Finance Quiz: Beta And Systematic Risk
20 questions · exam conditions
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Beta And Systematic RiskQuestion 1 of 20

A gold mining stock has a beta of -0.3. The expected return on the market is 11%, and the risk-free rate is 3%. According to the Capital Asset Pricing Model (CAPM), what is the expected return for this stock?

-0.3%
0.6%
3.0%
5.4%
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Finance Quiz

Finance Quiz: Beta And Systematic Risk

Practice Beta And Systematic Risk in Finance with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Beta And Systematic Risk, giving you a quick way to practice the rules, question types, and explanations that matter most for Finance.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

A gold mining stock has a beta of -0.3. The expected return on the market is 11%, and the risk-free rate is 3%. According to the Capital Asset Pricing Model (CAPM), what is the expected return for this stock?

  1. -0.3%
  2. 0.6% (correct answer)
  3. 3.0%
  4. 5.4%
Explanation: The CAPM formula is E(Ri)=Rf+βi[E(Rm)−Rf]E(R_i) = R_f + \beta_i [E(R_m) - R_f]. Plugging in the given values: E(Ri)=3%+(−0.3)[11%−3%]E(R_i) = 3\% + (-0.3) [11\% - 3\%] E(Ri)=3%+(−0.3)[8%]E(R_i) = 3\% + (-0.3) [8\%] E(Ri)=3%−2.4%E(R_i) = 3\% - 2.4\% E(Ri)=0.6%E(R_i) = 0.6\%. Common errors include: treating beta as positive rather than negative, leading to 3% + 2.4% = 5.4% (choice D), or multiplying beta by the market return instead of the risk premium, leading to 3% + (-0.3)(11%) = -0.3% (choice A).

Question 2

A regression of a stock's historical monthly returns against the market's returns produces a beta of 1.3 and an R-squared value of 0.70. Which of the following is the most accurate interpretation of these results?

  1. The correlation between the stock and the market is 1.3, and 70% of the risk is unsystematic.
  2. Market movements explain 30% of the stock's returns, and the stock has a systematic risk of 0.70.
  3. The stock is 30% more volatile than the market, and 70% of its total variance is attributable to market movements. (correct answer)
  4. The stock's return is expected to be 1.3% for every 1% return on the market, and its total risk is 70% systematic.
Explanation: When you encounter regression analysis in finance, you're looking at how well market movements explain a stock's behavior. Beta measures systematic risk (market sensitivity), while R-squared measures explanatory power. The correct interpretation starts with beta: a beta of 1.3 means the stock moves 1.3 times as much as the market in the same direction. If the market rises 10%, this stock typically rises 13%. This makes the stock 30% more volatile than the market (1.3 - 1.0 = 0.3 or 30% additional volatility). The R-squared of 0.70 means 70% of the stock's return variance is explained by market movements - this is the systematic portion of total risk. Answer C captures both interpretations correctly. Answer A confuses correlation with beta. Correlation ranges from -1 to +1, so 1.3 is impossible. Also, if R-squared is 0.70, then 70% of risk is systematic, not unsystematic. Answer B reverses the R-squared interpretation. If R-squared is 0.70, then 70% (not 30%) of returns are explained by market movements. Additionally, 0.70 represents the proportion of variance explained, not the systematic risk level itself. Answer D misinterprets beta as a return multiplier stating "1.3% for every 1%." Beta measures volatility relationship, not direct return calculation. While it's true that 70% of total risk is systematic, the return interpretation is incorrect. Remember: Beta measures relative volatility (systematic risk), while R-squared measures what percentage of a stock's variance comes from market movements versus company-specific factors.

Question 3

Two stocks, X and Y, have the exact same standard deviation of returns. The standard deviation of the market's returns is also equal to that of Stocks X and Y. However, Stock X has a correlation coefficient with the market of 0.9, while Stock Y has a correlation coefficient with the market of 0.6. Which of the following statements must be true?

