Uncovering Conviction

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INVESTMENT INSIGHTS SERIES

Uncovering Conviction Tracking Down Tracking Error

Summary An increasing number of investors are interested in high conviction, high tracking error managers. Some view high tracking error as a proxy for high conviction investing, and high conviction investing as the only way to generate alpha in equities. Currently, many investors are considering a “barbell approach” – with high tracking error managers on one end and index portfolios on the other end. This approach is based on a prevailing view that active managers who are not “active enough,” as measured by tracking error, have little hope of outperforming their respective benchmarks. We wholeheartedly agree that active managers, particularly fundamental managers, should demonstrate high conviction in their investment ideas. However, there are key flaws to relying on tracking error as a measure of conviction. Namely, not all tracking error is created equal. There is a difference between intended tracking error that is specifically taken with the goal of generating outperformance, and tracking error that arises from unintended and uncontrolled risk exposures. By focusing on total tracking error as a measure of portfolio manager conviction, investors unduly penalize active managers who prudently control risks unrelated to alpha generation. In this paper, we provide evidence that tracking error driven by security selection is related to the next 12 months’ outperformance, while other components of active risk represent historically uncompensated sources of risk on average. Therefore, instead of simply seeking managers with high tracking error, investors must consider the sources of active risk – mainly, tracking error associated with security selection. Likewise, portfolio managers should seek to maximize tracking error from value-added activity from security selection while minimizing other sources of active risk. This can potentially lead to more consistent outperformance versus the benchmark – offering benefits to investors that examine sources of risk to uncover true investment conviction.

READ INSIDE X

The components of tracking error unrelated to investment conviction

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The significant impact these components, and sources of risk, can have on total tracking error

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The primary driver of alpha for equity managers on average has been from tracking error related to security selection

Suny Park, CFA, CPA Chief Institutional Client Strategist

Tracking Error: Components of Active Risk Tracking error is a measure of risk, but is also considered by some to be an effective proxy for manager conviction. The general belief is that higher conviction managers express their views through higher tracking error, which is more likely to lead to future outperformance. What tracking error actually measures is the volatility of manager returns relative to a benchmark. This measure is useful to evaluate how much risk a manager takes relative to the strategic allocation. However, tracking error versus the policy benchmark can be a poor measure of a portfolio manager’s conviction level. To understand why, consider how tracking error can be generated. Important sources of tracking error relative to the policy benchmark include: X

Betas (systematic risk exposures): X

Market exposure – a manager with a benchmark beta that deviates from 1.0 will generate tracking error.

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Style exposure – a manager with tilts toward specific styles, such as small cap or value, relative to the benchmark will generate tracking error.

X

Beta timing – the variability in portfolio beta over time will generate tracking error.

X

Security selection – a manager who selects securities with idiosyncratic risks will generate tracking error.

All of these sources of tracking error are relevant in measuring risk versus a strategic benchmark. However, few would argue each source of risk is a strong proxy for manager conviction. Consider, hypothetically, two managers that both generate 4% tracking error from security selection. The first manager also generates an additional 1.5% tracking error due to lower beta relative

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to the benchmark. This manager has increased tracking error by 38%, but does he really have more conviction? Especially for fundamental managers, most would expect “conviction” to be driven by security selection. Tracking error can be significantly impacted by a manager’s beta. As a result, investors may overestimate manager conviction by using this simple measure. Exhibit 1, as shown on page 3, highlights the impact that a manager’s market exposure (beta to the benchmark) can have on tracking error. For simplicity, assume there are only two sources of risk: manager deviation from a benchmark beta of 1.0 and the “selection risk” of security selection. However, the ideas discussed can be generalized if we move from one systematic beta to multiple systematic betas. Exhibit 1 shows the impact of deviating from benchmark beta for different levels of active risk. A hypothetical manager with selection risk of 1% might be considered a “benchmark hugger.” However, if the manager’s portfolio has a beta that is plus/minus 0.2 or 0.3 relative to the benchmark, tracking error versus the policy benchmark will vary from 3% to 5%. This is the difference between a “benchmark hugger” and a truly active manager. The impact is smaller as active risk increases, but can still be large enough to change one’s perceptions about whether a manager is truly a “high conviction manager” – even though the increased tracking error is driven mostly by changes in beta, not security selection decisions. Exhibit 1 highlights that risk exposures unrelated to security selection can potentially be significant drivers of portfolio tracking error. Even Exhibit 1 does not capture the whole picture, though. It assumes a portfolio manager’s beta is constant throughout time. Most reports using manager returns effectively show the average beta over a certain period, such as 3, 5 or 10 years.

