Risk adjusted returns

What Are Risk Adjusted Returns?

Risk-adjusted returns represent the returns an investment generates in relation to the amount of risk taken. This concept falls under the broader financial category of portfolio theory, aiming to provide a more holistic view of investment performance than simply looking at raw gains or losses. While a high return might seem attractive, it means little if the investor took on an excessive amount of risk to achieve it. Conversely, a modest return achieved with very little risk can be highly desirable. Therefore, risk-adjusted returns help investors compare different investment opportunities on a level playing field by accounting for the inherent volatility and potential for loss.

History and Origin

The concept of evaluating investment performance beyond raw returns began to gain prominence with the advent of Modern Portfolio Theory in the mid-20th century. A pivotal development in quantifying risk-adjusted returns was the introduction of the Sharpe Ratio by Nobel laureate William F. Sharpe. Initially termed the "reward-to-variability ratio," Sharpe first proposed this measure in 1966. He later revisited and further formalized its application in his influential 1994 paper, "The Sharpe Ratio," published in The Journal of Portfolio Management.³ Sharpe's work provided a concrete framework for investors to understand whether the excess returns they were receiving adequately compensated them for the additional risk assumed. This innovation profoundly influenced modern portfolio management and the way financial professionals assess investment efficiency.

Key Takeaways

Risk-adjusted returns evaluate an investment's performance relative to the risk undertaken.
They provide a more comprehensive measure than raw returns, factoring in volatility and potential for loss.
Common metrics include the Sharpe Ratio and Sortino Ratio.
Higher risk-adjusted returns generally indicate a more efficient use of capital given the risk profile.
These measures are crucial for comparing diverse investments and aligning portfolios with an investor's risk tolerance.

Formula and Calculation

The most widely recognized formula for calculating risk-adjusted returns is the Sharpe Ratio. It quantifies the amount of return generated per unit of standard deviation (a common measure of total risk or volatility).

The formula for the Sharpe Ratio is:

\text{Sharpe Ratio} = \frac{R_p - R_f}{\sigma_p}

Where:

(R_p) = Portfolio Returns
(R_f) = Risk-free rate (e.g., the return on a U.S. Treasury bond)
(\sigma_p) = Standard deviation of the portfolio's excess return

Other formulas for risk-adjusted returns exist, such as the Sortino Ratio, which specifically considers downside deviation rather than total standard deviation, and Alpha, which measures a portfolio's performance relative to a benchmark after accounting for market risk (often quantified using Beta and the Capital Asset Pricing Model).

Interpreting Risk Adjusted Returns

Interpreting risk-adjusted returns involves understanding that a higher ratio generally signifies better performance. For instance, a higher Sharpe Ratio suggests that an investment is providing more excess return for each unit of volatility taken on. When comparing two investment options, the one with the higher risk-adjusted return is typically preferred, assuming all other factors are equal and the underlying risk measure is appropriate for the investment's characteristics.

It is important to evaluate risk-adjusted returns within the context of an investor's specific investment objectives and risk tolerance. For example, a conservative investor might prioritize an investment with a slightly lower return but significantly lower risk, resulting in a higher risk-adjusted return. Conversely, an aggressive investor might accept more volatility in pursuit of higher absolute returns, but still expects those returns to be justified by the level of risk.

Hypothetical Example

Consider two hypothetical portfolios, Portfolio A and Portfolio B, over a one-year period. The current risk-free rate is 2%.

Portfolio A:
- Annual Return ((R_p)): 10%
- Standard Deviation ((\sigma_p)): 8%
Portfolio B:
- Annual Return ((R_p)): 12%
- Standard Deviation ((\sigma_p)): 12%

Let's calculate the Sharpe Ratio for each:

Portfolio A Sharpe Ratio:

\text{Sharpe Ratio}_A = \frac{0.10 - 0.02}{0.08} = \frac{0.08}{0.08} = 1.00

Portfolio B Sharpe Ratio:

\text{Sharpe Ratio}_B = \frac{0.12 - 0.02}{0.12} = \frac{0.10}{0.12} \approx 0.83

In this example, Portfolio A, despite having a lower raw returns (10% vs. 12%), demonstrates a higher risk-adjusted return (Sharpe Ratio of 1.00 vs. 0.83). This suggests that Portfolio A generated more return for each unit of risk taken, making it a more efficient investment from a risk-adjusted perspective. This highlights how risk-adjusted returns provide a crucial metric for evaluating a portfolio's efficiency, especially when comparing investments with different risk profiles.

