Active Risk: Overview, Calculations, Examples (2024)

What Is Active Risk?

Active risk is a type of risk that a fund or managed portfolio createsas it attempts to beat the returns of thebenchmarkagainst which it is compared. Risk characteristics of a fund versus its benchmark provide insight on a fund’s active risk.

Key Takeaways

  • Active risk arises from actively managed portfolios, such as those of mutual funds or hedge funds, as it seeks to beat its benchmark.
  • Specifically, active risk is the difference between the managed portfolio's return less the benchmark return over some time period.
  • All portfolios have risk, but systematic and residual risk are out of the hands of a portfolio manager, while active risk directly arises from active management itself.

Understanding Active Risk

Active risk is the risk a manager takes on in their efforts to outperform a benchmark and achieve higher returns for investors. Actively managed funds will have risk characteristics that vary from their benchmark. Generally, passively-managed funds seek to have limited or no active risk in comparison to the benchmark they seek to replicate.

Active risk can be observed through a comparison of multiple risk characteristics. Three of the best risk metrics for active risk comparisons include beta, standard deviation or volatility, and Sharpe Ratio. Beta represents a fund’s risk relative to its benchmark. A fund beta greater than one indicates higher risk while a fund beta below one indicates lower risk.

Standard deviation or volatility expresses the variation of the underlying securities comprehensively. A fund volatility measure that is higher than the benchmark shows higher risk while a fund volatility below the benchmark shows lower risk.

The Sharpe Ratio provides a measure for understanding the excess return as a function of the risk. A higher Sharpe Ratio means a fund is investing more efficiently by earning a higher return per unit of risk.

Measuring Active Risk

There are two generally accepted methodologies for calculating active risk. Depending on which method is used, active risk can be positive or negative. The first method for calculating active risk is to subtract the benchmark's return from the investment's return. For example, if a mutual fund returned 8% over the course of a year while its relevantbenchmark indexreturned 5%, the active risk would be:

Active risk = 8% - 5% = 3%

This shows that 3% of additional return was gained from either active security selection, market timing, or a combination of both. In this example, the active risk has a positive effect. However, had the investment returned less than 5%, the active risk would be negative, indicating that security selections and/or market-timing decisions that deviated from the benchmark were poor decisions.

The second way to calculate active risk, and the one more often used, is to take the standard deviation of the difference of investment and benchmark returns over time. The formula is:

Active risk = square root of (summation of ((return (portfolio) - return (benchmark))² / (N - 1))

For example, assume the following annual returns for a mutual fund and its benchmark index:

Year one: fund = 8%, index = 5%
Year two: fund = 7%, index = 6%
Year three: fund = 3%, index = 4%
Year four: fund = 2%, index = 5%

The differences equal:

Year one: 8% - 5% = 3%
Year two: 7% - 6% = 1%
Year three: 3% - 4% = -1%
Year four: 2% - 5% = -3%

The square root of the sum of the differences squared, divided by (N - 1) equals the active risk (where N = the number of periods):

Active risk = Sqrt( ((3%²) + (1%²) + (-1%²) + (-3%²)) / (N -1) ) = Sqrt( 0.2% / 3 ) = 2.58%

Example Using Active Risk Analysis

The Oppenheimer Global Opportunities Fund is a good historical example of a fund that outperformed its benchmark with active risk, and it is useful for illustrating the concept.

The Oppenheimer Global Opportunities Fund is an actively managed fund that seeks to invest in both U.S. and foreign stocks. It uses the MSCI All Country World Index as its benchmark. For the year 2017, it recorded a one-year return of 48.64% versus a return of 21.64% for the MSCI All Country World Index.

Oppenheimer Global Opportunities Fund (data for year-end 2017)
Name3 Year Beta3 Year Standard Deviation3 Year Sharpe Ratio
Oppenheimer Global Opportunities Fund1.1217.191.29
MSCI ACWI1.0010.590.78

The Fund's beta and standard deviation show the active risk added in comparison to the benchmark. The Sharpe Ratio shows that the Fund is generating higher excess return per unit of risk than the benchmark.

Active Risk vs. Residual Risk

Residual risk is company-specific risks, such as strikes, outcomes of legal proceedings, or natural disasters. This risk is known as diversifiable risk, since it can be eliminated by sufficiently diversifying a portfolio. There isn't a formula for calculatingresidual risk; instead, it must be extrapolated by subtracting the systematic risk from the total risk.

