Diversification and the stock-bond split.
Stocks pay more in the long run but swing wider in the short. Bonds smooth the ride at the cost of some return. A real portfolio is a mix of both, tuned to your time horizon. The closing lesson of the course.
Stocks have historically delivered about 10% per year on average over long periods — the highest reliable return of any major asset class. Bonds, by contrast, have returned roughly 5% per year on average. The math seems obvious: if stocks pay twice as much as bonds, why would anyone ever buy bonds?
The answer is in the year-to-year experience. The 10% stock return is an average across many decades. In any individual year, stocks can be up 30% or down 30%. A 100% stock portfolio worth $100,000 at the start of 2007 was worth roughly $63,000 by early 2009 — a 37% drawdown that took until 2013 to fully recover. Bonds, over the same period, drifted gently up. If you needed to withdraw money from your portfolio in 2009 to pay for retirement, tuition, or a medical bill, the 100% stock allocation forced you to sell at exactly the wrong moment.
This is why real investors hold both stocks and bonds. Stocks for long-run growth, bonds for short-run predictability and to fund any near-term spending without selling stocks at a low. The right mix depends on how soon you'll need the money — your time horizon. This closing lesson develops the risk-return trade-off, the math of diversification, and the standard rules of thumb for tuning the mix to your life stage.
Mix them. Tune the mix to your time horizon.
Diversification means holding multiple asset classes so that no single one dominates the portfolio's behavior. A 60% stock / 40% bond portfolio has an expected return around 8% (a weighted average of 10% and 5%) but volatility much closer to the bond side than the stock side — because stocks and bonds often move in opposite directions in the short run, so combining them smooths out the swings.
The right time horizon tunes the mix. A 25-year-old saving for retirement at 65 has a 40-year horizon and can afford to ride out the worst stock-market drawdowns; an appropriate allocation might be 90% stocks, 10% bonds. A 65-year-old already drawing on the portfolio cannot afford a 40% drawdown that takes six years to recover; an appropriate allocation might be 40% stocks, 60% bonds. A common rule of thumb: percent in stocks = 110 − age.
The risk-return trade-off, sketched. Three portfolios on the curve: 100% bonds (low risk, low return), 60/40 mix (medium of both), 100% stocks (high risk, high return). The dashed curve traces all possible blends. Choose a point based on your time horizon.
Diversification is the practice of spreading investments across multiple asset classes (stocks, bonds, cash, real estate, etc.) to reduce the portfolio's overall volatility. The time horizon is the number of years until you expect to need the money; longer horizons permit greater stock allocation.
Words you'll see in every retirement-planning conversation
- Asset class A broad category of investment with similar risk-return characteristics. The three classic ones are stocks (equities), bonds (fixed income), and cash (money-market funds, short-term Treasury bills). Real estate, commodities, and others are commonly added in more sophisticated portfolios.
- Expected return The long-run average annual return of an asset class. Expected in the statistical sense (Lesson 5 of Topic 6: E(X) = Σ x · P(x)) — not a guarantee for any single year.
- Volatility The standard deviation of annual returns. (Topic 5 standard-deviation math applied to the annual-return distribution.) Higher volatility means wider year-to-year swings around the expected return.
- Asset allocation The percentages of a portfolio assigned to each asset class. "60/40" is shorthand for 60% stocks, 40% bonds. The biggest single decision in personal investing — far more impactful than picking individual stocks within the stock allocation.
- Time horizon The number of years until you expect to need the money. Drives the asset allocation: longer = more stocks. A common rule of thumb is percent in stocks = 110 − age, which gradually shifts from stock-heavy in youth to bond-heavy approaching retirement.
Choosing an allocation for two investors.
"Investor A is 30 years old and saving for retirement at age 65 (35-year horizon). Investor B is 60 years old and plans to retire at 65 (5-year horizon). Using the rule of thumb percent in stocks = 110 − age, suggest an allocation for each, then compute the expected return of each portfolio assuming stocks return 10% and bonds return 5%."
