We had taken the innovative step of customizing our “team of funds” to meet our client’s goal of achieving an alpha target within the context of their asset allocation. This matrix approach to fund selection aligns the client’s market exposure and active selection process with the total return and risk limits they established to meet their monetary goals, using the capital they have available. This is a true “client-centered, goals-based” approach to portfolio construction, within our holistic framework of fiduciary responsibility, sustainable spending policy and investment strategy.

After creating our 24 “fund teams” (4 asset strategies across 6 alpha targets) we summarized our results to demonstrate the value of both customization and alpha diversification. One critical observation was that our fund selection successfully balanced exposure to certain “core funds” (found across all our strategies) with a set of “opportunistic” funds that improved the efficiency of each portfolio. We also observed that these fund changes across the portfolios were “modest but meaningful.”

We begin with a review of the total return results for our globally-diversified portfolios of equity and fixed income that were featured in our previous article. We had noted that the market returns were rather modest, and provided only about 50 bps of additional return for moving from the most conservative to the most aggressive strategies. In this context, active return was a critical aspect of earning higher levels of total return. Our initial observation was both surprising and delightful*: the active portfolios earned higher returns without taking on additional volatility risk. In all these cases, volatility decreased slightly. *

We conclude that ** the active process increased portfolio efficiency**. How do we know this? The answer is definitional: the only difference between these portfolios and the benchmarks is the use of active funds. These results help us to define the

Two related measures of active efficiency are the Sharpe Ratio and the Information Ratio. While the first measures the return premium over cash (relative to total return volatility,) the second measures the active return relative to its own volatility. It is generally true that any volatility measure tends to increase more quickly than its corresponding return measure. In our illustration, total return volatility increases disproportionality to the risk premium over cash. This explains why the Sharpe Ratios decline as strategies move from more conservative to more aggressive. This does not indicate that these higher equity allocations reflect a decrease in efficiency. Rather, it is typical for any efficient frontier of market returns to “flatten out,” resulting from the “law of diminishing returns.” Our results confirm our expectation.

That said, we also see two surprising results…

First, as we move toward higher alpha targets, we observe greater efficiency across both measures of performance, with higher Sharpe Ratios and Information Ratios. Our fund teams were rewarded for taking on a higher level of active risk, and this effect was observed across all strategies. The only variable was the funds we selected for each strategy/alpha target.

Second, we saw a “leveling off” of the increasing dual efficiency at the top two-or-three alpha targets. In these instances, Information Ratio (or “active efficiency”) leveled off or decreased, while total return efficiency continued to improve. That is, our Information Ratios hit a maximum level and backed off a bit, while our Sharpe Ratios continued to increase.

We conclude that *efficiency **generally improved with higher alpha targets across all strategies.*

It has been said that “*A picture is worth a thousand words*” - and this is more likely to be true if we draw the right pictures!

In this analysis, we focus on the factors that drive performance, and our emphasis is on the key risk statistics. As we “peel the onion” in this risk analysis, ** we begin to see the relationships between these risk factors emerge**. Our first comparison is between active return volatility (tracking error) and total return volatility (standard deviation.) Our chart demonstrates how these values relate in the context of the strategies we employ and the alpha targets within each strategy.

Our first observation is that total return volatility increased somewhat linearly as we move across the strategies, indicating a relatively modest degree of market diversification. This creates a challenging investment environment for the client, increasing their reliance on an efficient active effect.

The next observation is the increasingly higher increments of tracking error for each increase in the alpha target. The first three targets (50, 75 and 100 bps) are relatively tightly clustered in terms of active risk. As we move to the top three targets (125, 150 and 175 bps) we see increasingly higher tracking error values. Active risk is increasing at an increasing rate, until the maximum attainable alpha values are reached.

So far, we see a direct relationship between total return volatility and tracking error.

Now we see a bit of mystery emerging: *“Why is total return volatility decreasing as tracking error and active return are both increasing?” *

*Solving this mystery requires finding the hidden relationships between market risk, active risk, and active return.*

Portfolio efficiency is often defined as “the highest return for a given level of risk” or “the lowest risk for a given level of return.” Each is a desirable outcome, and our task is to understand how to accomplish that goal, both for the portfolio’s market return (via asset allocation) and for its active return (via fund selection using our “team of funds” approach.)

*The first question is this: “What are the conditions that produce efficiency?” *

The answer is simple*: Efficiency is the result of every component of the portfolio contributing equally to risk and return.* These “components” of the portfolio can be arranged however best fits the investment decision process. When we examine the efficiency of the asset allocation, we examine the asset segments that make up the strategy. Our active process focuses on the excess return and active risk of our investment selections. In this initial analysis, we examine our portfolio’s market return and its active return as components of a “two-by-two” matrix of a benchmark component and an active component.

*The second question is: “What are the factors used to measure contribution to risk?”*

*The key factor driving contribution to overall portfolio volatility is the correlation to the portfolio’s total return. *This is true for both the *market* contribution to risk and the *active*
contribution to risk. We have noted in earlier articles that this correlation functions as the *percentage of individual risk that remains in the portfolio*, after the effect of diversification.

*Contribution to Portfolio Risk = Weighting * Individual Risk * Correlation to portfolio return. *

Since we are considering all the portfolio’s assets, the weighting for each performance component is 100 percent. In practical terms, we find the correlation between the benchmark return and the total portfolio return, and then apply this to the benchmark’s volatility; the result is the contribution to portfolio volatility from its market exposure.

We calculate the correlation between the portfolio’s active return and its total return, and then apply this to the portfolio’s tracking error to find the contribution to risk from the fund selection process.