EXHIBIT 1: INCREASE IN TRACKING ERROR (TE) VERSUS BENCHMARK DUE TO MANAGER BETA

EXHIBIT 2: BETA TIMING EXAMPLE OF A HYPOTHETICAL MANAGER

4.0%

1.4

Beta Average 1.05

1.0 0.8

2.0% Beta

0.6

1.0% 0.4 0.2

TE 4%

TE 5%

Based on annualized market standard deviation of 16%, and assumption of constant manager beta and zero covariance between manager alpha and market returns. See appendix for details.

Hypothetical beta calculated as auto-regressive process of order 1 with coefficient of 0.97 and standard deviation of 0.06. Benchmark: MSCI World Index. Source: Bloomberg as of 6/30/14.

In practice, however, manager beta is not constant; instead it is time-varying. This variability in portfolio beta can also impact portfolio tracking error. Consider the hypothetical manager in Exhibit 2. In this example, the manager’s beta varies from month to month. The manager generates no tracking error from security selection and the average beta of 1.05 is very close to 1.0 (market beta). At any point in time though, the manager may have a beta between 0.7 and 1.2. This may happen as existing stocks in the portfolio become more or less risky or as stocks are added and removed from the portfolio. Despite no tracking error from security selection, variability in beta –

beta timing – generates tracking error of 2.1%. In other words, by assuming betas are constant over time, one can underestimate a significant contributor to tracking error.

6/14

TE 3%

6/13

TE 2%

6/12

TE 1%

0.0 6/11

0.30

6/10

0.25

6/09

0.20

6/08

0.15

1.00 – Manager Beta

6/07

0.10

6/06

0.05

6/05

0.0% 0.00

6/04

Increase in Tracking Error

1.2 3.0%

These examples suggest that we may need multiple ways to measure tracking error. While tracking error relative to the policy benchmark is a useful measure of risk, to estimate active risk from security selection decisions, one needs to control other sources of active risk. As shown in Exhibit 3, by making a few simplifying assumptions, we can show what drives the variance in manager returns.1

EXHIBIT 3: DRIVERS OF MANAGER RETURN VARIANCE Variance from

Manager Return Variance

Average Beta

Beta Timing

Security Selection

OR, 100% = R2 + Timing Share + Selection Share 1 See appendix for calculation details. We use the same terminology here as Ekholm, Anders G. “Components of Portfolio Variance: Systematic, Selection and Timing.” Selection and Timing (August 8, 2014).

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This breakdown of manager variance can be estimated using historical manager returns. Exhibit 4 summarizes each type of tracking error, the underlying sources of risk and the associated return metrics. The key takeaway – we can estimate sources of risk from historical returns and can use these risk estimates to assess manager conviction. Further, we can also investigate which sources of risk are related to future outperformance (alpha) – what investors ultimately care about. In the next section we evaluate the evidence for the relationship between components of tracking error (beta, beta timing and security selection) and alpha.

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Active Share: This holdings-based metric measures how different a manager is from the benchmark. The authors show that historically, a manager’s active share is positively related with outperformance. Interestingly, the highest tracking error managers actually underperformed managers with more moderate tracking error.2

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R2: This metric is related to beta-adjusted tracking error.3 The authors find that managers with high historical alpha and tracking error were more likely to outperform, on average.4

High Conviction, Security Selection and Outperformance

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Selection Share: This metric estimates tracking error driven by security selection. The author finds that tracking error driven by security selection is positively related to alpha, while tracking error related to beta timing is negatively related to alpha.5

There is academic evidence that some measures of manager “conviction” are related to alpha. This includes some of the returns-based metrics in the previous section, as well as holdings-based metrics. This would seem to validate the logic behind the barbell approach. However, a closer look at these results indicates they are more nuanced than just “high tracking error is better.” Some metrics that have been examined with mutual fund data, along with a brief summary of the findings in their respective articles, include:

In summation, the results using mutual fund data are somewhat ambiguous. Using R2 as a proxy for tracking error may lead to a conclusion that higher tracking error leads to higher alpha. However, other results suggest that only certain types of tracking error are compensated. To test the relevance of these results for institutions, we investigate historical returns of eVestment Alliance manager data.

