Teacher Guide: Risk vs Reward
Learn how risk and potential return are connected in investing, and how to evaluate whether an investment makes sense for your goals.
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Class quiz
10 questions on Investing Basics. Students join with a name, you see everyone's score.
For Teachers
- Explain the fundamental relationship between risk and reward in investing
- Calculate and interpret standard deviation as a measure of investment risk
- Compute risk-reward ratios for investment decisions
- Compare investments using risk-adjusted returns
- Apply risk-reward analysis to real-world financial decisions
- • Understanding of percentages and percent change
- • Basic knowledge of mean (average) calculation
- • Familiarity with square roots
- • Understanding of basic investment concepts (stocks, bonds, returns)
- 1. If you had 1000 dollars to invest for 20 years, how much risk would you be comfortable with? Why?
- 2. Why do you think some people invest in very risky assets like cryptocurrency?
- 3. A lottery ticket has a terrible risk-reward ratio, yet millions of people buy them. Why?
- 4. How might your risk tolerance change as you get older?
Past high returns guarantee future high returns
Risk only means losing money
For Struggling Students:
- • Focus on the 2x2 concept: low risk/low reward vs high risk/high reward
- • Use simple risk-reward ratios with whole numbers (3:1, 2:1)
- • Provide step-by-step scaffolding for standard deviation calculations
For On-Level Students:
- • Calculate risk-adjusted returns for multiple investments
- • Analyze real investment options using historical data
- • Compare different portfolio allocations
For Advanced Students:
- • Explore the Sharpe ratio (excess return per unit of risk)
- • Research beta and systematic vs unsystematic risk
- • Analyze how correlation affects portfolio risk
- HSS.ID.A.2 (CCSS.MATH.CONTENT.HSS.ID.A.2)
Use statistics appropriate to the shape of the data distribution to compare center and spread
- HSS.ID.A.3 (CCSS.MATH.CONTENT.HSS.ID.A.3)
Interpret differences in shape, center, and spread in the context of the data sets
- MP.4 (CCSS.MATH.PRACTICE.MP4)
Model with mathematics - apply mathematics to solve problems in everyday life
- visualRisk-Return Graph
Interactive chart showing different investments plotted by risk and expected return
- activityPortfolio Simulator
Students build portfolios and see how different risk levels affect outcomes
- worksheetRisk-Reward Calculations
Practice calculating standard deviation and risk-reward ratios
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Definition
Worked Examples
Investment A has an expected return of 12% with a standard deviation of 20%. Investment B has an expected return of 6% with a standard deviation of 8%. Which has a better risk-adjusted return?
Calculate the return per unit of risk for Investment A
→ 0.60 return per unit of risk
Calculate the return per unit of risk for Investment B
→ 0.75 return per unit of risk
Compare the ratios
, so Investment B provides more return for each unit of risk taken → B has better risk-adjusted return
Answer: Investment B has a better risk-adjusted return (0.75 vs 0.60). Even though A has higher potential returns, B gives you more return for each unit of risk you take.
Common Mistakes
Thinking high returns guarantee high risk is worth taking
Why it's wrong: Expected returns are not guaranteed. A volatile investment might have great returns on average but could lose significantly in any given year.
Correct: Compare risk-adjusted returns. Ask: 'How much return am I getting per unit of risk?'
Assuming low-risk investments are always the best choice
Why it's wrong: Very safe investments (like savings accounts) may not keep pace with inflation, meaning your money loses purchasing power over time.
Correct: Match your risk level to your time horizon and goals. Long-term investors can often afford more risk.
Confusing volatility with permanent loss
Why it's wrong: A stock dropping 20% isn't a loss until you sell. Volatility is short-term price swings; actual loss only occurs when you realize it.
Correct: Understand that volatility is normal. Long-term investors can often ride out short-term drops.
Why It Matters
- Choosing investments: Should you buy stocks, bonds, or keep money in savings?
- Setting expectations: Higher potential returns always come with higher risk
- Avoiding scams: If something promises high returns with no risk, it's likely too good to be true
- Long-term planning: Young investors can often afford more risk; those near retirement typically want less
Real World Applications
Choosing Between Savings Account and Index Fund
A savings account might offer 2% return with virtually no risk, while a stock index fund might average 8% but with significant year-to-year variation.
Example:
Over 10 years, 1000 dollars at 2% becomes about 1219 dollars. At 8%, it becomes about 2159 dollars - but with years of gains and losses along the way.
You have 5000 dollars to invest. A savings account pays 2% guaranteed. A stock fund has returned an average of 10% but with a standard deviation of 15%.
What is the risk-adjusted return ratio for the stock fund?
Step 1: Write the mathematical expression
Divide expected return by standard deviation:
Evaluating a Trading Opportunity
Day traders constantly evaluate risk-reward ratios before entering trades. A good trader rarely takes a trade with less than a 2:1 reward-to-risk ratio.
Example:
If a trader risks 100 dollars on a trade, they should aim to gain at least 200 dollars to make the trade worthwhile over time.
You're considering buying a stock at 50 dollars. You set a stop-loss at 45 dollars (5 dollars risk) and a target price of 65 dollars.
What is the risk-reward ratio of this trade?
Step 1: Write the mathematical expression
Potential gain divided by potential loss:
Key Takeaways
- 1Risk and reward are directly connected: higher potential returns require accepting higher risk
- 2Standard deviation () measures how much returns vary from the average (volatility)
- 3Risk-reward ratio = Potential Gain / Potential Loss; ratios above 2:1 are generally favorable
- 4Risk-adjusted return compares return per unit of risk, helping compare different investments fairly
- 5Your appropriate risk level depends on your time horizon, goals, and ability to handle losses
Frequently Asked Questions
What is a 'good' risk-reward ratio?
Can I avoid risk entirely in investing?
Why would anyone choose lower returns?
Glossary
- Risk
- The uncertainty of investment returns; the possibility of losing money or earning less than expected
- Reward (Return)
- The gain or profit from an investment, usually expressed as a percentage
- Standard deviation
- A statistical measure of how much values spread from the average; higher values indicate more volatility
- Volatility
- The degree to which an investment's price fluctuates over time
- Risk-reward ratio
- The potential profit divided by the potential loss; helps evaluate if a trade is worth taking
- Risk-adjusted return
- Return divided by risk (standard deviation); allows fair comparison of investments with different risk levels
- Risk tolerance
- An investor's ability and willingness to accept potential losses in exchange for potential gains