Risk vs Reward

Show your work for each problem.

1.
If an investment has high potential returns, what can you generally expect about its risk?
1. a)Risk is unrelated to return
2. b)No risk
3. c)High risk
4. d)Low risk
Answer: High risk
Higher potential returns always come with higher risk. This is the fundamental trade-off in investing - you cannot expect high returns without accepting the possibility of significant losses.
2.
If the potential gain on a trade is 200 dollars and the potential loss is 50 dollars, what is the risk-reward ratio? (Enter as a whole number)
Answer: 4
. The risk-reward ratio is 4:1, meaning you could gain 4 dollars for every 1 dollar at risk. This is a favorable ratio.
3.
What does a higher standard deviation indicate about an investment?
1. a)More volatility (higher risk)
2. b)Higher guaranteed returns
3. c)Less volatility (lower risk)
4. d)Lower expected returns
Answer: More volatility (higher risk)
A higher standard deviation means the investment's returns vary more from year to year. This means more volatility - the investment is less predictable and therefore riskier.
4.
A stock has an expected return of 15% and a standard deviation of 25%. What is its risk-adjusted return ratio? (Round to 2 decimal places)
Answer: 0.60
. This means you get 0.60% return for every 1% of risk (standard deviation) you take on.
5.
You're comparing two investments. Investment X has a 10% expected return with 20% standard deviation. Investment Y has an 8% expected return with 10% standard deviation. Which has the better risk-adjusted return?
Answer: Y
1. Calculate the risk-adjusted return for Investment X: 10 / 20 = ? 0.5
2. Calculate the risk-adjusted return for Investment Y: 8 / 10 = ? 0.8
3. Which ratio is higher: 0.5 or 0.8? 0.8
4. Which investment has the better risk-adjusted return? (X or Y) Y
6.
A trader is considering a trade with a potential gain of 80 dollars and a potential loss of 40 dollars. What is the risk-reward ratio, and is this typically considered favorable?
1. a)2:1, No it's not favorable
2. b)2:1, Yes it's favorable
3. c)1:2, Yes it's favorable
4. d)1:2, No it's not favorable
Answer: 2:1, Yes it's favorable
, so the ratio is 2:1. Professional traders typically aim for at least 2:1, making this a favorable trade setup.
7.
An investment has annual returns of 6%, 10%, 4%, 8%, and 12% over 5 years. What is the mean (average) return? (Enter as a percentage without the % sign)
Answer: 8
. The average annual return is 8%.
8.
You buy a stock at 100 dollars, set a stop-loss at 90 dollars, and target a sale price of 130 dollars. Calculate the risk-reward ratio.
Answer: 3
1. What is the potential gain? (Target price - Buy price: 130 - 100) 30
2. What is the potential loss? (Buy price - Stop-loss: 100 - 90) 10
3. What is the risk-reward ratio? (30 / 10) 3
9.
Someone near retirement should typically prefer which type of investment?
1. a)Lower risk, lower return
2. b)Higher risk, higher return
3. c)Any investment is equally suitable
4. d)Only cryptocurrency
Answer: Lower risk, lower return
People near retirement typically prefer lower-risk investments because they don't have time to wait for markets to recover from potential crashes. They need stability to protect the savings they'll soon need to live on.
10.
Calculate the variance for these investment returns: 2%, 8%, 4%, 6%, 10%. The mean is 6%.
Answer: 8
1. Find (2 - 6)^2 16
2. Find (8 - 6)^2 4
3. Find (4 - 6)^2 4
4. Find (6 - 6)^2 0
5. Find (10 - 6)^2 16
6. Sum all squared deviations: 16 + 4 + 4 + 0 + 16 = ? 40
7. Divide by the number of values (5): 40 / 5 = ? 8
11.
If the variance is 8 (from the previous problem), what is the standard deviation? (Round to 2 decimal places)
Answer: 2.83
. This means returns typically deviate about 2.83 percentage points from the 6% average.
12.
If someone promises you 50% annual returns with "zero risk," what should you think?
1. a)Risk and return are unrelated, so this is possible
2. b)It sounds like a great opportunity
3. c)Only moderately risky investments can have high returns
4. d)It's likely a scam - high returns always come with high risk
Answer: It's likely a scam - high returns always come with high risk
The promise of very high returns with no risk is the classic sign of a scam (like Ponzi schemes). Legitimate high-return investments always come with significant risk. If someone claims otherwise, they're either lying or don't understand investing.
13.
Investment A: 12% return, 15% standard deviation. Investment B: 9% return, 6% standard deviation. Calculate the risk-adjusted return for each and determine which is better.
Answer: B
1. Calculate risk-adjusted return for A: 12 / 15 = ? 0.8
2. Calculate risk-adjusted return for B: 9 / 6 = ? 1.5
3. Which is higher: 0.8 or 1.5? 1.5
4. Which investment has better risk-adjusted return? (A or B) B
14.
What does volatility in investing refer to?
1. a)The total return of an investment
2. b)The company's profit margin
3. c)How much the price fluctuates over time
4. d)The minimum investment required
Answer: How much the price fluctuates over time
Volatility measures how much an investment's price goes up and down over time. High volatility means big swings - the price might jump 10% one day and drop 8% the next. This unpredictability is what makes volatile investments risky.
15.
A trade has a 60% chance of succeeding with a 100 dollar gain, and a 40% chance of failing with a 75 dollar loss. What is the expected value? (Enter as a number, positive or negative)
Answer: 30
Expected value = . On average, you'd expect to make 30 dollars per trade with this setup.
16.
An investment has returns of -5%, 12%, 8%, -2%, and 17% over 5 years. Calculate the mean return and determine if this investment is more or less volatile than one with a standard deviation of 10%.
Answer: less
1. Calculate the mean: (-5 + 12 + 8 + -2 + 17) / 5 = ? 6
2. Calculate (-5 - 6)^2 = ? 121
3. Calculate (12 - 6)^2 = ? 36
4. Calculate (8 - 6)^2 = ? 4
5. Calculate (-2 - 6)^2 = ? 64
6. Calculate (17 - 6)^2 = ? 121
7. Variance = (121 + 36 + 4 + 64 + 121) / 5 = ? 69.2
8. Standard deviation = sqrt(69.2) ≈ ? (round to 1 decimal) 8.3
9. Is 8.3% more or less than 10%? (more/less) less