Risk–Return Trade-Off

The risk–return trade-off is the principle that investments offering higher potential returns generally come with higher risk: a greater chance of losing money, or of seeing the value swing widely before the gains arrive. Investors who want more safety must usually accept lower expected returns. The relationship is about expectations over time, not guarantees; a risky asset can lose money for years. Economists distinguish this measurable risk from uncertainty, where the possible outcomes or their chances cannot be known, so no reliable premium can be calculated.

The idea underlies how investors choose between cash, bonds, shares and other assets, and how financial advisers match a portfolio to a client's risk tolerance and time horizon. Fund documents often describe it as "relative risk and potential return". It was formalised in modern portfolio theory in the 1950s and in the capital asset pricing model (CAPM) in the 1960s.

Think of three ways to travel to a far-off city. A slow train is almost certain to arrive, though late. A fast car is quicker on average but can get stuck in traffic. A small plane is fastest of all but may be grounded by weather and leave you stranded for days. No option is the fastest and the most certain at the same time.

Investing works the same way. Money in a bank account or government bills grows slowly but steadily. Shares have historically grown faster over long periods, but with bad years along the way. Riskier ventures can grow fastest or fail completely. People accept the bumpier routes only because, on average, they expect to arrive further ahead. If anyone offers the speed of the plane with the certainty of the train, something is usually wrong.

Return is usually expressed as the yearly percentage gain, including income such as dividends or interest. Risk is most often measured by volatility, the standard deviation of returns, though investors also look at the worst historical loss, the chance of default, liquidity risk and the risk of losing purchasing power to inflation. Ratios such as the Sharpe ratio combine the two into a single measure of return per unit of risk.

Across asset classes the pattern has been broadly consistent over long periods in major markets. Short-term Treasury bills have had the lowest returns and the least volatility; government and investment-grade bonds have had higher returns with more variation; shares have had higher long-run returns again, with much larger swings; and small-cap stocks, emerging markets and venture capital have shown higher variation still.

Harry Markowitz's 1952 article "Portfolio Selection" in the Journal of Finance showed that investors should judge each holding by its effect on the risk and return of the whole portfolio. Because assets do not move in perfect step, combining them reduces risk without giving up expected return; this is the logic of diversification. Plotting every possible mix produces a curve called the efficient frontier: the set of portfolios with the highest expected return for each level of risk. A rational investor chooses a point on that curve according to how much risk they can bear, which is the task of asset allocation.

Markowitz shared the 1990 Nobel memorial prize in economics with Merton Miller and William Sharpe.

The CAPM, published by Sharpe in 1964 and independently developed by John Lintner, Jan Mossin and Jack Treynor, turns the trade-off into a formula. It says that only market-wide risk, measured by beta, earns a reward, because company-specific risk can be diversified away:

• $E(R_i)$ is the expected return on investment $i$.
• $R_f$ is the risk-free rate.
• $\beta_i$ is the investment's beta, its sensitivity to the market.
• $E(R_m) - R_f$ is the market risk premium, the extra return expected for holding the market rather than risk-free assets.

With a risk-free rate of 4%, a market risk premium of 5% and a beta of 1.2, the expected return is 4% + 1.2 × 5% = 10%. A defensive share with a beta of 0.6 would be expected to earn 4% + 0.6 × 5% = 7%. Returns above the model's prediction are called alpha.

• Fund risk scales. EU key information documents rank products on a summary risk indicator from 1 (lowest) to 7 (highest), many US fund companies place funds on a conservative-to-aggressive scale, and regulators in many countries require advisers to assess suitability before recommending riskier products.
• Time horizon. A long horizon gives an investor time to recover from falls, which is why retirement savers far from retirement often hold more shares and shift towards bonds as the date approaches.
• Credit markets. Lenders charge higher interest rates to weaker borrowers; the extra yield on junk bonds is compensation for credit risk.
• Fraud warning. Promises of high returns with little or no risk are a classic sign of fraud. High-yield investment programme fraud and Ponzi schemes rely on investors ignoring the trade-off.

The trade-off describes long-run averages, not what any investor will receive. Higher risk does not guarantee higher return: during a bear market or a crisis such as the 2008 financial crisis, risky assets can lose heavily. Research has also found exceptions. Low-volatility and low-beta shares have, over many periods, delivered higher risk-adjusted returns than the CAPM predicts, a finding documented in studies such as Andrea Frazzini and Lasse Pedersen's 2014 paper "Betting Against Beta". Some risks, such as holding a single company's shares or an undiversified portfolio, carry no expected reward at all, because they could have been diversified away.

• The Sveriges Riksbank Prize in Economic Sciences 1990 (Nobel Prize)