EXHIBIT 4: ESTIMATING RISK FROM SECURITY SELECTION Benchmark Tracking Error

Beta-Adjusted Tracking Error

Selection Tracking Error

Source of Risk

Static beta exposures, beta timing, selection risk

Beta timing, selection risk

Selection risk

Return Metric(s)

Standard deviation of benchmark excess returns

R2; Standard deviation of regression residuals

Selection share; standard deviation of regression residuals adjusted for timing

Tracking Error: 3.3%

Tracking Error: 3.0%

Average Beta

3.0%

Beta Timing

2.0%

Selection

1.0%

Tracking Error: 4.0%

0.0% -0.1%

Dec

Oct

Nov

Sep

Jul

Aug

Jun

Apr

May

Feb

Mar

Jan

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

-0.3%

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

-0.2%

Source: Hypothetical estimates, see appendix for details on assumptions.

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Cremers, KJ Martijn, and Antti Petajisto. “How active is your fund manager? A new measure that predicts performance.” Review of Financial Studies 22.9 (2009): 3329-3365. R2 estimated percentage of variance explained by risk. Thus 1-R2 equals percentage of variance explained by tracking error. Amihud, Yakov, and Ruslan Goyenko. “Mutual fund’s R2 as predictor of performance.” Review of Financial Studies (2013): hhs182. 5 Ekholm, Anders G. “Components of Portfolio Variance: Systematic, Selection and Timing.” Selection and Timing (August 8, 2014). See also: Ekholm, Anders G. “Portfolio returns and manager activity: How to decompose tracking error into security selection and market timing.” Journal of Empirical Finance 19.3 (2012): 349-358. 3 4

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EXHIBIT 5: PREDICTING HISTORICAL ALPHA WITH TRACKING ERROR DECOMPOSITION 0.05

Coefficient Estimates

0.041 0.04

Coefficient

Estimate

Standard Error

Pr( > |t |)

0.03

Trailing Alpha

-0.0008

0.0092

0.928

0.0411

0.0058

0.000*

0.01

Selection Share

0.00

Timing Share

-0.0042

0.0107

0.689

0.02

-0.001 -0.01

-0.004 Trailing Alpha

Selection Share

Timing Share

Adjusted R 2 : 8.129% *Significance: <0.01%

Source: eVestment Alliance, Ken French’s website, Janus estimates. We use the Fama French three factor model (Mkt, SMB, HML) to estimate alpha, then estimate selection share and timing share as in Ekholm (2014). The regression equation shown in Exhibit 5 is: , where I() is an indicator function; controlling for year is consistent with research that investment manager alpha may be contingent on market environment; 6 NTM = next 12 months and LTY = last three years. The dataset contains all monthly log returns of U.S. based eVestment Alliance managers with USD denominated returns for the years 1998-2014. There were 28,878 observations across 4,338 managers.

The goal is to test which components of tracking error, if any, have historically been related to future alpha. Based on our simplified model, which components of tracking error drive outperformance on average? Recall that timing share is defined as the percentage of manager variance related to beta timing, and selection share is the percentage of manager variance related to security selection. Using eVestment Alliance returns, we estimate manager alpha, timing share and selection share every three years. We then test to determine how these metrics are related to alpha over the next 12 months. Our results indicate that historically, selection share, not timing share, has been positively related to future equity manager alpha. As shown in Exhibit 5, historically, only certain types of tracking error were rewarded in terms of future outperformance. In particular, after controlling for other variables, tracking error related to selection share is positively related to future outperformance over the next 12 months, and tracking error related to timing has no significant relationship with outperformance. Each 1% increase in selection share increased expected alpha by an estimated 4 basis points. Overall, there is evidence that tracking error has a relationship with outperformance. However, in contrast to the barbell approach which naively advocates for high tracking error managers, it appears that not all tracking error is necessarily rewarded.

