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Understanding Investor Behaviour, Market Risk Premium, and Financial Product Design
Loss Aversion, Risk Aversion, and Discontinuous Market Movements
Amos Tversky’s remark, “It is not so much that people hate uncertainty but rather they hate losing” (1975), underlines a key insight from behavioural economics: loss aversion. This refers to the tendency of individuals to prefer avoiding losses more strongly than acquiring equivalent gains. It contrasts with risk aversion, which is the preference for certainty over uncertainty in outcomes with the same expected value.
In standard expected utility theory, a risk-averse agent maximises the expected utility of wealth, where utility is a concave function of wealth. This framework assumes symmetric preferences over gains and losses. In contrast, loss aversion, as formalised by Kahneman and Tversky (1979) in Prospect Theory, suggests that losses loom larger than gains, typically by a factor of around 2:1. The value function is kinked at the reference point and steeper in losses than in gains.
Portfolio behaviour of loss-averse agents differs markedly from that of risk-averse agents. Specifically, loss aversion leads to disposition effects, where investors are reluctant to sell losing investments, hoping for a rebound, and quick to realise gains. It also leads to narrow framing and myopic loss aversion, where investors evaluate outcomes frequently and avoid risky assets even when the long-term return is favourable (Benartzi and Thaler, 1995).
Such behaviour can contribute to discontinuous stock market movements.
For instance:
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Sudden sell-offs: If prices drop below a certain threshold (the "reference point"), many investors may react simultaneously to avoid further perceived losses, triggering sharp declines.
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Momentum effects: Loss aversion can exacerbate trends, as rising prices lead to profit-taking and falling prices cause panic selling.
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Nonlinear demand curves: As demonstrated by Barberis et al. (2001), markets composed of loss-averse investors may show non-continuous demand for risky assets, resulting in jumps or crashes in prices rather than smooth adjustments.
In sum, loss aversion leads to market instability, particularly during periods of stress, where fear of loss outweighs rational evaluation of expected returns.
Market Risk Premium, Volatility, and the Mean-Variance Framework
The market risk premium (MRP), the excess return investors demand for holding risky assets over the risk-free rate , is central to modern finance. The Capital Asset Pricing Model (CAPM) asserts that expected return equals the risk-free rate plus beta times the MRP. Within the mean-variance framework (Markowitz, 1952), higher variance (volatility) should correlate with higher expected returns, assuming investors are risk-averse.
However, empirical research, including Mayfield’s observation (2004) , finds that expected returns do not always increase with volatility, and sometimes, higher volatility even precedes lower returns. This challenges the positive risk-return trade-off predicted by theory.
Several explanations and models have emerged:
Empirical Evidence
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Low-volatility anomaly: Studies (e.g., Ang et al., 2006) show that low-volatility stocks often outperform high-volatility stocks on a risk-adjusted basis.
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Time-varying risk premium: MRP may not be constant over time. During high volatility periods (e.g., crises), risk aversion increases, but returns fall, possibly due to flight to safety.
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Behavioural factors: Investors may overweight recent volatility or misjudge risk, leading to mispriced risk premia.
Regime-Switching Models
Hamilton’s (1989) regime-switching model assumes stock returns follow different statistical regimes (e.g., high-return/low-volatility vs low-return/high-volatility). These models better capture the nonlinear dynamics and asymmetric relationships between risk and return.
For instance:
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In low-volatility regimes, returns are stable and slightly positive.
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In high-volatility regimes, markets may enter crisis mode, where uncertainty leads to herd behaviour and risk aversion spikes, but returns decline.
Guidolin and Timmermann (2005) found that regime-switching models provide better out-of-sample predictions of return volatility and risk premium than constant-parameter models. They suggest that risk-return relationships are not monotonic and depend on market state.
In conclusion, the mean-variance framework provides a theoretical baseline, but real-world data suggests a more complex relationship between risk and return, with regime changes and behavioural biases playing key roles in determining market outcomes.
