Downside risk

What Is Downside Risk?

Downside risk refers to the financial risk of an investment losing value. In the realm of portfolio theory and investment analysis, it specifically focuses on the potential for an asset's price to decline. Unlike volatility, which measures both upward and downward price fluctuations, downside risk zeroes in solely on the negative movements, aiming to quantify the possibility and magnitude of losses. This concept is crucial for investors who are primarily concerned with capital preservation and avoiding unfavorable outcomes.

History and Origin

While the broader concept of risk has been central to finance for centuries, the specific focus on downside risk as a distinct measure gained prominence with the evolution of modern portfolio theory. Early risk measures, such as standard deviation, treated both positive and negative deviations from the mean equally. However, many investors perceive upside volatility (large gains) as desirable, while downside volatility (large losses) is seen as undesirable.

This recognition led to the development of alternative risk metrics. One notable example is the Sortino ratio, developed in the early 1980s by Dr. Frank A. Sortino. The Sortino ratio specifically uses "downside deviation" in its calculation, only penalizing returns that fall below a specified target or required rate of return. The first reference to the Sortino ratio appeared in Financial Executive Magazine in August 1980, with initial calculations published in the Journal of Risk Management in September 1981.¹¹

Key Takeaways

• Downside risk quantifies the potential for an investment to lose value.
• It distinguishes between negative and positive price movements, focusing only on the former.
• Measures like the Sortino ratio specifically address downside risk.
• Understanding downside risk is vital for effective risk management and capital preservation strategies.
• Investors consider downside risk when evaluating potential investments and constructing a portfolio.

Formula and Calculation

A common way to quantify downside risk, particularly for use in metrics like the Sortino ratio, is through downside deviation (also known as downside volatility). This measures the standard deviation of only the negative returns, or returns below a specified minimum acceptable return (MAR) or target return.

The formula for downside deviation is:

Where:

• (\sigma_D) = Downside deviation
• (N) = Total number of observations (returns)
• (R_t) = The return for period (t)
• (MAR) = Minimum Acceptable Return (or target return)

This formula calculates the standard deviation of only those returns that fall below the Minimum Acceptable Return, with positive deviations or returns above the MAR being treated as zero.

Interpreting the Downside Risk

Interpreting downside risk involves understanding not just the possibility of losses, but also their potential magnitude and frequency. A higher downside deviation, for instance, indicates a greater likelihood or size of negative returns relative to a chosen benchmark or minimum acceptable return.

For example, two investments might have similar overall volatility, but one might have a significantly higher downside deviation, implying that its volatility is more concentrated in negative movements. Investors often use downside risk metrics in conjunction with return metrics to assess a risk-adjusted return, aiming to achieve desired returns while minimizing exposure to significant losses. The Securities and Exchange Commission (SEC) often provides investor bulletins that highlight the importance of understanding risks, including the potential for loss, before making investment decisions.¹⁰,⁹

Hypothetical Example

Consider two hypothetical investment portfolios, Portfolio A and Portfolio B, over a year, with a Minimum Acceptable Return (MAR) of 0% (i.e., investors want to avoid any losses).

Portfolio A Monthly Returns:
[2%, 3%, 1%, 0%, -0.5%, 4%, -1%, 2.5%, 3%, 1.5%, -0.8%, 2%]

Portfolio B Monthly Returns:
[1%, 0.5%, 2%, 3%, -3%, 5%, -2%, 1%, 4%, 0.5%, -4%, 3%]

To calculate the downside deviation for Portfolio A:
Negative returns relative to MAR (0%): -0.5%, -1%, -0.8%
Squared differences from MAR (only for negative returns):
((-0.005 - 0)^2 = 0.000025)
((-0.01 - 0)^2 = 0.0001)
((-0.008 - 0)^2 = 0.000064)
Sum of squared differences for negative returns = (0.000025 + 0.0001 + 0.000064 = 0.000189)
Average sum of squared differences (dividing by N=12): (0.000189 / 12 = 0.00001575)
Downside Deviation (Portfolio A) = (\sqrt{0.00001575} \approx 0.003968) or 0.3968%

For Portfolio B:
Negative returns relative to MAR (0%): -3%, -2%, -4%
Squared differences from MAR (only for negative returns):
((-0.03 - 0)^2 = 0.0009)
((-0.02 - 0)^2 = 0.0004)
((-0.04 - 0)^2 = 0.0016)
Sum of squared differences for negative returns = (0.0009 + 0.0004 + 0.0016 = 0.0029)
Average sum of squared differences (dividing by N=12): (0.0029 / 12 = 0.0002416)
Downside Deviation (Portfolio B) = (\sqrt{0.0002416} \approx 0.01554) or 1.554%

In this example, Portfolio B has a significantly higher downside deviation (1.554%) compared to Portfolio A (0.3968%), indicating that Portfolio B experienced larger and more frequent negative returns below the 0% MAR, representing greater downside risk.