Compute Investor A's stock allocation.
So Investor A: 80% stocks, 20% bonds. The 35-year horizon gives plenty of time to ride out drawdowns.
→ stock-heavyCompute Investor A's expected return.
Weighted average:
= 8% + 1% = 9%
Compute Investor B's allocation.
So Investor B: 50% stocks, 50% bonds. The 5-year horizon cannot tolerate a deep stock drawdown without delaying retirement.
→ balancedCompute Investor B's expected return.
= 5% + 2.5% = 7.5%
Lower expected return than Investor A's, but much lower volatility — the right trade-off for the shorter horizon. Investor B sleeps better at night.
→ lower return, lower swingsThree portfolios. Compute the expected return.
A portfolio is invested 60% in stocks (10% expected return) and 40% in bonds (5% expected return). What is the portfolio's expected return?
Using the rule of thumb stocks % = 110 − age, what stock percentage would you recommend for a 45-year-old?
A retiree wants very low volatility and chooses a 20% stocks, 80% bonds allocation. With stocks returning 10% and bonds 5%, what is the expected return of this portfolio (to one decimal place)?
Three fast questions before you finish the course.
Q1. Why do most investors hold both stocks and bonds rather than just the higher-returning stocks alone?
Q2. Using the rule of thumb stocks % = 110 − age, which allocation fits a 70-year-old retiree?
Q3. A portfolio with 70% stocks (10% expected return) and 30% bonds (5%) has what expected return?
The course finale.
You have now finished the content of the course. Across seven topics you have built a complete financial-literacy toolkit:
- Topic 1 — Linear functions: the algebra that underlies every cost-curve, salary projection, and supply-and-demand diagram in a basic financial model.
- Topic 2 — Conversions and budgeting: percent of total, percent change, and the math of how money flows between categories of a household budget.
- Topic 3 — Savings: simple and compound interest, future value, the machinery of how money grows over time.
- Topic 4 — Loans: amortization, monthly payments, the flip side of savings — how money grows against you when you borrow.
- Topic 5 — Statistics: descriptive measures, normal distributions, margins of error — the tools to read a data set and a poll headline.
- Topic 6 — Probability: counting, combinations, expected value, the Law of Large Numbers — the math of uncertainty itself.
- Topic 7 — Taxes and the stock market: paycheck reading, bracket math, stocks, bonds, and the diversification frame that ties everything together.
The themes recur across topics. Compound interest from Topic 3 is the same exponential growth that drives long-run stock returns in this topic. The progressive-bracket math from Lesson 2 is structurally identical to the percent-change cascades from Topic 2. The expected-value formula from Topic 6 underpins the "expected return" vocabulary of asset allocation in this lesson.
The Final Exam ahead is cumulative across all seven topics; the Final Exam Review (~38 questions) gives you a structured preparation path. Beyond the exam, the math you have built is yours for life. The next time you read a poll headline, calculate a tip, sign a lease, take out a loan, or read an investment quote, you'll be doing it with the full apparatus of seven topics' worth of math behind you.
Back to Topic 7Different angle? Need another rep? These are optional — tap any that look helpful.
What the Heck Are Mutual Funds?
Introduces the case for diversification through pooled vehicles (mutual funds) — why owning hundreds of stocks via one fund reduces idiosyncratic risk. Hosted on PBS; the YouTube version is harder to track down. 2019, evergreen.
What The Heck Is An Index Fund?
Follow-up to the mutual fund video. Covers index funds as the practical implementation of diversification for most investors, and includes Warren Buffett's 2007-2017 bet against hedge funds as the worked example. PBS-hosted; 2019, evergreen.
Are 401(k)s a Financial Silver Bullet?
Optional third video for retirement-account context. Covers how 401(k) contributions get invested in stock and bond funds and acknowledges target-date funds — useful for the glide-path concept.