Why invest through a portfolio

Why not put everything in one security?

The portfolio approach means judging each security by how it contributes to the investment characteristics of the whole portfolio, not on its own. The first reason is protection against disaster.

Take an employee of a freight company, Halden Freight, who holds most of her retirement savings in her employer’s shares. If the company fails, she loses her job and her savings together, because both depend on the same business. Diversification , spreading money across many securities, is the cure: one failure then costs only a small slice.

What does a portfolio do to risk and return?

A portfolio cuts risk without cutting expected return. An equally weighted portfolio earns the average return of its holdings, which is also what you would expect from picking one holding at random. Its standard deviation, however, is lower than the average of the holdings’ standard deviations, because the holdings do not move together: when one falls, another may rise.

So portfolios affect risk more than they affect return.

The portfolio approachjudge each holding by what it adds to the whole

• Reduces risk Memorize volatility below the average of the holdings
• Keeps return Use it equal weights earn the average expected return
• Avoids disaster Know the idea no single failure can ruin the investor
• Does NOT guarantee downside protection Memorize severe sell-offs hit most assets at once
  • Correlations rise in a crash the ratio moves toward 1
  • Benefit shrinks when needed most
• Does NOT eliminate risk Memorize market-wide risk remains

The diversification ratio puts a number on the risk reduction.

$$DR = \frac{\sigma_p}{\bar{\sigma}}$$

Here $\sigma_p$ is the standard deviation of the equally weighted portfolio and $\bar{\sigma}$ is the average standard deviation of the individual holdings. Compare against the average because, without any special foresight, picking one holding is a draw from the group: its expected risk is the average risk. The portfolio’s standard deviation goes on top, so a ratio below 1 means diversification is working.

DR = portfolio σ ÷ average single-holding σlower is better

• Well below 1 Use it strong diversification benefit
• Close to 1 Use it little benefit left, as in a global crash
• Exactly 1 Know the idea no benefit at all (perfect correlation)

Slide the number of holdings and the average correlation. More holdings and lower correlation push the ratio down. Then switch on crash mode and watch the ratio jump.

What moves the ratio: number of holdings and correlation

When all holdings have the same standard deviation, the ratio depends only on how many there are, $N$, and on their average pairwise correlation, $\rho$.

$$DR = \sqrt{\frac{1}{N} + \frac{N-1}{N}\,\rho}$$

This is an idea to understand, not a formula to memorize. Adding holdings helps, but with diminishing returns: with $\rho = 0.20$, four shares give 0.63, twenty give 0.49, and even endless holdings cannot go below $\sqrt{0.20} = 0.45$. Only a lower correlation lowers the floor.

Does diversification protect you in a crash?

No, not reliably. Downside protection , the guarantee of limited losses when markets fall, is not something diversification delivers. Co-movement is not fixed. In a severe global sell-off, correlations between assets and between countries rise, so most holdings fall together just when the investor most wants them to offset each other.

Run crash mode on the four-share example with the correlation at 0.90: the ratio becomes √(1 ÷ 4 + 3 ÷ 4 × 0.90) = √0.925 = 0.96. The portfolio is nearly as risky as a single share. In normal times diversification works well, and against a company-specific blow it still helps. Against a panic that spreads around the world it is a weak shield.

Exam tip Portfolio approach: yes to risk reduction, no to risk elimination, no to guaranteed downside protection.

Go deeper Why the average single holding is the right yardstick

A portfolio has the same expected return as one randomly chosen holding, so what separates the two is risk alone. If you could pick the future winner in advance you would not need a portfolio, but nobody can. Comparing with the average holding therefore measures the benefit of diversifying without needing to guess a winner.

Weights matter too. Holdings need not be equal: a smarter mix of the same securities can give a lower standard deviation for the same expected return, which is why portfolio construction is more than just owning many things.

What is modern portfolio theory?

Modern portfolio theory (MPT) grew from Harry Markowitz’s 1952 work on portfolio selection. Its main message: investors should hold portfolios, and should focus on how the securities in them are related to one another. An asset is judged by what it adds to the risk of the whole portfolio, not by its own volatility.

Taken further by Sharpe, Lintner and Treynor, the idea gives the capital asset pricing model. Only the risk that cannot be diversified away (systematic risk) should affect an asset’s price, because everything else can be removed by holding a portfolio.

Go deeper Diversification across countries in global crises

Holding shares from many countries is a classic way to diversify. In calm periods the markets of different countries move fairly independently. Over time, and especially during global crises, their movements became more closely linked, and in the worst quarters nearly all of them fell together. The lesson is to expect less benefit in a crisis than the long-run correlations suggest, and not to treat international diversification as insurance.