Sterling Ratio

Overview

Sterling Ratio is a risk-adjusted performance metric that evaluates investment returns in relation to downside risk. Developed by Deane Sterling Jones in the 1980s, this ratio was initially designed for evaluating commodity trading advisors (CTAs) and hedge funds but has since been adopted more broadly across various investment strategies.

The Sterling Ratio modifies the well-known Calmar Ratio by using the average annual maximum drawdown minus an arbitrary 10% buffer in its denominator, rather than simply using the maximum drawdown. This modification aims to account for the fact that drawdowns are an inevitable part of investing and to prevent exceptional but rare drawdown events from disproportionately affecting the ratio.

By incorporating this adjustment, the Sterling Ratio provides investors with a nuanced view of risk-adjusted performance that may be more representative of typical risk levels encountered in an investment strategy over time, rather than being overly influenced by a single extreme event.

Intuitive Explanation

Imagine you're comparing two mountain climbers on their ability to ascend various peaks safely and efficiently. The height they reach represents returns, while the drops they encounter along the way represent drawdowns.

The Calmar Ratio would look at each climber's total height gained divided by their single worst fall. But a climber might have one unusually bad fall due to a rare weather event, while otherwise maintaining excellent stability.

The Sterling Ratio takes a different approach: it looks at the average of their significant falls over several climbing seasons and subtracts a "normal fall allowance" of 10%. This provides a more balanced view of each climber's risk-adjusted performance by not allowing a single extreme event to dominate the assessment.

Detailed Mathematical Explanation

The Sterling Ratio is formally defined as:

Drawdown Calculation

To calculate the average annual maximum drawdown:

1. For each calendar year in the evaluation period, identify the maximum peak-to-trough decline (maximum drawdown):

   $$\text{Annual Maximum Drawdown}_i = \max_{t,s \in \text{Year}_i, t > s} \left( \frac{V_s - V_t}{V_s} \right)$$

   where $V_t$ is the portfolio value at time t.

2. Calculate the average of these annual maximum drawdowns:

   $$\text{AAD} = \frac{1}{N} \sum_{i=1}^{N} \text{Annual Maximum Drawdown}_i$$

   where N is the number of years in the evaluation period.

The 10% Adjustment

The subtraction of 10% in the denominator serves several purposes:

• Recognition of normal market fluctuations: It acknowledges that some level of drawdown is expected in any investment strategy.

• Preventing division by zero or negative values: In cases where the average annual drawdown is less than 10%, the ratio would use a positive value in the denominator.

• Risk normalization: It establishes a baseline threshold for what constitutes "significant" risk.

Relationship to Other Metrics

The Sterling Ratio can be related to other risk metrics as follows:

• Calmar Ratio: $\text{Calmar Ratio} = \frac{R}{\text{MDD}}$, where MDD is the maximum drawdown over the entire period. The Sterling Ratio adjusts this by using average annual drawdowns minus 10%.

• Sterling-Calmar Ratio: A variant where $\text{Sterling-Calmar} = \frac{R}{\text{AAD}}$ without the 10% adjustment.

• Burke Ratio: A related metric that uses the square root of the sum of squared drawdowns in its denominator.

Implementation in Portfolio Analysis

In our portfolio optimization service, we calculate the Sterling Ratio using the following approach:

1. Annual Return Calculation: We compute the compounded annual growth rate (CAGR) of the portfolio over the evaluation period.

2. Drawdown Identification: For each calendar year, we identify all drawdowns and determine the maximum drawdown for that year.

3. Average Calculation: We calculate the arithmetic mean of these annual maximum drawdowns.

4. Adjustment Application: We subtract 10% from the average annual maximum drawdown.

5. Ratio Computation: We divide the annualized return by the adjusted average drawdown figure.

This implementation allows investors to:

• Compare multiple strategies: The Sterling Ratio provides a standardized metric for comparing different investment approaches.

• Evaluate managers: It helps assess whether investment managers are delivering returns commensurate with the risks they are taking.

• Set performance expectations: The ratio assists in establishing realistic performance targets that account for typical drawdown patterns.

Worked Example

Let's calculate the Sterling Ratio for a hypothetical investment fund over a 5-year period:

Step 1: Annual Returns

Suppose the fund has the following annual returns:

• Year 1: +15%
• Year 2: +8%
• Year 3: -3%
• Year 4: +20%
• Year 5: +12%

The average annual return is: (15% + 8% - 3% + 20% + 12%) ÷ 5 = 10.4%

Step 2: Annual Maximum Drawdowns

The maximum drawdown observed in each year:

• Year 1: 7%
• Year 2: 12%
• Year 3: 18%
• Year 4: 5%
• Year 5: 9%

The average annual maximum drawdown is: (7% + 12% + 18% + 5% + 9%) ÷ 5 = 10.2%

Step 3: Apply the Sterling Ratio Formula

Sterling Ratio = Average Annual Return ÷ (Average Annual Maximum Drawdown - 10%)

Sterling Ratio = 10.4% ÷ (10.2% - 10%) = 10.4% ÷ 0.2% = 52

Step 4: Interpretation

A Sterling Ratio of 52 is quite high, indicating that the fund generates substantial returns relative to its risk-adjusted drawdowns. This high value results partly from the fact that the average annual maximum drawdown (10.2%) is only slightly above the 10% buffer.

For comparison, let's also calculate the Calmar Ratio using the largest overall drawdown in the entire period, which is 18%:

Calmar Ratio = 10.4% ÷ 18% = 0.58

The significant difference between the Sterling Ratio (52) and the Calmar Ratio (0.58) illustrates how the Sterling Ratio's adjustments can dramatically affect the assessment of risk-adjusted performance, especially when a single bad year (Year 3 in this example) contains a drawdown much larger than other years.

Practical Applications

The Sterling Ratio serves several important functions in investment analysis and portfolio management:

Manager Selection

When evaluating investment managers, particularly in alternative investments like hedge funds or managed futures, the Sterling Ratio helps identify those who deliver consistent returns while managing drawdown risk effectively. It's especially valuable for strategies that experience regular but moderate drawdowns rather than rare but severe ones.

Risk-Adjusted Performance Comparison

The Sterling Ratio enables more nuanced comparison between different investment strategies or asset classes by accounting for their typical drawdown patterns. This is particularly useful when comparing strategies with different risk profiles or market exposures.

Trend-Following Strategy Evaluation

Trend-following strategies often experience numerous small drawdowns but can perform well over time. The Sterling Ratio is well-suited for evaluating such strategies because it doesn't overly penalize the frequent small drawdowns that are characteristic of these approaches.

Due Diligence Process

Institutional investors and fund allocators incorporate the Sterling Ratio into their due diligence processes to ensure that investment strategies are delivering returns commensurate with the risks taken. The ratio's treatment of drawdowns aligns well with how many institutional investors conceptualize risk.

Advantages and Limitations

References

• Jones, D. S. (1981). "The Sterling Ratios." The Handbook of Stock Index Futures and Options.

• Bacon, C. R. (2013). "Practical Risk-Adjusted Performance Measurement." Wiley Finance.

• Lhabitant, F. S. (2004). "Hedge Funds: Quantitative Insights." Wiley Finance.

• Young, T. W. (1991). "Calmar Ratio: A Smoother Tool." Futures, 20(1).

• Schuhmacher, F., & Eling, M. (2011). "Sufficient conditions for expected utility to imply drawdown-based performance rankings." Journal of Banking & Finance, 35(9), 2311-2318.

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