Market Portfolio
The 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.
In plain language
Draw a line from the risk-free rate so that it just touches the efficient frontier. The point it touches is the market portfolio, labelled M in the workbook.
It is special because every combination of the risk-free asset with M beats every combination of the risk-free asset with any other risky portfolio. So every rational investor, whatever their risk appetite, holds the same risky portfolio — M — and expresses their appetite only through how much they lend or borrow alongside it.
In theory M contains all risky assets: the workbook lists domestic and foreign stocks and bonds, real estate, coins, stamps, art, antiques and any other marketable risky asset from around the world.
That is impossible to build, so in practice broad-based equity indices stand in for it.
How it works
Why M wins (section 3.12, Exhibit 3.4). Combinations of the risk-free asset with portfolio A on the frontier are inferior to combinations with B, which are inferior to combinations with M. So M is the most desirable risky portfolio, and the line from the risk-free rate through M is the Capital Market Line.
Only systematic risk (section 3.13). Because M is completely diversified, it has only systematic risk; unsystematic risk is diversified away and needs no compensation. The fourth sample question for Chapter 3 follows directly: a completely diversified portfolio has a correlation of one with the market portfolio.
Beta of 1. The risk of the market portfolio is its covariance with itself, which is its variance. Plugged into beta = Cov(i,m) ÷ σ²m, the market's beta is always exactly 1.
The proxy problem (section 3.12.1). The theoretical market portfolio cannot be constructed, so proxies are used, and there is no unanimity about which proxy to use. The workbook warns that an incorrect market proxy will affect both the beta risk measures and the position and slope of the SML used to evaluate portfolio performance. Chapter 8 repeats the point: broad-based indices are used as the proxy for the market portfolio when calculating systematic risk.
A worked example
The betas are illustrative. The 8% risk-free rate and 14% market risk premium are the workbook's own SML figures.
An analyst is setting a required return for Rs 1 crore in a mid-cap stock. Two colleagues measure its beta against different proxies for the market portfolio:
| Proxy used for M | Beta | Required return (CAPM) | Required gain on Rs 1 crore |
|---|---|---|---|
| A 50-stock large-cap index | 1.2 | 8% + 1.2 × 14% = 24.8% | Rs 24.8 lakh |
| A 500-stock broad index | 1.0 | 8% + 1.0 × 14% = 22.0% | Rs 22.0 lakh |
Same stock, same risk-free rate, same market premium — and a Rs 2.8 lakh a year difference in the hurdle the stock must clear, purely from the choice of proxy.
If the stock is forecast to return 23%, it looks overvalued against the first proxy (below the SML) and undervalued against the second (above it). The analysis has not changed; the definition of "the market" has.
This is precisely the workbook's warning: the proxy moves beta and the SML, and so it moves every performance judgement built on them.
Why NISM asks about it
Chapter 3, section 3.12, identifies M as the tangency portfolio; section 3.12.1 lists its theoretical contents and the proxy problem; section 3.13 explains why only systematic risk is priced and why the market beta is 1. Chapter 8, section 8.2, gives "proxy for the market portfolio" as a use of indices. Sample question 4 (correlation of a completely diversified portfolio with the market is one) comes straight from this material.
Common exam traps
- The market portfolio contains all risky assets worldwide, not just listed Indian equities. An index is a proxy.
- Its beta is exactly 1 — because its covariance with itself is its variance.
- It has only systematic risk. A completely diversified portfolio has correlation one with M, not zero.
- Every investor holds the same M. Risk appetite is expressed through lending or borrowing, not through a different risky portfolio.
- A wrong proxy distorts beta and the SML — both, not just one.
- The market portfolio is not the optimum portfolio. The optimum is investor-specific; M is common to all.
Check yourself
1.A completely diversified portfolio would have a correlation with the market portfolio that is:
- a)Equal to zero, because it has only unsystematic risk
- b)Equal to one, because it has only systematic risk
- c)Less than zero, because it has only systematic risk
- d)Less than one, because it has only unsystematic risk
Show the answer
Answer: (b) Equal to one, because it has only systematic risk
Equal to one, because it has only systematic risk.
A completely diversified portfolio has, by definition, eliminated all unsystematic risk. What remains is only the risk common to the whole market - so nothing is left to make the portfolio move differently from the market, and its correlation with the market must be +1, which the workbook defines as perfect positive correlation, meaning that returns for the two assets move together in a completely linear manner.
This is the fact on which CAPM rests. When investors invest in the portfolio M (market portfolio), THAT HAS ONLY SYSTEMATIC RISK, they need to be COMPENSATED FOR BEARING ONLY THE SYSTEMATIC RISK. BECAUSE THE UNSYSTEMATIC RISK IS DIVERSIFIED, THERE IS NO NEED FOR ANY COMPENSATION FOR THE SAME.
That is why the CAPM equation contains beta and not total standard deviation: beta is a good proxy of the NON-DIVERSIFIABLE portion of the risk.
