Two risky stocks. One perfectly safe result.
The story so far You still have $10,000 to invest. Two stocks catch your eye. Raincoat Co. sells rain gear: in a rainy summer it gains 30%, in a sunny one it loses 10%. Sunny Co. sells sunscreen and does the exact opposite. Each one alone is a coin flip, just like the stock fund in Lesson 14.1. But put $5,000 in each, and something strange happens: you make the same money no matter what the weather does. That's the power of diversification.
Diversification means spreading your money across investments that don't all move together, so one bad bet can't sink you.
It lowers risk without lowering expected return. It's often called the only free lunch in investing.
Own many companies in different industries, so their individual surprises cancel out. Index funds do this for you.
Portfolio managers and asset allocators decide how to spread money across stocks, bonds and other assets. Risk managers watch for too much money in one place.
What you're looking at: two stocks that zigzag in opposite directions. When the blue one is up, the yellow one is down. The green line is a 50/50 mix of the two: the zigs and zags cancel, and it stays flat at +10%.
Mix things that don't move together.
In Lesson 14.1 you measured risk with standard deviation. Now you'll see how to shrink it without giving up any expected return.
Diversification
Diversification is spreading your money so that no single surprise can hurt you much. When one investment zigs, another zags, and the bumps partly cancel.
- Rainy summer
- $5,000 × 1.30 = $6,500 in Raincoat, $5,000 × 0.90 = $4,500 in Sunny. Total $11,000.
- Sunny summer
- $4,500 + $6,500 = $11,000. The same 10% either way: expected return still 10%, standard deviation 0%.
Correlation
How much two investments move together is their correlation, a number from −1 to +1. At +1 they move in lockstep, and mixing them doesn't help at all. At 0 they're unrelated. At −1 they move exactly opposite, and the risk can vanish. The lower the correlation, the more risk the mix removes.
- Raincoat and Sunny
- Correlation −1, so the 50/50 mix has no risk.
- Two stocks with 20% risk each, 50/50
- Correlation +1: still 20%. Correlation 0.5: about 17%. Correlation 0: about 14%. Correlation −1: 0%.
Unique risk vs. market risk
Real stocks almost never have a correlation of −1. Most pairs of U.S. stocks move somewhat together, because they all live in the same economy. So a stock's risk has two parts. Unique risk comes from that one company: a product recall, a lawsuit, a factory fire. Market risk hits nearly everyone at once: a recession, a jump in interest rates, a pandemic.
- Raincoat's unique risk
- The weather, or a factory fire. Owning Sunny and dozens of other companies cancels it out.
- Raincoat's market risk
- A recession that makes everyone buy less of everything. Every other stock you own feels it too.
Adding stocks
Here's a typical single stock: expected return 10%, standard deviation 40%, twice as wild as the whole market. Spread your money evenly across more stocks like it, and the unique risk melts away. The market risk doesn't. Slide to add stocks.
- 1 stock
- 40% standard deviation.
- 10 stocks
- About 23%. Most of the unique risk is gone.
- 30 stocks
- About 21%. Close to the floor: the market's own 20%, which no amount of mixing removes.
What you're looking at: how risky your portfolio is (standard deviation, up the side) as you own more stocks (along the bottom), with the money split evenly. The dashed line is market risk at 20%, the floor. The gap between the curve and the floor is unique risk. Every portfolio here still expects 10%.
Only market risk gets paid
If anyone can delete unique risk for free by diversifying, nobody has to pay you for carrying it. So the risk premium from Lesson 14.1 only rewards market risk, the part measured by beta in the CAPM (Lesson 13.3). Holding one stock means taking extra risk with no extra expected return.
- One stock vs. 30
- Both expect 10%. One swings 40%, the other about 21%. The extra 19 points of swing earn you nothing.
Two minutes. Just listen.
Tap any line to jump to it.
Spread it out.
Eight questions about mixing investments. Each one gives you the facts. One try each.
What you're looking at: made-up companies and events. Each lists the facts, then asks one question.
The logic, step by step.
Checking whether a portfolio is diversified takes four steps.
Step 1: How many companies?
- One stock
- 40% swing. Thirty stocks: about 21%.
Step 2: Do they move together?
- Raincoat and Sunny
- Correlation −1: the mix never moves.
Step 3: Different industries?
- The weather
- Two rain gear makers would both lose in a sunny summer.
Step 4: What's left?