Active risk arises through portfolio management decisions that deviate a portfolio or investment away from its passive benchmark. Active risk comes directly from human or software decisions. Active risk is created by taking anactive investment strategyinstead of a completely passive one. Residual risk is inherent to every single company and is not associated with broader market movements.

Active risk and residual risk are fundamentally two different types of risks that can be managed or eliminated, though in different ways. To eliminate active risk, follow a purely passive investment strategy. To eliminate residual risk, invest in a sufficiently large number of different companies inside and outside of the company's industry.

Active Risk: Overview, Calculations, Examples (2024)


How do you calculate the active risk? ›

Active risk is calculated by subtracting the benchmark return from the portfolio return and then calculating the standard deviation of the difference. The formula is: Active Risk = Standard Deviation (Portfolio Return - Benchmark Return).

What is the formula for optimal active risk? ›

The formula is STD (RA) = IR/SRB * STD (RB) = 0,15/0,33 * 18% = 8,11% optimal active risk. The weight on the active portfolio (Indigo) would be 8.11%/8.0% = 1.014 and the weight on the benchmark portfolio would be 1 – 1.014 = –0.014.

What are the metrics for active risk? ›

Three of the best risk metrics for active risk comparisons include beta, standard deviation or volatility, and Sharpe Ratio. Beta represents a fund's risk relative to its benchmark. A fund beta greater than one indicates higher risk while a fund beta below one indicates lower risk.

What is the active risk in CFA? ›

Active risk, also known as tracking error, represents the standard deviation of active returns. Portfolios with substantial fluctuations in active returns will exhibit high active risk.

What is an example of risk exposure calculation? ›

It is calculated by multiplying the probability of a risk occurring by the magnitude of its consequences. For example, if there is a 20% chance that a key feature will be delayed by two weeks, and that will cost you $10,000 in lost revenue, then the risk exposure is 0.2 x 10,000 = $2,000.

How to calculate risk in Excel? ›

Calculating Risk Premium in Excel

If not, enter the expected rate into any empty cell. Next, enter the risk-free rate in a separate empty cell. For example, you can enter the risk-free rate in cell B2 of the spreadsheet and the expected return in cell B3. In cell C3, you might add the following formula: =(B3-B2).

What is the formula for managed risk? ›

In conclusion, the Risk = Likelihood x Impact formula is a powerful tool for MSPs to manage their risks effectively. By identifying potential risks, assessing their likelihood and impact, and taking proactive measures to mitigate them, MSPs can protect their business, their clients, and their reputation.

What is active risk management? ›

Active risk management includes the assignment of mitigation responsibilities to appropriate project participants and the oversight of follow-through regarding every risk factor.

What are the 5 risk measure? ›

Risk measures are also major components in modern portfolio theory (MPT), a standard financial methodology for assessing investment performance. The five principal risk measures include alpha, beta, R-squared, standard deviation, and the Sharpe ratio.

What is the formula for active risk squared? ›

Active risk squared can be decomposed as the sum of active factor risk and active specific risk. The information ratio (IR) is mean active return divided by active risk (tracking error). The IR measures the increment in mean active return per unit of active risk.

Is tracking error same as active risk? ›

Active risk, also known traditionally as tracking error or tracking risk, is a risk that a portfolio manager creates in an attempt to outperform benchmark returns against which it is compared.

What is the active risk in CFA Level 3? ›

Active risk = tracking error. It's the difference in the standard deviation of returns on the portfolio vs. that of the benchmark. Active share = the number of active decisions made by the manager to overweight/underweight securities.

What is the optimal amount of risk? ›

Optimum level of risk retention is a risk financing term referring to the level of retention at which the organization achieves a comfortable balance between relative cost and cost stability.

How do you determine optimal risk portfolio? ›

The optimal risky portfolio is found at the point where the CAL is tangent to the efficient frontier. This asset weight combination gives the best risk-to-reward ratio, as it has the highest slope for CAL.

What is the formula for Roy's safety first ratio? ›

The value given by Roy's safety-first criterion indicates the number of standard deviations below the mean. The formula for Roy's safety-first criterion is [E(RP) – RL] / σ

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