
Alternatively, the muse could decide to weight its goal return and loss limit in a different way than equally. In fact, decision makers will probably want to evaluate a wide selection of weights and outcomes. There isn’t any right answer. But with the metrics described here, the dialogue goes beyond vague general statements about “a lot,” “a little,” or “some” to more precise statements about probabilities related to goals, particularly risks, which might be relevant to the institution using a typical Language and the agreed preferences of those involved are vital.
A complementary method for assessing whether one portfolio is preferable to a different is to convert differences in potential outcomes into dollars. The board of trustees can ask, “How much money would we need to add to our current portfolio to achieve the higher Pi score of the higher stock value portfolio?”
The chart below illustrates the differences in dollar value (and percentage return) – i.e. Weight on the loss limit.
Economic value differences between portfolios: 80% goal return, 20% risk limit weighting
The chart above shows that the upper equity portfolio is “worth” roughly $2.2 million greater than the present portfolio over the five-year investment horizon, given the endowment’s goal return targets, loss limits, and weights. This represents a further return of 0.44% per yr – a return that’s left on the table with the present portfolio. This will not be a small sum for the muse and a worth that’s difficult to realize through Manager-Alpha.
However, the board of trustees might not be satisfied with the low probability of achieving its return goal or may not feel confident concerning the downside risks. Using these metrics, the muse could revisit its goal return objective and consider changes to its portfolio structure, energetic vs. passive managers, risk management activities, and other investment lifecycle features to balance its desires and material risks.
Unfortunately, these metrics don’t provide absolute, definitive, unassailable answers. Rather, they contextualize investment concepts, particularly the concept of investment risk, so that everybody involved speaks the identical language and understands the potential impact of their decisions.
Diploma
Each fiduciary, no matter role or experience, can clearly communicate key investment objectives and risks. Direct measurements of the chances of achieving baseline goals and thresholds, weighted by agreed-upon preferences and matched with comprehensive dollar comparisons of portfolio strategies, provide a more accessible and disciplined decision-making framework for all stakeholders. Even newcomers to the investment world might be more confident that they understand their decisions and are doing their best to guard and maintain the aim of the investment assets.
1. is published by the Investments & Wealth Institute®. The full original article might be found here: “Clear communication about investment goals and risks”.
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