Risk and Return

What Is the Relationship Between Risk and Return?

The relationship between risk and return is a foundational principle in financial theory. There is a positive correlation between these two variables, the general rule being “the greater the level of risk, the higher the potential return (or loss respectively). To achieve an optimal risk and return outcome, investors use different approaches to analyze risk and assess risk-adjusted returns through metrics such as the Sharpe ratio and Sortino ratio.

Risk vs. Return

While the definition for return is simple and easy to calculate, several types of risk are typically considered. Investment returns are expressed as a percentage and represent the gain or loss (factoring in both capital appreciation and income) made on an asset over a specific period.

A portfolio’s total return is calculated as follows:

The formula for calculating the return of a portfolio is a weighted average of the individual returns of its individual holdings:

Where:

Rp – the portfolio return

R1, R2,…, Rn – the individual returns of the portfolio’s holdings

w1, w2,…, wn – the individual weightings of each holding in the portfolio

On the other hand, investment risk is defined as the degree of uncertainty and/or potential financial loss inherent in an investment decision. Many measures quantify risk, some examples of which include:

Standard Deviation – this is the most popular risk measure used by investors to quantify the volatility of a security, a specific market, or a portfolio. A higher standard deviation indicates greater volatility and higher risk.

• Beta – this is a measure of how sensitive an investment is to market movements. A beta higher than 1 suggests a higher sensitivity to market movements, while a beta of less than 1 indicates the opposite.
• Maximum Drawdown – it shows the peak-to-trough decline in an asset’s price. Larger drawdowns are an indicator of higher risk
• Tracking Error – it measures the deviation of a portfolio’s returns from that of its benchmark

Risk and Return Analysis

To assess whether they have been rewarded for the risk taken, investors use a range of risk-adjusted measures. However, while most of these ratios can be quite useful and aid in making decisions on portfolio changes, they should be very carefully considered against the investment objectives of that portfolio. For example, comparing a portfolio that seeks higher returns (and therefore, allows higher volatility) with a conservative, low-risk portfolio could be quite misleading. Therefore, it is recommended that investors run their risk-return analysis against a portfolio with similar investment features. For instance, a large cap equity portfolio that has a growth bias should be compared with similar portfolios (or market indices such as the MSCI World Growth Index for global or the S&P 500 Growth for US-focused portfolios) to establish whether its risk and return profile is more competitive.

The below chart gives a good indication about the level of risk and potential returns that different asset classes would deliver.

Source: Standard Life Investments

Risk and Return Examples

Let’s compare two strategies that have similar investment features and establish which has yielded better risk-adjusted returns over a 5-year period. In this case, we will compare active equity managers and use the Information ratio, which helps in assessing the risk-adjusted returns of a portfolio using excess return over a benchmark. It is tracking the amount of return generated by the manager per incremental unit of risk created by deviation from the benchmark. Therefore, for consistency it is important that the two strategies we look at use the same benchmark index.

*For benchmark data we use an ETF that closely tracks the index as a proxy – iShares MSCI ACWI UCITS ETF

Source: Fidelity Investments and Morningstar

Calculating Risk-Return

To calculate and compare the information ratios for each fund individually, we need to divide the excess return over the benchmark (i.e. the active return of the portfolio) by the standard deviation of these excess returns (i.e. the active risk). The formula is:

Where:

Rp = Investment portfolio’s rate of return

RB = Benchmark rate of return

σ (p-B) = Standard deviation of these excess returns or Tracking Error

How to Calculate Portfolio Risk and Return in Excel

Solution

To calculate the Information ratios for both funds we need to:

1. Calculate the excess return that the fund has achieved over 5 years, i.e. the return of the fund less the return of the benchmark (unlike the Sharpe ratio, here the benchmark doesn’t need to be the risk-free rate).
2. Divide the excess return by the fund’s tracking error (i.e. the standard deviation of the difference between the portfolio and the benchmark).

As higher Information ratio indicates better risk-adjusted returns, the Capital Group New Perspective is just marginally better than the T. Rowe Price Global Growth Focus Equity fund, despite having achieved more than double its returns over 5 years. This is because the Capital Group fund has lower tracking error.

What Type of Risk Exists in a Fully-Diversified Portfolio?

Although the main goal of diversification is to reduce the overall level of risk in a portfolio, some risks cannot be fully mitigated. While currency or stock-specific risk can be managed and potential implications for the portfolio minimized, risk that affects the whole market cannot be offset. Systematic risk typically brings higher cross asset correlation and lower market liquidity, so therefore even a very well-diversified portfolio is unlikely to deliver positive absolute return during periods of severe market stress. Examples of the events that can trigger this include:

• Natural Disasters
• Geopolitical Unrest (wars)
• Global Pandemics
• Global Recession

Risk and Return Models

There are various models that investors use to assess and find the best risk-return opportunities. One of the fundamental concepts in finance theory is the Capital Asset Pricing Model (CAPM) ,which helps investors determine the expected return on an investment given its level risk.

Another popular model is Arbitrage Pricing Theory (APT), which investors use to determine the expected return of an asset by considering multiple sources of risk (factors) and their sensitivity, allowing for a more flexible approach to modelling asset returns, unlike the CAPM, which uses a single-factor assumption.

The Fama-French Three Factor Model is another model that was developed by Eugene Fama and Kenneth French, both professors at the University of Chicago. It aims to determine asset returns through three factors:

• Market Risk (or Market Risk Premium) – i.e. the return on the market less the risk-free rate.
• The excess return of companies with small market capitalization relative to large caps.
• The excess return of high book-to-market value companies against low book-to-market value companies.

The predictive abilities of this approach are quite high compared to the traditional CAPM – the model can explain over 90% of the returns of a diversified portfolio.

Conclusion

Understanding the trade-off between risk and return is crucial for effective portfolio management. While higher returns are positively correlated with higher risk, investors should be using an appropriate level of risk that is consistent with their investment philosophy and objectives. To get the right mix of assets in the portfolio, investors should also run regular risk assessments by using a range of risk metrics such as Standard Deviation, along with risk-adjusted metrics such as the Sharpe ratio or the Information ratio. These metrics need to be compared against a peer group average or a specific market index. For example, an approach that targets undervalued opportunities in the large cap universe in the US might be looked against the S&P 500 Value Index.

Models such as the Capital Asset Pricing Model (CAPM), the Arbitrage Pricing Theory (APT) and the Fama-French Three Factor Model offer frameworks to assess and manage risk. Explore these models in the Modern Portfolio Theory playlist on Felix, as well as 25+ other playlists on the asset management topic. Take our portfolio management courses and learn all the topics to kick off your career.

Additional Resources

Types of Portfolio Risks

Types of Risks in Investing