- The floor
- 20%. Lower it further by mixing in bonds or T-bills (Lesson 14.1), not more stocks.
Worked example: all in on your employer
Jordan works at a regional grocery chain and has $100,000 saved. Here are the facts:
- Jordan's plan: put it all in the chain's stock, because "I know this company."
- The chain's stock: expected 10%, standard deviation 40%.
- An index fund: expected 10%, standard deviation 20%.
- Same expected return. Both expect 10%, so Jordan gains nothing on average by picking the one stock.
- A typical bad year, one stock. 10% − 40% = −30%: $100,000 × 0.70 = $70,000, a $30,000 loss.
- A typical bad year, index fund. 10% − 20% = −10%: $100,000 × 0.90 = $90,000, a $10,000 loss.
- The hidden link. If the chain struggles, Jordan's paycheck is at risk too. The job and the savings would fall together: a correlation close to +1.
- The answer. Move most of it into a diversified fund. Many Enron employees learned this in 2001, when the company collapsed and took both their jobs and their company-stock savings.
Salmon run a portfolio.
Bristol Bay, Alaska, has one of the world's biggest sockeye salmon runs. It isn't one population but hundreds, each spawning in its own stream, lake or river. In any year, some do well and others do poorly. Scientists found that the total catch is about 2 times steadier than it would be from a single population, and that without this mix, fishing would have to be shut down about 10 times as often. They named it the portfolio effect.
What you're looking at: an illustration, not data. Four streams, each with a different number of salmon this year, flowing into one bay. Some streams are crowded and others have few fish, but the bay's total stays fairly steady.
Why this sticks. No single stream is reliable, but together they are. That's exactly why owning hundreds of companies in an index fund is steadier than owning one.
The page you'd copy down.
- Diversification: spread money across investments that don't move together. $5,000 Raincoat + $5,000 Sunny = $11,000 either way.
- Correlation: −1 (opposite) to +1 (lockstep). Two 20%-risk stocks, 50/50: +1 → 20%, 0 → about 14%, −1 → 0%.
- Unique risk: one company's surprises. Diversification removes it.
- Market risk: recessions, rate jumps, crises. Can't be diversified away. 20% floor.
- Adding stocks: 1 stock 40%, 10 about 23%, 30 about 21%, all expecting 10%.
- Only market risk is paid (beta). Extra unique risk earns nothing.
- Don't bet your job and savings on one company.
Fill in the blanks
Grab a friend or a study group.
Find the opposites
Each person names a business. The group tries to find another business that does well exactly when the first one struggles.
Dice portfolio
Roll one die 10 times and track the results. Then roll five dice 10 times and track the average. Which bounces around less, and why?
Look inside a fund
Look up an S&P 500 index fund's top holdings and industries. How much is in its single biggest company? Its biggest industry?
Just you and your money.
These stay on this device. Nobody else sees them.
Exam-style questions.
Written the way a college exam would ask them. Each right answer on the first try is worth 10 xp.
On the job: you're a financial advisor
A new client asks you to review their savings. Here's the situation:
- Total savings: $200,000.
- In their employer's stock: $160,000. The rest, $40,000, is in an S&P 500 index fund.
- The employer's stock: expected 10%, standard deviation 40%.
- The index fund: expected 10%, standard deviation 20%.
- Their job: at the same company.
Your task: what share of their savings is in one company? What would a typical bad year cost each part? What would you recommend, and why?
See a model answer
Concentration: $160,000$200,000 = 80% in one company, the same company that pays their salary.
A typical bad year: the employer's stock at 10% − 40% = −30% loses $160,000 × 0.30 = $48,000. The index fund at 10% − 20% = −10% loses $40,000 × 0.10 = $4,000.
If it were all in the index fund: a typical bad year would cost $200,000 × 0.10 = $20,000, with the same 10% expected return.
Recommendation: sell most of the employer stock over time, keeping no more than about 10% in it, and move the rest into a diversified fund. They give up no expected return, cut their risk sharply, and stop tying their savings to their paycheck. Check for taxes on the gains before selling.
Many bets beat one.
What you're looking at: a map of where this lesson fits in the course. Read it left to right: the lessons it builds on, this lesson in the middle, and the lesson that comes next.
- Back · Unit 14Risk and return
- Back · Unit 5Index funds and the S&P 500
- Back · Unit 13The cost of capital
- You are hereDiversification
- Next · Unit 14How bonds work