Risks and rewards

What Is Risk-Adjusted Return?

Risk-adjusted return measures an investment's or portfolio's profit or potential profit in relation to the amount of risk taken to achieve it. Rather than looking solely at the total return generated, this metric provides a more comprehensive view of investment performance by accounting for the inherent risk assumed. It is a critical concept within portfolio theory, helping investors understand how efficiently an investment generates returns relative to the associated volatility and potential for loss. Investors use risk-adjusted return to compare different investment opportunities on a level playing field, favoring those that deliver higher returns for a given level of risk, or lower risk for a given level of return.

History and Origin

The concept of evaluating investment performance beyond mere gains emerged with the advancement of modern financial theory. A pivotal moment came with the work of economists like Harry Markowitz, who introduced Modern Portfolio Theory (MPT) in the 1950s, emphasizing the importance of diversification to optimize portfolios based on risk and return. Building on this foundation, William F. Sharpe introduced the Sharpe Ratio in 1966, a widely adopted measure of risk-adjusted return. Sharpe's contributions to financial economics, including the Capital Asset Pricing Model, earned him the Nobel Memorial Prize in Economic Sciences in 1990.³⁵, ³⁶, ³⁷ His development of the Sharpe Ratio provided a practical tool for investors to quantify the excess return per unit of total risk. His biography on the Stanford University website notes his extensive work in developing models to aid investment decisions.³⁴

Key Takeaways

• Risk-adjusted return assesses investment gains relative to the level of risk taken.
• It offers a more complete picture of performance than absolute return.
• Metrics like the Sharpe Ratio, Treynor Ratio, and Sortino Ratio are commonly used to calculate risk-adjusted return.
• A higher risk-adjusted return indicates more efficient risk management and better performance.
• Understanding risk-adjusted return helps in making informed portfolio allocation decisions.

Formula and Calculation

The most common formula for calculating risk-adjusted return is the Sharpe Ratio. This ratio measures the excess return (return above the risk-free rate) per unit of total risk, as measured by standard deviation.³³

The formula for the Sharpe Ratio is:

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

Where:

• (R_p) = Portfolio's average rate of return
• (R_f) = Risk-free rate of return (e.g., U.S. Treasury bond yield)
• (\sigma_p) = Standard deviation of the portfolio's return (a measure of market volatility or total risk)

Other popular risk-adjusted return measures include the Treynor Ratio, which uses Beta as its risk measure (focusing on systematic risk), and the Sortino Ratio, which considers only downside deviation (negative volatility) as risk.

Interpreting the Risk-Adjusted Return

Interpreting risk-adjusted return involves understanding that a higher value generally indicates a better investment. For example, a higher Sharpe Ratio means the investment is generating more return for each unit of risk it assumes.³² When comparing two investments with similar absolute returns, the one with a higher risk-adjusted return is often preferred because it achieved its results with less volatility or risk.³⁰, ³¹

It helps investors evaluate if they are being adequately compensated for the risks undertaken. A portfolio with a 10% return might seem excellent, but if it was achieved by taking on extreme risk, its risk-adjusted return might be poor compared to a 7% return from a much less volatile portfolio. The ultimate goal for many investors is to optimize their portfolio to achieve the highest possible return for their given risk tolerance.

Hypothetical Example

Consider two hypothetical investment funds, Fund A and Fund B, over a five-year period. The risk-free rate during this period is 2%.

• Fund A:
  • Average Annual Return ((R_p)): 10%
  • Standard Deviation ((\sigma_p)): 8%
• Fund B:
  • Average Annual Return ((R_p)): 12%
  • Standard Deviation ((\sigma_p)): 15%

Let's calculate the Sharpe Ratio for each:

Fund A Sharpe Ratio:
$\frac{0.10 - 0.02}{0.08} = \frac{0.08}{0.08} = 1.00$

Fund B Sharpe Ratio:
$\frac{0.12 - 0.02}{0.15} = \frac{0.10}{0.15} \approx 0.67$

Even though Fund B had a higher average return (12% vs. 10%), Fund A's Sharpe Ratio of 1.00 indicates it provided a better risk-adjusted return than Fund B's 0.67. This means Fund A delivered more excess return per unit of risk, suggesting it was a more efficient investment.