  1. The total risk of Stock X is greater than the total risk of Stock Y.
  2. The betas of Stock X and Stock Y are equal because their standard deviations are equal.
  3. The unsystematic risk of Stock X is greater than that of Stock Y.
  4. The beta of Stock X is greater than the beta of Stock Y. (correct answer)
Explanation: This question tests your understanding of beta calculation and the relationship between systematic and unsystematic risk. When you see correlation coefficients and standard deviations together, think about how they combine to determine a stock's beta and risk components. Beta measures systematic risk and is calculated as: β=ρ×σstockσmarket\beta = \rho \times \frac{\sigma_{stock}}{\sigma_{market}}, where ρ is the correlation with the market. Since both stocks have identical standard deviations that equal the market's standard deviation, the formula simplifies to β=ρ×1=ρ\beta = \rho \times 1 = \rho. Therefore, Stock X has a beta of 0.9 while Stock Y has a beta of 0.6, making Stock X's beta higher. Looking at the wrong answers: Choice A is incorrect because total risk (standard deviation) is explicitly stated to be equal for both stocks. Choice B makes a common error—beta depends on both standard deviation AND correlation with the market, not just standard deviation alone. Choice C reverses the relationship: unsystematic risk equals total risk minus systematic risk. Since both stocks have equal total risk but Stock X has higher systematic risk (higher beta), Stock X actually has lower unsystematic risk than Stock Y. Remember this key insight: when comparing stocks with equal volatility, the one more highly correlated with the market will have higher beta (more systematic risk) but lower unsystematic risk. Beta captures only the market-related portion of a stock's risk—correlation determines how much of that risk moves with the market versus independently.

Question 4

A manufacturing company with a stable business has historically been financed entirely with equity and has an unlevered beta of 0.8. The company's board approves a major debt issuance to repurchase 30% of its outstanding shares. Assuming no corporate taxes, what is the most likely effect on the firm's asset beta and equity beta?

  1. Both the asset beta and the equity beta will increase.
  2. The asset beta will remain unchanged, but the equity beta will increase. (correct answer)
  3. The asset beta will increase, but the equity beta will remain unchanged.
  4. The asset beta will remain unchanged, but the equity beta will decrease.
Explanation: A firm's asset beta (unlevered beta) reflects the systematic risk of its underlying business operations. Changing the capital structure does not change the business operations, so the asset beta remains at 0.8. However, issuing debt increases the financial risk for equity holders. This additional financial leverage increases the systematic risk borne by shareholders, causing the equity beta (levered beta) to increase to a value greater than the asset beta.

Question 5

A conglomerate's beta has been historically calculated at 1.4 using 60 months of past data. The company just announced a major strategic restructuring, divesting its highly cyclical industrial machinery division and using the proceeds to acquire a large, stable portfolio of consumer food brands. What is the primary limitation of using the historical 1.4 beta for valuation purposes going forward?

  1. A 60-month period is too long to calculate a reliable beta; a 24-month period would be more accurate.
  2. The divestiture and acquisition will primarily affect the firm's unsystematic risk, which is not captured by beta.
  3. The historical beta reflects a business mix and systematic risk profile that is no longer representative of the firm's future. (correct answer)
  4. Any historical beta is a poor predictor of future beta, so it should be disregarded entirely in favor of management forecasts.
Explanation: When you encounter questions about beta in the context of major corporate restructuring, focus on what beta actually measures and whether the underlying business has fundamentally changed. Beta measures a company's systematic risk—how much the stock moves relative to the overall market. It's calculated using historical price data and reflects the business mix and risk profile during that historical period. When a company undergoes major structural changes like divesting cyclical divisions and acquiring stable businesses, the fundamental nature of the company changes, making historical beta potentially obsolete. The historical 1.4 beta reflects the risk profile of the old business mix, including the highly cyclical industrial machinery division. After restructuring toward stable consumer food brands, the company's systematic risk profile will likely be quite different—probably lower and less volatile. Using the old beta of 1.4 would overstate the company's systematic risk going forward. Looking at the wrong answers: A) is incorrect because 60 months is actually a standard and appropriate timeframe for calculating beta—longer periods provide more data points and reduce noise. B) misses the point because this restructuring primarily affects systematic risk (the core business profile), not just unsystematic risk. D) goes too far by suggesting all historical betas should be disregarded; the issue isn't that historical data is useless, but that it's no longer representative after major structural changes. Study tip: Remember that beta reflects the business you're in, not just statistical history. Major business changes require beta adjustments or comparable company analysis.

Question 6

An analyst observes that for a particular stock, the covariance of its returns with the market's returns has recently increased. Simultaneously, the variance of the market's returns has decreased. Assuming no other changes, what is the net effect on the stock's beta?

