In classical finance theory, investors are assumed to be mean-variance optimisers: rational agents who seek to maximise expected return for a given level of risk, or equivalently, minimise risk for a given expected return. This insight, formalised through Harry Markowitz’s (1952) Modern Portfolio Theory, lays the groundwork for the Capital Asset Pricing Model (CAPM), introduced by Sharpe (1964), Lintner (1965), and Mossin (1966). But what if this elegant framework is incomplete—overly simplistic in its assumptions and narrow in its view of investor preferences?

That’s where the Intertemporal Capital Asset Pricing Model (ICAPM) enters the picture. Proposed by Robert Merton (1973), the ICAPM expands the CAPM’s static, single-period framework into a dynamic, multi-period one, allowing for a more realistic representation of investor behaviour. This post explores the intuition behind both models, the assumptions they rest on, and the implications for portfolio construction and asset pricing.

CAPM Recap: Mean-Variance Optimisation and Market Equilibrium

If investors are mean-variance optimisers and markets clear (i.e., every asset bought is also sold), then the aggregate of all investor portfolios must be the tangency portfolio. This refers to the mean-variance efficient portfolio of risky assets that lies on the efficient frontier and is tangent to the capital market line (CML). This logic implies that the market portfolio of risky assets is itself the mean-variance optimal portfolio. Prices reflect the collective assessment of expected returns, variances, and covariances. If any asset’s expected return is too high or too low for its level of variance and covariance, prices adjust until its weight in the market becomes optimal.

This leads to CAPM’s most fundamental insight: the risk that matters is systematic risk—the covariance of an asset with the market, not its standalone volatility. The beta of an asset, which captures this co-movement, becomes centrally important.

**Figure 1.** This chart illustrates three core ideas from modern portfolio theory: the efficient frontier, the tangency portfolio, and the Capital Market Line (CML).
The efficient frontier (the curved line) shows the best possible portfolios **made up exclusively of risky assets.** It represents the trade-off between risk and return *before* the introduction of a risk-free asset. Portfolios below the curve are inefficient, as they deliver lower returns for the same or more risk.
The Capital Market Line (the dashed line) shows all the combinations of the risk-free asset and the tangency portfolio. It starts at the risk-free rate and is tangent to the efficient frontier at a single point—the tangency portfolio (the red cross). This portfolio has the highest possible Sharpe ratio, meaning it offers the best risk-adjusted return. It represents the optimal mix of risky assets. The key clarification is that once the risk-free asset is introduced, **the only risky portfolio needed is the tangency portfolio.** Investors don’t combine the risk-free asset with *any* risky portfolio—only with that one specific optimal mix.
By combining the tangency portfolio with the risk-free asset—either lending (low risk) or borrowing (higher risk)—investors can build any portfolio along the CML. All points on this line dominate portfolios on the efficient frontier alone, because they achieve better return for each unit of risk.

The CAPM pricing equation is:

E(Rᵢ) = Rf + βᵢ × [E(Rm) − Rf]

Where:

E(Rᵢ) is the expected return of asset i,
Rf is the risk-free rate,
βᵢ is the asset’s beta = Cov(Rᵢ, Rm) / Var(Rm),
E(Rm) is the expected return of the market.

This framework introduces alpha as the unexplained return beyond what is predicted by beta. If a fund has a beta of 1.2 and the market excess return is 5%, then we expect a return of:

Rf + 1.2 × 5% = Rf + 6%

If the actual return is 8%, the alpha is 2%.

As John Cochrane (2005) summarises the CAPM, this one-period model assumes investors care only about return and volatility today and have no concern for how investment opportunities may change in the future. But real-world investors do care about changes in income, interest rates, inflation, and other risks. That’s where ICAPM becomes crucial.

ICAPM: Extending CAPM into Time

The ICAPM generalises the CAPM by recognising that investors care not only about expected returns and risk in the current period, but also about how their investment opportunities change over time. As Merton (1973) shows, when future returns, volatilities, or consumption opportunities are uncertain, rational investors hedge against changes in those future states.

So, in addition to holding the tangency portfolio (the optimal risky portfolio from mean-variance analysis), investors also hold hedging portfolios that help manage their exposure to changing economic conditions—what Merton calls state variables, such as income uncertainty, interest rates, inflation, or market volatility.

For example, an investor employed in a cyclical industry like construction or finance may be particularly vulnerable to economic downturns. To hedge against the risk of losing their income during a recession, they may tilt their portfolio towards defensive assets, such as government bonds or consumer staples, that tend to perform better in bad economic times. This is precisely the type of intertemporal risk that the ICAPM attempts to capture.

Instead of a single mean-variance efficient portfolio, the ICAPM predicts a continuum of optimal portfolios, tailored to investors' intertemporal preferences. As Fama (1996) puts it, there are infinite ‘tastes’ and therefore infinite optimal portfolios.

The pricing equation now includes multiple sources of risk:

E(Rᵢ) − Rf = βᵢ₁λ₁ + βᵢ₂λ₂ + ... + βᵢₖλₖ

Where:

βᵢₖ is asset i's exposure to risk factor k,
λₖ is the price of risk for factor k.

This means that multiple betas matter—not just how an asset moves with the market, but how it moves with broader economic risks.

