Capital Market Theory
Also written CMT
The extension of Modern Portfolio Theory that adds a risk-free asset and builds a model for pricing all risky assets, giving the Capital Market Line, the market portfolio and CAPM.
In plain language
Modern Portfolio Theory (MPT) answers one question: which mixes of risky assets are efficient? It stops at the efficient frontier.
Capital Market Theory asks the next question. What happens when investors can also hold something riskless? And what does that mean for the price of every risky asset?
Here is the workbook's definition. Capital market theory builds on MPT and develops a model for pricing all risky assets. It does so by introducing a risk-free asset while building efficient portfolios of risky assets. Having that risk-free asset has major effects on the portfolio choices investors make.
Its best-known results are the Capital Market Line, the market portfolio and the Capital Asset Pricing Model (CAPM). Together they gave the first clear framework for how an investment's risk should affect its expected return.
How it works
Assumptions (section 3.11). All of MPT's assumptions hold, plus:
| Assumption | Can it be relaxed? |
|---|---|
| All investors target points on the efficient frontier | — |
| Unlimited borrowing and lending at the risk-free rate | Yes — a higher borrowing rate does not change the general results |
| Homogeneous expectations | Yes — minor effects if differences are not large |
| Same one-period horizon | Results could be affected by a different horizon |
| Infinitely divisible investments | Little impact |
| No taxes or transaction costs | Modifies results, not the basic theory |
| No inflation (or fully anticipated) | — |
| Capital markets in equilibrium | Very important; cannot be relaxed as such |
What follows. Combine a risk-free asset (zero standard deviation, zero covariance with risky assets) with a risky portfolio, and both return and risk become linear in the weight. Every rational investor then prefers combinations with the tangency portfolio M — the market portfolio — and the line from the risk-free rate through M is the Capital Market Line, the new efficient frontier.
CAPM was developed concurrently by Jack Treynor (1962), William Sharpe (1964), John Lintner (1965) and Jan Mossin (1966).
The formula
E(Rp) = (1 − Wmp) × Rf + Wmp × Rm = Rf + Wmp (Rm − Rf)
σp = Wmp × σmp → Wmp = σp ÷ σmp
A worked example
The rupee amounts are illustrative; the 5%, 12%, 10% and 70/30 figures are the workbook's section 3.12 example.
Sunita has Rs 10 lakh. She puts 70% in the risk-free asset returning 5% and 30% in a risky portfolio expected to return 12% with a standard deviation of 10%.
E(Rp) = 0.70(5%) + 0.30(12%) = 3.5% + 3.6% = 7.10%
σp = 0.30 × 10% = 3%
In rupees: Rs 7 lakh earns Rs 35,000, Rs 3 lakh is expected to earn Rs 36,000, total Rs 71,000, with a one-standard-deviation swing of about Rs 30,000. Because the risk-free asset has zero variance and zero covariance, the risk is simply 30% of the risky asset's risk — linear, not curved.
Now run it backwards. Sunita decides she can live with 6% risk. Treat the risky portfolio as the market portfolio:
Wmp = 6% ÷ 10% = 0.60
E(Rp) = 5% + 0.60(12% − 5%) = 9.2%
Rs 6 lakh goes to the market portfolio and Rs 4 lakh to the risk-free asset. That is the whole of Capital Market Theory's advice on allocation: everyone holds the same risky portfolio; only the mix with the risk-free asset changes.
Why NISM asks about it
Chapter 3 is titled "Introduction to Modern Portfolio Theory and Capital Market Theory". Sections 3.10 (Introduction to Capital Market Theory), 3.11 (Assumptions and the implication of relaxing them) and 3.12 onwards (CML, market portfolio, CAPM, SML) carry it. Chapter 8 then uses broad-based indices as the practical proxy for the market portfolio. Expect "which assumption cannot be relaxed", the four CAPM originators, and a CML allocation computation.
Common exam traps
- CMT extends MPT by adding a risk-free asset. MPT alone has no risk-free asset and no CML.
- The one assumption that cannot be relaxed is market equilibrium. Homogeneous expectations, borrowing rates, taxes and divisibility can be relaxed with minor or no change to the basic theory.
- Borrowing at the risk-free rate is not realistic — the workbook says so — but a higher borrowing rate does not change the general results.
- With a risk-free asset, portfolio risk is linear in the weight (σp = Wmp × σmp); with two risky assets it is not.
- CAPM is a product of CMT, not a synonym. Its originators are Treynor, Sharpe, Lintner and Mossin — Markowitz is MPT.
- The theoretical market portfolio cannot be built; broad-based indices are used as proxies, and the wrong proxy distorts beta and the SML.
Where this is taught
Free preparation for NISM Series XXI-BRelated terms
- CAPMA model that prices the return an investor should demand from a share: the risk-free rate plus beta times the market risk premium.
- Modern Portfolio TheoryMarkowitz's framework for building portfolios on expected return and risk together, in which the co-movement between holdings — not their individual riskiness — decides the risk of the whole.
- Capital Market LineThe straight line from the risk-free rate tangent to the efficient frontier at the market portfolio — with a risk-free asset available, it is the efficient frontier, priced in standard deviation.
- Market PortfolioThe tangency portfolio M of all risky assets worldwide in market proportions — the one risky portfolio every rational investor holds once a risk-free asset exists; indices serve as its proxy.
- Risk-free AssetAn asset whose return is certain: zero standard deviation, zero correlation with every risky asset, earning the risk-free rate and plotting on the vertical axis of a risk-return graph.
- Security Market LineThe graph of CAPM: expected return plotted against beta. In equilibrium every asset lies on it — a security plotting above is undervalued, one plotting below is overvalued.
- Homogeneous expectationsThe Capital Market Theory assumption that all investors estimate identical probability distributions for future returns — one the workbook says can be relaxed with minor effects if differences are small.
- Infinite divisibilityThe Capital Market Theory assumption that any asset or portfolio can be bought or sold in fractions — which is what lets the theory draw its frontiers and lines as continuous curves.