Practical Applications

Risk-adjusted returns are fundamental to many areas of finance and portfolio management. They are extensively used by:

Fund Managers: To evaluate the effectiveness of their investment performance strategies and to communicate their results to clients. Managers often strive to maximize these ratios to show superior skill in generating returns while controlling for volatility.
Individual Investors: To make informed decisions when selecting mutual funds, exchange-traded funds (ETFs), or other investment products. By comparing the Sharpe Ratio or Sortino Ratio of various funds, investors can align their choices with their personal risk tolerance and desired risk-return trade-off.
Financial Advisors: To construct diversified portfolios that meet clients' specific financial goals and risk appetites. Understanding risk-adjusted returns helps advisors recommend appropriate asset allocations.
Regulatory Bodies: While not explicitly mandating specific risk-adjusted return metrics, regulatory bodies like the U.S. Securities and Exchange Commission (SEC) emphasize comprehensive risk disclosure for investment products. The Investment Company Act of 1940, for instance, requires investment companies to disclose their investment objectives, policies, and material risks to investors, ensuring transparency in how risk and returns are presented.²
Academic Research: For analyzing market efficiencies, validating financial models, and developing new performance measures.

Limitations and Criticisms

While highly valuable, risk-adjusted returns, particularly measures like the Sharpe Ratio, have several limitations and criticisms:

Assumption of Normal Distribution: Many risk-adjusted return calculations assume that investment returns follow a normal distribution. In reality, financial market returns often exhibit skewness (asymmetrical returns) and kurtosis (fatter tails, indicating more frequent extreme events than a normal distribution would predict). For investments with non-normal distributions, such as certain hedge fund strategies or those involving derivatives, standard deviation may not fully capture the true risk of extreme losses, potentially leading to an inaccurate or misleading risk-adjusted return.¹
Focus on Total Volatility: The Sharpe Ratio treats both upside and downside volatility equally. However, most investors are more concerned with downside risk (the risk of losses) than upside volatility (returns exceeding expectations). Measures like the Sortino Ratio attempt to address this by focusing solely on downside deviation.
Reliance on Historical Data: Risk-adjusted returns are calculated using historical returns and volatility. Past performance, however, is not indicative of future results. Market conditions can change, and an investment's historical risk-adjusted performance may not persist.
Manipulation Potential: Fund managers might engage in practices that artificially inflate their risk-adjusted returns, such as shortening the measurement period during favorable market conditions or by taking on specific risks (like "tail risk") that aren't fully captured by standard deviation.
Comparison Challenges: Comparing risk-adjusted returns across vastly different asset classes or investment strategies can be challenging due to differing risk profiles and underlying return distributions. Effective comparisons typically require similar investment universes and benchmarks.
Definition of Risk-free Rate: The choice of the risk-free rate can influence the calculated ratio. While U.S. Treasury bills are commonly used, their yields fluctuate, which can affect the comparison of risk-adjusted returns over different periods.

Despite these limitations, risk-adjusted returns remain essential tools for investment performance evaluation, especially when used in conjunction with other qualitative and quantitative analyses.

Risk Adjusted Returns vs. Absolute Return

The distinction between risk-adjusted returns and absolute return is crucial for investors.

Absolute Return refers to the total gain or loss of an investment over a specific period, expressed as a percentage. It is a straightforward measure of raw returns, showing how much money an investment made or lost without any consideration for the volatility or risk taken to achieve that return. For example, if a stock rises from $100 to $110, its absolute return is 10%.

Risk-Adjusted Returns, as discussed, go a step further by evaluating the returns relative to the level of risk incurred. This means an investment with a lower absolute return might actually have a superior risk-adjusted return if it achieved that gain with significantly less volatility or downside exposure. The core point of confusion often arises when an investment boasts high absolute returns but achieves them through excessively high risk, which may not be sustainable or suitable for a given investor's risk tolerance. Risk-adjusted measures provide a more nuanced and insightful view of true investment efficiency.

FAQs

What is a "good" risk-adjusted return?

What constitutes a "good" risk-adjusted return depends on the specific metric used and the context of the investment. For the Sharpe Ratio, a ratio greater than 1.0 is generally considered good, indicating that the investment is generating more excess return than its standard deviation. A ratio of 2.0 or higher is often seen as very good, and above 3.0 as excellent. However, these are general guidelines, and the comparison should always be made against similar investments or benchmarks within the same market conditions.

How do I calculate risk adjusted returns for my own portfolio?

To calculate risk-adjusted returns for your portfolio, you would typically use historical data for your portfolio's returns and its standard deviation over a specific period (e.g., monthly or annually). You also need to identify an appropriate risk-free rate for that period. Then, you can apply formulas like the Sharpe Ratio (as shown in the "Formula and Calculation" section) to derive a quantitative measure. Many financial tools and platforms can also calculate these metrics for you automatically.

Why are risk adjusted returns important?

Risk-adjusted returns are important because they provide a more complete picture of an investment's quality than raw returns alone. They help investors and portfolio management professionals understand whether the returns generated are commensurate with the level of risk taken. This is crucial for making informed investment decisions, comparing diverse assets, and building portfolios that align with an individual's capacity and willingness to take on risk. They highlight the efficiency of an investment strategy, rather than just its gross profitability.