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First, tracking error relative to the benchmark can be heavily influenced by the variability in portfolio beta. Investors should take care to adjust for this impact, especially when comparing across managers with very different betas. Second, there is evidence that, on average, tracking error from security selection, not beta timing, is related to future outperformance. This is consistent with the idea that it is very difficult to successfully time risk factors. Given that beta timing is likely an uncompensated form of risk, our research suggests prudent investors should typically seek to minimize this source of tracking error. In turn, they should seek to maximize the percentage of tracking error driven from activities expected to add value, such as security selection. As a final note, market environment also matters. We do not explore this in depth in this brief, but tracking error in a portfolio can and likely will fluctuate over time due to changes in cross-sectional stock correlations and volatilities. Targeting arbitrary levels of tracking error regardless of market environment can be problematic. For example, the measured level of risk in equity portfolios in 2006 was low by historical standards. However, few would argue increasing portfolio risk leading up to a market crash in 2008 would have been a prudent course of action.

Ferson, Wayne E., and Rudi W. Schadt. “Measuring fund strategy and performance in changing economic conditions.” The Journal of Finance 51.2 (1996): 425-461.

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In Summary We believe that the naive reliance on the level of portfolio tracking error as a proxy for high conviction investing is ill-advised. When it comes to generating outperformance, how tracking error is generated is more important than how much tracking error is generated. Thus, managers should strive to maximize the contribution of tracking error from value-added activity. For fundamental managers especially, this means maximizing tracking error from security selection. By focusing too much on the level of tracking error, investors risk penalizing those who exercise prudent risk management to avoid uncompensated active risk. We believe high conviction investing does not equate to high tracking error investing. Conviction, especially for fundamental managers, is driven by security selection decisions. Therefore, active managers should seek to maximize tracking error from value-added activity such as security selection, while minimizing other sources of risk.

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Appendix Exhibit 1: Assume manager returns are of the form below, where m stands for benchmark returns andƠis random:

For simplicity, Exhibit 1 assumes no correlation between alpha returns and market returns. Then tracking error (T) is:

Exhibit 3: We use a single ơ, but the result easily generalizes to multiple ơs. This is a simplified version of the derivation in Ekholm (2014). Assume that manager returns are of the form described previously, except nowơcan change over time. Then estimate the regression equation:

ů as the averageƠ and ơ over time. Then: We can think of the estimates Ơ ů andơ

The variance

is equal to:

We can estimate

with ordinary least squares as:

By making the simplifying assumption that changes in Ơ andơ are not correlated over time and taking expectations:

Where is the variance of idiosyncratic return and is the variance in risk factor exposures. Hence, regressing the squared residuals from the original regression equation on squared risk factor returns can provide an estimate of the sources of active risk. We then define timing share as the percentage of total manager variance explained by variance in risk factor exposures (beta timing). We define the percentage of remaining unexplained manager return variance as selection share. With R2 from the original regression equation, we get: 100%=R2+Timing Share+Selection Share

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This publication is for investors and investment consultants interested in the institutional products and services available through Janus Capital Management LLC and its affiliates. Various account minimums or other eligibility qualifications apply depending on the investment strategy or vehicle. Past performance is no guarantee of future results. Investing involves risk, including the possible loss of principal and fluctuation of value. This paper is for information purposes only and should not be used or construed as an offer to sell, a solicitation of an offer to buy, or a recommendation for any security. There is no guarantee that the information supplied is accurate, complete, or timely, nor does it make any warranties with regards to the results obtained from its use. It is not intended to indicate or imply in any manner that current or past results are indicative of future profitability or expectations. As with all investments, there are inherent risks that individuals would need to address. The views expressed are those of the author as of November 2014. They do not necessarily reflect the views of other Janus portfolio managers or other persons in Janus’ organization. These views are subject to change at any time based on market and other conditions, and Janus disclaims any responsibility to update such views. No forecasts can be guaranteed. These views may not be relied upon as investment advice or as an indication of trading intent on behalf of any Janus fund. In preparing this document, Janus has relied upon and assumed, without independent verification, the accuracy and completeness of all information available from public sources. In preparing this document, Janus has relied upon and assumed, without independent verification, the accuracy and completeness of all information available from public sources. Janus Capital Management LLC serves as investment adviser. FOR MORE INFORMATION CONTACT JANUS CAPITAL INSTITUTIONAL 151 Detroit Street, Denver, CO 80206 I www.janusinstitutional.com C-0415-89336 12-30-15 8

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