# Equity and Equity Risk Premium

Equity refers to a security with an indefinite size and timing of dividends. Moreover, these dividends may stop in the event of bankruptcy. This makes equities riskier than debt. Equities, therefore, require an additional risk premium.

More precisely, investors who invest in equities require a return given by:

$$\left(R+\theta_t+\pi_t+\gamma_t+k_t\right)$$

Where:

• $$R$$ is the risk-free rate of interest.
• $$\theta_t$$ is the expected inflation.
• $$\pi_t$$ is the risk premium.
• $$\gamma_t$$ is the additional risk premium for credit risk (credit spread).
• $$k_t$$ is the additional risk premium relative to risky debt for investment in the equities.

The equity risk premium is the reward to investors over and above the compensation for risk required for holding a risk-free government bond. It is equal to $$(\gamma_t+k_t)$$.

The consumption hedging property highlights that the payoffs of securities during bad economic times matter more rather than their returns. In other words, assets that provide higher payoffs during economic downturns are highly valued because of the consumption hedging property. Thanks to this, such assets attract lower risk premiums.

Equity provides a poor hedge against bad consumption outcomes. This is because when there is a recession, the value of equity declines. On the other hand, government bonds pay off substantially during bad economic times. A risk-averse investor would, therefore, demand a higher premium on an equity holding than a government bond holding. It is equity’s poor consumption hedging ability that informs such a preference.

## Question

Which of the following statements about equity is the least accurate?

1. Equity provides a poor hedge against bad consumption outcomes.
2. Assets that provide a higher payoff during economic downturns have lower risk premiums.
3. The consumption hedging property highlights that the payoff of a security during good economic times is what matters more than its return.

#### Solution

The consumption hedging property highlights that the payoff of a security during bad economic times is what matters more than its return.

A is incorrect. Equity provides a poor hedge against bad consumption outcomes. This is because when there is a recession, the value of equity declines.

B is incorrect. Assets that provide a higher payoff during economic downturns are highly valued because of the consumption hedging property. As such, the risk premiums on the asset are lower.

Reading 44: Economics and Investment Markets

LOS 44 (i) Explain the relationship between the consumption-hedging properties of equity and the equity risk premium.

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