Modern Portfolio Theory (MPT)

This section builds the foundation for the whole unit: how correlation drives diversification and why the efficient frontier is the boundary of optimal portfolios.

Modern Portfolio Theory (MPT) changed how investors think about portfolios. Instead of analyzing individual securities in isolation, MPT focuses on how securities interact within a portfolio.

What Is the Central Principle of MPT?

• Investors can construct portfolios that maximize expected return for a given level of risk
• Risk is measured by standard deviation of portfolio returns (total risk)
• Key insight: combining assets that are not perfectly correlated reduces overall portfolio risk
• MPT assumes investors are risk-averse - given equal returns, they prefer the less risky portfolio
• Portfolio risk depends on three factors: (1) weight of each asset, (2) standard deviation of each asset, (3) correlation between assets

Think of it this way: Before MPT, investors analyzed stocks one at a time, asking "Is this a good stock?" MPT changed the question to "How does this stock fit with my other investments?" A stock might be risky on its own, but if it tends to go up when your other stocks go down, adding it actually reduces your overall portfolio risk.

How Does Correlation Affect Diversification?

Correlation coefficient (r): ranges from -1.0 to +1.0

• In practice, most asset pairs have correlations between 0 and +1
• Diversification benefit begins at any correlation below +1.0
• The lower the correlation, the greater the risk reduction

How Many Holdings Does Diversification Take?

• Diversification works by averaging away risk that is specific to one company, so each added holding helps less than the one before it
• A widely cited rule of thumb puts most of that benefit in place at roughly 20 to 30 stocks drawn from different sectors, with little further gain past about 30
• Treat the number as an approximation rather than a defined threshold. What the exam tests is the shape of the curve: diminishing returns, and a floor that more holdings never break through
• That floor is systematic risk. No number of stocks removes it

What Does MPT Assume, and Where Does It Break Down?

MPT's conclusions follow from four assumptions:

• Investors are rational and risk-averse, preferring the less risky portfolio at equal expected return
• Investors judge portfolios using only expected return and standard deviation, which is called a mean-variance framework
• All investors share the same time horizon and the same expectations about returns, risk, and correlations
• Correlations between assets are stable over time

The last assumption is the one that fails, and it is the standard criticism of MPT:

• Correlations are not fixed. Under market stress, correlations across asset classes tend to converge toward +1.0
• So the diversification benefit shrinks exactly when an investor needs it most, because assets that looked uncorrelated in calm markets move together in a downturn

Exam Tip: Gotchas

• Correlation of +1.0 provides ZERO diversification benefit - the portfolio's risk is simply the weighted average of individual risks. Any correlation below +1.0 reduces portfolio risk below the weighted average. The exam loves testing whether candidates know that diversification works at any correlation less than +1.0, not just negative correlations.
• MPT's diversification benefit depends on stable correlations, and correlations are not stable. Assets that were historically uncorrelated or negatively correlated often move together in a crisis. This is the standard criticism of MPT, and the exam may test it as such.

What Is the Efficient Frontier?

The efficient frontier is the set of portfolios offering the highest expected return for each level of risk (or lowest risk for each return).

• Appears as a curved line on a risk-return graph representing all optimal portfolios
• Portfolios on the frontier: offer the highest return for each level of risk
• Portfolios below the frontier: suboptimal (same risk, lower return, or same return, higher risk)
• Portfolios above the frontier: impossible - the frontier is the upper boundary of attainable risk-return combinations
• No rational investor would choose a portfolio below the efficient frontier
• Adding the risk-free asset creates the Capital Market Line

Think of it this way: Imagine plotting hundreds of possible portfolios on a graph with risk (standard deviation) on the x-axis and expected return on the y-axis. The efficient frontier is the "best case" boundary curve connecting all the portfolios that offer the maximum return at each risk level. There is no "above" - if you could earn a higher return at the same risk, that portfolio would already be on the frontier.

Where Do Individual Securities Plot on the Efficient Frontier?

A common misconception is that a high-flying individual stock should plot above the efficient frontier because it offers high potential return. It does not. Portfolios on the frontier are optimal; portfolios below it (inside the curve) are suboptimal, offering the same risk for a lower return or the same return for higher risk.

• An individual stock carries two kinds of risk: systematic (market) risk and unsystematic (company-specific) risk
• A portfolio on the frontier is diversified - the unsystematic risk has been eliminated through correlation effects
• An individual stock still carries that unsystematic risk, so it typically has more total risk for the same expected return than an efficient portfolio, placing it below the frontier

Exam Tip: Gotchas

• The exam loves the trap "where does a single stock plot vs. the efficient frontier?" Wrong answer to avoid: above the frontier. Nothing plots above the frontier. The frontier is the upper boundary of attainable risk-return space.
• Individual securities typically plot inside the curve (below and to the right) because they carry unsystematic risk that diversified portfolios on the frontier have eliminated.
• For the same level of risk as an individual stock, a diversified portfolio on the frontier offers a higher expected return. That is the payoff of diversification.

Think of it this way: Imagine you and a fully diversified portfolio both take on the same amount of total risk (same standard deviation). The diversified portfolio earns more, because none of its risk is wasted on company-specific noise. Your single stock is paying for company-specific risk it gets nothing back for.

What Should You Check on Exam Day?

• Diversification benefit exists at any correlation below +1.0, not only at negative correlation.
• Nothing plots above the efficient frontier; individual stocks typically plot inside it (below and to the right) because they carry unsystematic risk that diversified portfolios have eliminated.
• Portfolio risk depends on three factors: the weight of each asset, the standard deviation of each asset, and the correlation between assets.
• Diversification shows diminishing returns, with most of the benefit in place around 20 to 30 stocks across different sectors. No number of holdings removes systematic risk.
• MPT assumes rational risk-averse investors, a mean-variance framework, shared horizons and expectations, and stable correlations.
• The standard criticism of MPT is that correlations converge toward +1.0 in a crisis, cutting the diversification benefit exactly when it is needed most.
• Adding the risk-free asset to the efficient frontier creates the Capital Market Line.