The inter-temporal rate of substitution represents the trade-off between real consumption today vs real consumption in the future. For a given quantity, investors will always prefer current consumption over future consumption.

Inter-temporal
rate of substitution = m_{t} =

We can explain risk aversion of investors by the covariance of the inter-temporal marginal rate of substitution and expected returns on savings. Risk aversion refers to the phenomenon where investors experience a larger loss of utility from losing wealth than they gain in utility from gaining wealth.

The risk premium is the covariance between the expected future return on an investment and the Inter-temporal rate of substitution. For risk-averse investors, the covariance is negative; when the expected future price of the asset is high, the marginal utility of future consumption relative to current consumption is low.