Risk Adjusted Value-Added & Portfolio Performance

A simple definition of an actively managed portfolio is one with asset allocations different from the benchmark portfolio. The active bets are simply the differences between these two allocations over time. Good bets result in positive active returns and vice-versa. The presence of negative active returns results in the portfolio’s active risk, typically measured by the standard deviation (volatility) of the active returns. The question is whether the average active return is worth the active risk, the effort, and the fee cost of achieving it. The question applies to self-managed or externally managed portfolios.

This evaluation depends upon the owner’s risk preferences and how the returns from the active portfolio, equal to the benchmark plus the active returns, are valued in comparison to those of the passive benchmark.

This is not an easy evaluation nor one that is typically done by manager/brokers or commercial performance measurement firms. RoboPPA™ uses several theoretically acceptable evaluation methods and provides a numerical opinion on the manager’s active value-added.

Value-Added without Considering Risk

The following chart shows the active annualized monthly returns from a managed equity portfolio and suggests that in practice, both positive (28) and negative (32) active returns are to be expected over the 60-month period. In this real example, the positives seem to be larger than the negatives, potentially indicating but not proving outperformance by the portfolio, relative to its benchmark.

A more recent low-active, self-managed portfolio is shown in the following chart of portfolio values per $100 of starting value, plotted by RoboPPA™. At the end of the analysis period, the portfolio is the top black line and its blue benchmark is immediately below it. The remaining orange line is the equity ETF index and the green line is rollovers of a one-month Treasury bill.

The portfolio’s starting value on Dec 31, 2018 was $883,000. There was one $4,900 contribution on Jan 15, 2019 and one $38,000 withdrawal on Jan. 31, 2020. The end of analysis period value at the Dec. 31, 2020 end was $1,194,964 and the IRR was 18.12%/year. The corresponding benchmark values, including transfers, were $883,000 on Dec 31, 2018 and $1,137,569 on Dec. 31, 2020 and the benchmark IRR was 15.5%/year.

Therefore, the actual $value-added was $57,395 or $6.50 per $100 of initial investment, over the two-year period, and the active IRR increase was 2.62%/year. Similar to the previous chart, the active return was positive 50% of the months with an average of 0.16%/month or an annualized 1.94%/year.

The analysis period was clearly a strong market for both the benchmark and the portfolio. The manager has performed well after removal of the effects of transfers, fees, and the benchmark but, there was no accounting for the risk of the active portfolio or consideration of the length of the analysis period.

Value-Added Considering Risk

A look at the portfolio’s risks shows that the portfolio has smaller volatility (4.1%/month vs. 5.1%/month), less 5%-value at risk (-5.5%/month vs. -6.1%/month), and smaller expected shortfall (-3.5%/month vs. -5.1%/month), than the benchmark. (See the RoboPPA™ glossary for the definitions.) Thus, there is no disagreement that the portfolio was less risky than the benchmark. Therefore, it outperformed the benchmark, after removal of the effects of transfers, fees, and generally accounting for the risk of the active portfolio. Missing is an explicit estimate of the risk-adjusted, value-added by the manager. In general, this is useful in determining whether the manager should be terminated or the maximum fees that could be paid to a retained manager.

In a situation where the portfolio has larger return but is riskier than the benchmark, it isn’t clear which is preferred. A theoretical and commonly used solution compares the reward to volatility (Sharpe) ratios of the portfolio to the benchmark and adjusts for a short analysis period. In our example, the adjusted Sharpe ratios reported by RoboPPA™, are 0.32 and 0.23, but they are not statistically significantly different. This doesn’t confirm our preceding conclusion of a superior risk-return portfolio because the number of analysis months was too small, for statistical significance. It also does not provide a specific risk-adjusted value-added.

Risk Adjusted Value-Added

There are at least two theoretically accepted methods of determining the risk-adjusted, value-added. The first is based on what is called certainty equivalents and the second on derivative valuation methodology. RoboPPA™ calculates and provides its single estimate of the manager value-added based on one or both methods. In our example, the value-added estimate is 0.3% of the portfolio’s value in each month or 3.71%/year. This is larger than the actual added value of 0.26%/month or 3.17%/year and is due to the portfolio’s low risk and high return.

This is a large added value-added by a manager for a real-world portfolio. Should we expect this magnitude of manager performance in the future? The answer is no because the estimate is based on only 24 months of analysis. It is a question of statistical significance at some % confidence level. The Sharpe ratios are different so we have some confidence that the value-added is positive, but the confidence level is not high based on 24 months of analysis.

RoboPPA™ uses tests of statistical significance in its analysis to provide confidence in the overall conclusions of superior performance and specific added value. This is a self-managed portfolio and without more monthly evidence, we cannot confidently claim superior performance; however, the manager should be pleased with the performance.

A significant advantage of RoboPPA™ is that the required inputs for its performance analysis can be saved in its template and updated monthly. This can be done entirely on the user’s computer and never stored on the software’s servers. The software maintains the benchmark databases thereby reducing the user’s work. Finally, the software allows analyses over any selected period contained in the data template’s horizon, providing it exceeds eight months.

Caveats

The analysis and the results in this document are not to be interpreted as representative of real markets and asset classes and are not warranted to be correct or complete. The example is based upon our opinion and interpretation of the data and results, which may be incomplete or incorrect. RoboPPA™ or the data suppliers are not responsible for any damages or losses arising from use of this blog. Details on the performance calculations are available on www.RoboPPA.com.