We expect a very high correlation between the portfolio and its benchmark. This means that almost all the benchmark’s volatility remains in the portfolio. We also expect that the portfolio’s idiosyncratic excess return will have a lower correlation to the portfolio’s total return. The result should be a smaller fraction of tracking error remaining in the portfolio.

*But what if the correlation of active return and portfolio return is a negative value?*

That delightful result would be an active process that adds to return while subtracting portfolio risk. Is that possible? Happily, this was the case with our fund teams!

The correlation between excess return and total portfolio return (our “alpha diversification factor”) indicates the percentage of tracking error that remains in the portfolio. Our earlier review of tracking error showed a range between 60 bps and 120 basis points. As expected, tracking error increased as the strategies became more growth oriented, and it also increased as the alpha targets increased.

However, we also observed several offsetting risk effects:

- Correlations were generally negative, so that tracking error subtracted volatility;
- Correlations were generally more negative for less-aggressive strategies;
- Correlations became more negative as alpha targets increased;
- Correlations declined by a greater proportion in more aggressive strategies.

This explains why more aggressive strategies and alpha targets subtracted more significantly from the portfolio’s total return volatility. A larger tracking error combined with a more-negative correlation produces a greater reduction in portfolio volatility. *This runs counter to the traditional view that greater active risk produces higher total return risk.*

We have unlocked the mystery behind why our portfolios lowered volatility while increasing total return!

Our higher alpha target teams produced increasingly-negative correlations relative to their portfolios’ total returns. Contrary to the traditional view of tracking error (where more tracking error is always bad) our higher level of active risk produced greater reductions in portfolio volatility risk - even as the active returns contributed more to total return. Our solutions became more efficient as they increased their exposure to higher market returns and active returns.

** We bring together tracking error and alpha correlation to show the contribution of alpha to portfolio volatility**. These increasing reductions in volatility are accompanied by increasing additions to portfolio return. This is the condition for maximum possible efficiency. For example, the most opportunistic fund teams contribute about 175 bps of return while subtracting over 30 bps of volatility. This explains why total portfolio volatility within each strategy declined as its total return increased, as we moved up in alpha target by 125 basis points.

Our illustrations are presented in two ways: across alpha targets and across strategies.

This “macro attribution” shows the interactions of the portfolios’ market and active factors, and how each contributes to portfolio risk. The trend lines for each reflect an inverse relationship between the market and active effects, where the active reduction in risk offsets the increasing risk contribution from market exposure. As noted earlier, the market factor is typically inefficient, since its high correlation with the portfolio means that it contributes essentially all its individual volatility. However, the active factor’s negative correlation with the portfolio turns its tracking error into a “*risk subtractor*” that offsets the increasing volatility contribution from market exposure.

Our first chart demonstrates the general trend of these effects, and the second chart is a detailed risk attribution across the strategies and the alpha targets.

We measure efficiency as “*percent contribution to return minus percent contribution to risk*.” In this context, an asset (or a factor) within a portfolio is perfectly efficient when it contributes an equal proportion to both return and risk. Inefficiency occurs when contributions to risk are greater than the corresponding contributions to return. “Super-efficiency” occurs when return contributions are greater than risk contributions. Our two-factor “macro attribution” analysis illustrates the typical dynamic of inefficient market exposure and offsetting “super-efficiency” from the active factor. This is characteristic of a sound active process, which increases the efficiency of an investment portfolio.

Our team approach to fund selection produced extraordinary results, because our active process subtracted portfolio volatility while adding to return. This allowed us to achieve higher total returns with lower levels of total volatility risk. Our final charts illustrate the dynamics of these factors across all strategies and alpha targets.

Our market factor contributed between 100% to 105% of the portfolio’s volatility risk, with a corresponding contribution to return that declined from 95% to 80 percent.

The active factor’s complementary super-efficiency offset the market factor, contributing as much as 20% of the portfolio’s total return while lowering its risk by as much as 5 percent. The trends of these two factors were completely offsetting, and the efficiencies were equally offsetting (by definition) with an average of about +/- 15% (in a range of between 7% and 24% depending on strategy and alpha target.) The overall efficiencies across the strategies were equivalent.

Our approach of creating fund teams around strategies and alpha targets provides a truly client-centered and goals-based approach to portfolio construction. We customized 24 solutions to cover a variety of strategies and alpha targets, and we accomplished this with a reasonable number of funds and a modest amount of change between the fund teams. This balanced the need for both customization and practical, operational efficiency.

This holistic approach to portfolio construction began with a robust platform of funds. We then selected investments in the context of the total portfolio, using our risk attribution methodology to identify efficiencies that would have gone unnoticed, using the traditional approach of evaluating funds in isolation, relative to their benchmarks. Our results demonstrated the efficiencies around both active risk and total portfolio risk, resulting in higher expected returns and downside returns.

The initial “macro attribution” of both risk and return focuses on the broadest component factors in any investment portfolio: market exposure and the active process. Surprisingly, this level of analysis is typically ignored in the industry. We feel that it is essential to understand the relationship between these critical components of performance. When completed, it creates a “feedback loop” from performance evaluation to the prior decision around asset allocation and investment selection.

Our next paper provides a “micro attribution” that focuses on the drivers of active efficiency. This aligns with the more typical view of performance analysis, examining how the investment segments contributed to the active results. However, our “risk aware” approach incorporates the missing piece in most attribution analysis: contribution to active risk. We will show the contribution to both risk and return for each investment segment, revealing their relationships over time, with an eye toward how they contribute to the efficiencies we observed in this macro analysis. For the overall portfolio manager (“OCIO”) and the client, these insights into “what’s working and what isn’t” are crucial parts of the decision process. This brings the performance evaluation process into true partnership with the portfolio management process.

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*Written in Partnership with Stephen Campisi.*