Practical Applications

Downside risk analysis has several practical applications across various financial domains:

• Portfolio Management: Investors and fund managers use downside risk measures, such as the Sortino ratio, to construct portfolios that align with an investor's risk tolerance, particularly for those with a strong aversion to losses. It helps in selecting investments that offer better potential returns for a given level of acceptable downside exposure.
• Risk Reporting: Financial institutions and investment advisors use downside risk metrics in client reports to provide a more nuanced view of portfolio performance and potential risks, going beyond traditional volatility measures. This enables better communication of investment performance to clients.
• Hedge Funds and Alternative Investments: These investments often exhibit non-normal return distributions, making traditional volatility less effective. Downside risk measures are particularly valuable here for assessing the risk-adjusted performance of strategies that may generate infrequent but significant losses.
• Regulatory Compliance: Regulatory bodies, such as the SEC, emphasize the importance of transparent risk disclosures. Companies are required to disclose material risks to investors in their filings, ensuring that potential downsides are clearly communicated.⁸,⁷ This helps investors make informed decisions, especially during periods of market stress, such as the 2008 financial crisis, which highlighted the broad and severe impact of unmitigated financial risks.,,

Limitations and Criticisms

While focusing on undesirable outcomes, downside risk metrics also have limitations:

• Backward-Looking Nature: Like most historical risk measures, downside risk is calculated based on past performance. It does not guarantee future outcomes. A sustained period of low downside risk in the past does not preclude significant losses in the future, particularly during unforeseen market downturns.⁶
• Choice of Minimum Acceptable Return (MAR): The selection of the MAR can significantly influence the calculated downside deviation. Different MARs will yield different results, and there is no universally agreed-upon standard for setting this threshold. This subjectivity can lead to inconsistencies when comparing investments.
• Ignores Upside Volatility: While its focus on the downside is its strength, it inherently ignores positive volatility, which can be an important characteristic of growth-oriented investments. For investors who welcome large positive returns, this narrow focus might not capture the full picture of an investment's return profile.⁵,⁴
• Does Not Capture All Risks: Downside risk measures typically focus on price movements. They may not fully capture other forms of risk, such as liquidity risk, credit risk, or operational risk, which can also lead to significant losses.³ Academic discussions often highlight that volatility, while widely used, may not be a comprehensive measure of risk, especially when considering behavioral factors or "tail risks."²,¹

Downside Risk vs. Volatility

The primary distinction between downside risk and general volatility (often measured by standard deviation) lies in what they quantify. Volatility measures the total dispersion of returns around an average, meaning large positive swings contribute to volatility just as much as large negative ones. This can be counter-intuitive for investors who welcome large gains. Downside risk, on the other hand, isolates the unfavorable movements, providing a more intuitive measure for investors concerned with capital preservation. While volatility is a fundamental concept in financial modeling and portfolio construction, downside risk offers a more specific lens through which to view potential losses.

FAQs

What is the main purpose of measuring downside risk?

The main purpose of measuring downside risk is to quantify the potential for an investment to lose money, allowing investors to better understand and manage their exposure to unfavorable market movements. It helps in assessing the magnitude and frequency of losses below a certain threshold.

How does downside risk differ from total risk?

Total risk, often represented by volatility (standard deviation), measures the overall dispersion of an investment's returns, including both gains and losses. Downside risk, however, focuses exclusively on the portion of risk associated with negative returns or returns falling below a specified target, making it a more targeted measure for investors concerned with capital impairment.

Can downside risk be completely eliminated?

No, downside risk cannot be completely eliminated in most investments, particularly those with exposure to market fluctuations. However, it can be mitigated through various risk management strategies such as asset allocation, diversification, and hedging.

Why do some investors prefer downside risk measures over volatility?

Some investors prefer downside risk measures because they align more closely with the psychological concept of loss aversion. These investors are typically more concerned about losing money than they are about missing out on potential gains. Therefore, metrics that specifically quantify the risk of losses provide a more relevant assessment for their investment objectives.

Is downside risk only relevant for conservative investors?

While particularly relevant for conservative investors and those focused on capital preservation, downside risk is important for all types of investors. Even growth-oriented investors need to understand the potential for significant drawdowns that could impact their long-term financial goals and require adjustments to their investment strategy.