Why would anyone invest in risky stocks when you could safely put money in a bank account or Treasury bills? Because higher potential returns require taking on higher risk. This positive relationship between risk and expected return is the most fundamental principle in finance.
Every investment decision boils down to one question: Is the expected return sufficient to justify the risk I'm taking? To answer it, we need to measure both return and risk precisely. This chapter gives you the tools to do both.
Before we can talk about risk, we need to know how to measure return. There are two basic ways:
The actual profit or loss in dollars, including both income and price changes:
Dollar Return = (Ending Price − Beginning Price) + Cash IncomeExample: Buy a stock at $100, receive $3 in dividends, sell at $110. Dollar return = ($110 − $100) + $3 = $13.
The dollar return as a percentage of the amount invested — more useful for comparison:
Percentage Return = Dollar Return / Beginning PriceUsing the same example: $13 / $100 = 13%.
Percentage returns let you compare investments of different sizes. A $130 return on a $1,000 investment (13%) is better than a $200 return on a $5,000 investment (4%), even though the dollar amount is smaller.
From 1950 through 2023, the three major asset classes delivered very different returns — and very different levels of volatility:
| Period | Stocks | Long-Term Treasury Bonds | T-Bills (Cash) |
|---|---|---|---|
| 1950–2023 (Average) | 12.8% | 6.0% | 4.1% |
| 1950s | 20.9% | 0.0% | 2.0% |
| 1980s | 18.2% | 13.5% | 8.9% |
| 1990s | 19.0% | 9.5% | 4.9% |
| 2000s | 0.9% | 8.0% | 2.7% |
| 2022 | −18.1% | −29.3% | 2.1% |
| 2023 | 26.3% | 3.1% | 5.1% |
How do we quantify risk? The most common measure is standard deviation — a statistical measure of how much returns bounce around their average.
If an investment returns exactly 5% every year, its standard deviation is zero — no risk. If it returns +30% one year and −20% the next, the standard deviation is large — high risk. Standard deviation captures the total volatility of an investment.
| Asset Class | Standard Deviation | Average Return |
|---|---|---|
| Stocks | 17.2% | 12.8% |
| Long-Term Treasury Bonds | 11.6% | 6.0% |
| T-Bills | 3.0% | 4.1% |
To compare risk-adjusted returns across investments, use the coefficient of variation (CoV):
CoV = Standard Deviation / Average ReturnLower CoV = better risk-reward ratio. Stocks: 17.2/12.8 = 1.34. Bonds: 11.6/6.0 = 1.93. T-Bills: 3.0/4.1 = 0.73. Despite higher absolute risk, stocks actually offer a better risk-reward ratio than bonds over the long run.
Diversification is the process of spreading investments across different assets to reduce overall portfolio risk. It's often called the only "free lunch" in finance — you can reduce risk without reducing expected return.
Diversification only works when your stocks don't all move together. The statistical measure of co-movement is correlation, ranging from −1 to +1:
| Correlation | Meaning | Diversification Benefit |
|---|---|---|
| +1.0 | Perfect positive — move in lockstep | No benefit (no risk reduction) |
| 0.0 | No relationship — move independently | Good benefit |
| −1.0 | Perfect negative — move opposite | Maximum benefit (theoretical) |
In practice, most stocks have positive correlations (0.2 to 0.6) because they're all affected by the same economy. But some pairs have very low or even negative correlations:
Harry Markowitz revolutionized finance in 1952 with Modern Portfolio Theory (MPT) — a mathematical framework for building optimal portfolios. It earned him a Nobel Prize and changed how institutions invest forever.
Markowitz showed that you shouldn't look at stocks individually — you should look at how they interact in a portfolio. Two risky stocks, when combined, can produce a portfolio with lower risk than either stock alone. The key is their correlation.
For any set of stocks, there's a curve called the efficient frontier — the set of portfolios that offer the highest expected return for each level of risk. Every portfolio below this curve is suboptimal — you could get more return for the same risk, or less risk for the same return.
The efficient frontier curves upward — you must take increasingly more risk to get each additional unit of return. This is why extremely aggressive portfolios don't necessarily earn proportionally more. The relationship is not linear.
Once you've built a portfolio, how do you calculate its return? It's simply a weighted average of the returns of each asset:
Portfolio Return = Σ (wₖ × rₖ)Where wₖ = weight (proportion) of asset k, and rₖ = return of asset k. The weights must sum to 1 (100% of your investment).
You invest 60% in stocks (returning 12%), 30% in bonds (returning 6%), and 10% in T-bills (returning 4%):
But here's the crucial insight: portfolio risk is NOT a simple weighted average. Because of diversification (low or negative correlations), the portfolio's standard deviation is less than the weighted average of individual standard deviations. This is the magic of diversification — you get the weighted average return but less than the weighted average risk.
Explore these to deepen your understanding of this chapter's topics:
▶ YouTube Risk and Return — Financial Analysis ▶ YouTube Standard Deviation, Variance — Statistics for Finance 📚 Khan Academy Investment Vehicles — Khan Academy 📖 Investopedia Sharpe Ratio — Measuring Risk-Adjusted Returns 💬 Reddit r/investing — Risk management discussions