Cochrane’s Contributions: State Variables and Pricing Kernels

John Cochrane (1996, 2005) plays a pivotal role in deepening our understanding of ICAPM through the lens of consumption-based models and stochastic discount factors (SDFs). He reframes asset pricing as:

E(m × Rᵢ) = 1

Where m is the stochastic discount factor—a variable that reflects how marginal utility changes across states and time. In Cochrane’s (2005) framework, the expected return of an asset is related to how it covaries with m. Assets that do well when m is high (i.e. in bad economic states when marginal utility is high) are more valuable and thus require lower expected returns.

This framework provides a unifying view of ICAPM and macroeconomic models: risk premia arise from assets' exposure to shocks that investors care about, such as consumption, income, volatility, or labour market risk. The ICAPM is essentially a special case of this broader consumption-based asset pricing model.

As Cochrane (1996, 2005) argues, many anomalies in the CAPM can be rationalised by expanding the set of priced risk factors to include these intertemporal risks. In other words, by extending the CAPM through the ICAPM lens, we can better account for the variation in returns across diversified portfolios. This makes the ICAPM a more flexible and empirically useful framework than the CAPM alone.

Why the Market Portfolio Is Not Mean-Variance Efficient

In CAPM, the market portfolio is mean-variance efficient because it reflects the aggregation of all optimal portfolios under a shared assumption of mean-variance preferences.

But in ICAPM, the market portfolio is not mean-variance efficient because it reflects the aggregation of diverse investor demands—each combining a tangency portfolio with different hedging portfolios.

For example:

One investor may prefer assets that do well in a recession to offset job risk.
Another may favour assets that hedge inflation to preserve consumption power.
A third may tilt towards long-duration bonds when interest rates are expected to fall.

All of these portfolios deviate from the CAPM tangency portfolio. When aggregated, the result—the market portfolio—is not mean-variance efficient, but instead multifactor efficient. In other words, because each investor chooses a portfolio that reflects their unique risks and preferences, the overall market ends up holding a mix of assets that hedge various economic shocks—not just the portfolio with the highest Sharpe ratio.

This realisation has significant implications:

CAPM’s assumptions no longer hold in dynamic, real-world markets.
Asset pricing anomalies (e.g. value, momentum, low volatility) may be explained by investor preferences or intertemporal hedging needs.
Multifactor models (e.g. Fama and French, Arbitrage Pricing Theory) arise naturally from this theoretical framework.

Portfolio Construction in an ICAPM World

The practical takeaway is that investors may willingly deviate from mean-variance optimality if doing so reduces losses in bad states of the world. The optimal portfolio is not just about maximising return relative to volatility—it is also about managing risk relative to future consumption, labour income, or macroeconomic shocks.

As Cochrane (2005) explains, long-term investors should consider their state-contingent needs: it may be optimal to hold assets with lower expected returns if those assets provide insurance against economic downturns.

For advisers and asset managers, this means that alpha must be interpreted carefully. If an asset appears to underperform on a CAPM basis, it might still deliver positive utility by hedging against recession risk or inflation—benefits that CAPM simply cannot capture.

Conclusion: From Simplicity to Sophistication

The ICAPM invites us to move beyond the static simplicity of the CAPM. It acknowledges that investors are forward-looking, risk-sensitive, and deeply concerned about uncertainty over time. By integrating intertemporal preferences and multiple sources of risk, the ICAPM provides a richer, more realistic theory of asset pricing.

Whether you're building a portfolio, assessing fund performance, or studying anomalies, the ICAPM offers a more complete framework—one that reflects the real decisions investors face in an uncertain world.

References

Campbell, John Y. 1993. ‘Intertemporal Asset Pricing without Consumption Data.’ American Economic Review 83 (3): 487–512.

Campbell, John Y., and Luis M. Viceira. 2002. Strategic Asset Allocation: Portfolio Choice for Long-Term Investors. Oxford: Oxford University Press.

Chen, Nai-Fu, Richard Roll, and Stephen A. Ross. 1986. ‘Economic Forces and the Stock Market.’ Journal of Business 59 (3): 383–403.

Cochrane, John H. 1996. ‘A Cross-Sectional Test of an Investment-Based Asset Pricing Model.’ Journal of Political Economy 104 (3): 572–621.

Cochrane, John H. 2005. Asset Pricing. Revised Edition. Princeton: Princeton University Press.

Fama, Eugene F. 1996. ‘Multifactor Portfolio Efficiency and Multifactor Asset Pricing.’ Journal of Financial and Quantitative Analysis 31 (4): 441–465.

Fama, Eugene F., and Kenneth R. French. 1993. ‘Common Risk Factors in the Returns on Stocks and Bonds.’ Journal of Financial Economics 33 (1): 3–56.

Fama, Eugene F., and Kenneth R. French. 2015. ‘A Five-Factor Asset Pricing Model.’ Journal of Financial Economics 116 (1): 1–22.

Lintner, John. 1965. ‘The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.’ Review of Economics and Statistics 47 (1): 13–37.

Markowitz, Harry. 1952. ‘Portfolio Selection.’ Journal of Finance 7 (1): 77–91.

Merton, Robert C. 1973. ‘An Intertemporal Capital Asset Pricing Model.’ Econometrica 41 (5): 867–887.

Mossin, Jan. 1966. ‘Equilibrium in a Capital Asset Market.’ Econometrica 34 (4): 768–783.

Roll, Richard. 1977. ‘A Critique of the Asset Pricing Theory’s Tests Part I: On Past and Potential Testability of the Theory.’ Journal of Financial Economics 4 (2): 129–176.

Sharpe, William F. 1964. ‘Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.’ Journal of Finance 19 (3): 425–442.

Rethinking Risk and Return: The Intertemporal Capital Asset Pricing Model (ICAPM)