And it explains why the market's own beta is 1. The risk of the market portfolio is the covariance of the market portfolio WITH ITSELF, which is the VARIANCE of the market portfolio - the workbook noting that the covariance of an asset with itself is its variance - so the beta formula's numerator and denominator are identical.
2.The correlation coefficient between the return on the market portfolio and the return on a risk-free asset is:
- a)+1
- b)-1
- c)Between 0 and +1
- d)Zero
Show the answer
Answer: (d) Zero
Zero. Since the return of a risk-free asset is CERTAIN, its STANDARD DEVIATION IS ZERO. Also, the COVARIANCE between the return of the risk-free asset and the risky asset IS ZERO TOO.
Box 3.2 lists four characteristics of a risk-free asset:
- An asset where its returns yield ZERO STANDARD DEVIATION
- ZERO CORRELATION with all other risky assets
- Provides the RISK-FREE RATE OF RETURN
- Will lie on the VERTICAL AXIS of a portfolio graph, as it has no risk
The intuition is simple: correlation measures how two things move together. A risk-free asset does not move at all - its return is certain - so it cannot move with anything. There is nothing to correlate.
And this fact has a large consequence. When a risk-free asset is combined with a risky portfolio, every term in the Markowitz risk formula involving the risk-free asset vanishes, leaving portfolio risk as simply the weight in the risky asset multiplied by the risk of the risky asset. Because that relationship is linear, such portfolios plot on a straight line - which is what makes the Capital Market Line straight, where Markowitz's frontier was curved.
3.The market portfolio returns 20 per cent and the risk-free rate is 5 per cent. An investor borrows an amount equal to 50 per cent of her wealth at the risk-free rate and invests 150 per cent of her wealth in the market portfolio. Her portfolio return is:
- a)20.0 per cent
- b)27.5 per cent
- c)32.5 per cent
- d)12.5 per cent
Show the answer
Answer: (b) 27.5 per cent
(1.5 x 20%) - (0.5 x 5%) = 30% - 2.5% = 27.5 per cent
Note the MINUS sign, and the workbook's explanation for it: the debt component is SUBTRACTED from the return on the risky portfolio, because for the investor this represents REPAYMENT OR PAYMENT and NOT RECEIPT. Option 3 makes exactly this error by adding instead.
How the gain arises. Borrowing at the risk-free rate and investing in the market portfolio generates the return on the market portfolio on EVERY SINGLE UNIT of investment, INCLUDING ON THE BORROWED PORTION. However, the investor pays only the RATE OF THE RISK-FREE ASSET on the borrowing, and therefore SAVES an amount of (Return on Market Portfolio LESS Return on Risk Free Asset) - here 15 percentage points on the borrowed half, or 7.5 points of extra return.
Where it sits on the line: for all combinations of BORROWING at the risk-free rate and investing in the market portfolio, the returns lie TO THE RIGHT of point M on the CML. Lending combinations lie to the left, and 100 per cent in the market portfolio at 20 per cent is the maximum achievable without borrowing.
The practical caveat the workbook concedes: it is NOT POSSIBLE TO BORROW at the risk-free rate - a real investor's borrowing rate is higher - however, assuming a higher borrowing rate does not change the general results.
Where this is taught
Free preparation for NISM Series XXI-BRelated terms
- BetaHow sharply a share moves relative to the market index — beta 1 moves with the index, above 1 amplifies it, below 1 dampens it. The standard measure of systematic risk.
- Systematic riskThe part of an investment's risk that comes from economy-wide forces moving every asset at once — it cannot be diversified away, and it is the only risk the market pays you to carry.
- BenchmarkThe independently published index a scheme's performance is measured against, chosen to match its investment objective, asset allocation and strategy, and disclosed in the Scheme Information Document.
- Efficient frontierThe umbrella-shaped curve of portfolios offering the highest expected return for each level of risk, or the lowest risk for each level of return — any portfolio below it is dominated.
- 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.
- 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.
- Market ProxyA practical stand-in for the theoretical market portfolio — usually a broad-based equity index. The choice matters: an incorrect proxy distorts beta and the security market line.
- Lending portfolioAny mix of the risk-free asset and the market portfolio that uses only the investor's own money — it plots on the Capital Market Line between the risk-free rate and M, and lending means buying the risk-free asset.
- Regression of beta toward the meanAn empirical finding in the tests of CAPM: high-beta portfolios tend to drift down towards 1.00 over time, and low-beta portfolios tend to drift up towards 1.00.
- Optimum portfolioThe combination of investments, chosen from the feasible portfolios, that has desirable risk-return characteristics within the investor's constraints and meets that investor's objectives.
- 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.
- Capital Market TheoryThe 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.
- 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.
- Broad based indexA stock index representing an entire market segment and a significant share of that market — e.g. NIFTY 500 — used as the practical proxy for the market portfolio and as a benchmark for equity funds.
- 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.