Practical Applications

Risk-adjusted return is widely used in various facets of finance:

• Portfolio Management: Fund managers and financial advisors use these metrics to construct and manage client portfolios, ensuring the level of risk aligns with investor objectives and that returns are efficiently generated.²⁸, ²⁹
• Fund Selection: Investors commonly use risk-adjusted return measures to compare mutual funds, exchange-traded funds (ETFs), and hedge funds. It provides a standardized way to evaluate how well a fund manager performed relative to the risk they assumed.
• Regulatory Compliance: Regulatory bodies, such as the Securities and Exchange Commission (SEC), provide guidance on how investment performance, including risk-adjusted figures, should be presented in advertising and client communications to ensure transparency and prevent misleading claims.²⁴, ²⁵, ²⁶, ²⁷
• Capital Allocation: Institutions and individual investors use risk-adjusted return to make decisions about allocating capital across different asset classes or investment strategies, aiming to maximize overall portfolio efficiency.²³
• Performance Attribution: Analysts use risk-adjusted measures to dissect why a portfolio performed as it did, attributing parts of the return to specific risks taken versus pure skill or alpha generation.

Limitations and Criticisms

While risk-adjusted return metrics offer valuable insights, they are not without limitations. A primary criticism, particularly of the Sharpe Ratio, is its reliance on standard deviation as the sole measure of risk. Standard deviation treats both upside (positive) and downside (negative) volatility equally.²¹, ²² However, most investors are primarily concerned with downside risk—the potential for losses—rather than large positive swings. Oth¹⁹, ²⁰er measures like the Sortino Ratio attempt to address this by focusing only on downside volatility.

Another critique is the assumption that asset returns follow a normal distribution. In ¹⁷, ¹⁸reality, financial market returns often exhibit skewness (asymmetrical distribution) and kurtosis (fat tails, indicating more extreme events than a normal distribution), which standard deviation may not fully capture. Thi¹⁵, ¹⁶s can lead to an underestimation or overestimation of true risk. Fur¹⁴thermore, these metrics can be sensitive to the chosen measurement period, with short-term fluctuations potentially distorting the long-term risk-adjusted picture. The¹³ Bogleheads Wiki highlights that managers might manipulate data or lengthen time horizons to artificially boost their risk-adjusted returns.

Th¹²e Federal Reserve Bank of San Francisco has noted the complexities of risk management, particularly in times of financial crisis, underscoring that models, including those for risk-adjusted returns, are always subject to real-world complexities.

Risk-Adjusted Return vs. Absolute Return

The distinction between risk-adjusted return and absolute return is fundamental in investment analysis. Absolute return simply refers to the total gain or loss an investment or portfolio achieved over a specific period, expressed as a percentage or monetary value. It does not account for the level of risk taken to achieve that gain or loss. For example, if an investment grows from $100 to $110, its absolute return is 10%, regardless of how volatile the path was to reach that $110.

In¹¹ contrast, risk-adjusted return evaluates that same 10% gain in the context of the associated risk. An investment with a 10% absolute return achieved with minimal volatility would have a higher risk-adjusted return than another investment also yielding 10% but with extreme price swings. Whi¹⁰le absolute return provides a straightforward measure of growth, risk-adjusted return offers a deeper insight into the efficiency and sustainability of that growth, making it a more robust metric for long-term investment performance evaluation.

##⁹ FAQs

What does a "good" risk-adjusted return look like?

A "good" risk-adjusted return is typically indicated by a higher numerical value for metrics like the Sharpe Ratio. For instance, a Sharpe Ratio above 1.0 is generally considered good, indicating the investment generated more than its fair share of return per unit of risk. A ratio above 2.0 is often considered very good, and above 3.0, excellent. How⁸ever, what constitutes "good" can also be relative to the specific asset class, market conditions, and the benchmark being used for comparison.

Can risk-adjusted return be negative?

Yes, risk-adjusted return can be negative. If an investment's return is less than the risk-free rate, or if the investment experiences significant losses, the numerator in metrics like the Sharpe Ratio (Portfolio Return - Risk-Free Rate) would be negative, resulting in a negative risk-adjusted return. This indicates that the investment did not even cover the return available from a risk-free asset, let alone compensate for the risk taken.

Why is risk-adjusted return important for investors?

Risk-adjusted return is crucial because it helps investors make more informed decisions by evaluating investments not just on potential gains, but also on the efficiency with which those gains are achieved given the level of risk. It allows for a more meaningful comparison between diverse investment options and encourages a focus on sustainable, long-term portfolio growth rather than chasing high-return, high-risk strategies blindly. It aligns with the principle of diversification, aiming to maximize returns for a given level of acceptable risk.

##⁶, ⁷# How does risk-adjusted return relate to diversification?
Risk-adjusted return is closely linked to diversification within Modern Portfolio Theory. Diversification aims to reduce a portfolio's overall risk (specifically unsystematic risk) by combining assets that do not move in perfect synchrony. By ⁵reducing the total volatility of a portfolio without necessarily sacrificing expected return, diversification can improve the portfolio's risk-adjusted return. A w², ³, ⁴ell-diversified portfolio seeks to achieve a higher return for the level of risk taken, thereby improving its risk-adjusted performance.¹