  1. The beta will decrease.
  2. The beta will increase. (correct answer)
  3. The beta will remain unchanged.
  4. The effect on beta is indeterminate without knowing the magnitudes of the changes.
Explanation: The formula for beta is βi=Cov(Ri,Rm)Var(Rm)\beta_i = \frac{\text{Cov}(R_i, R_m)}{\text{Var}(R_m)}. The question states that the numerator (covariance) has increased, and the denominator (market variance) has decreased. Both of these changes will cause the value of the fraction to increase. Therefore, the stock's beta will unambiguously increase.

Question 7

A gold mining stock has a beta of -0.3. The expected return on the market is 11%, and the risk-free rate is 3%. According to the Capital Asset Pricing Model (CAPM), what is the expected return for this stock?

  1. -0.3%
  2. 0.6% (correct answer)
  3. 3.0%
  4. 5.4%
Explanation: The CAPM formula is E(Ri)=Rf+βi[E(Rm)−Rf]E(R_i) = R_f + \beta_i [E(R_m) - R_f]. Plugging in the given values: E(Ri)=3%+(−0.3)[11%−3%]E(R_i) = 3\% + (-0.3) [11\% - 3\%] E(Ri)=3%+(−0.3)[8%]E(R_i) = 3\% + (-0.3) [8\%] E(Ri)=3%−2.4%E(R_i) = 3\% - 2.4\% E(Ri)=0.6%E(R_i) = 0.6\%. Common errors include: treating beta as positive rather than negative, leading to 3% + 2.4% = 5.4% (choice D), or multiplying beta by the market return instead of the risk premium, leading to 3% + (-0.3)(11%) = -0.3% (choice A).

Question 8

A portfolio manager allocates 150% of the portfolio's capital to a mutual fund with a beta of 1.2. The additional 50% of capital is raised by borrowing at the risk-free rate. What is the beta of this leveraged portfolio?

  1. 1.20
  2. 1.50
  3. 1.80 (correct answer)
  4. 0.60
Explanation: The portfolio is a weighted combination of the mutual fund and the risk-free asset. The weight in the mutual fund is +1.5 (150%), and the weight in the risk-free asset (borrowing) is -0.5 (-50%). The beta of the risk-free asset is 0. The portfolio beta is calculated as: βp=wfundβfund+wrfβrf\beta_p = w_{fund}\beta_{fund} + w_{rf}\beta_{rf} βp=(1.5)(1.2)+(−0.5)(0)\beta_p = (1.5)(1.2) + (-0.5)(0) βp=1.8+0=1.80\beta_p = 1.8 + 0 = 1.80

Question 9

A publicly traded technology firm announces that its primary supplier has unexpectedly declared bankruptcy, causing major disruptions to its production line. Assuming the overall market conditions remain stable, what is the most likely immediate impact on the technology firm's systematic and unsystematic risk?

  1. Systematic risk will increase, while unsystematic risk will remain largely unchanged.
  2. Unsystematic risk will increase, while systematic risk will remain largely unchanged. (correct answer)
  3. Both systematic and unsystematic risk will increase significantly.
  4. Both systematic and unsystematic risk will decrease due to investor flight to safety.
Explanation: The supplier bankruptcy is a company-specific event. Such events increase the firm's idiosyncratic, or unsystematic, risk. Systematic risk, which is measured by beta, reflects the firm's sensitivity to broad market movements (e.g., economic cycles, interest rate changes). A supplier issue does not fundamentally alter this sensitivity to market-wide factors, so systematic risk remains largely unchanged.

Question 10

A traditionally conservative, domestic-focused utility company announces a new strategy involving significant investment in international infrastructure projects and the acquisition of a renewable energy technology firm. How are these strategic moves most likely to affect the utility's beta?

  1. The beta will likely decrease due to the benefits of geographic and product diversification.
  2. The beta will likely increase due to exposure to global economic cycles and a more volatile technology sector. (correct answer)
  3. The beta will remain unchanged because the core utility business provides a stabilizing influence on the firm.
  4. The unsystematic risk will decrease significantly, causing a corresponding decrease in the company's beta.
Explanation: While these moves might diversify the firm's operations (reducing unsystematic risk), they also increase its sensitivity to systematic risk factors. International projects expose the firm to global economic cycles and currency risk, while a technology acquisition brings it into a more cyclical, higher-growth sector. Both factors tend to increase a firm's correlation with the overall market, thus increasing its beta.

Question 11

An analyst is comparing the expected systematic risk of a large, publicly-owned water utility company and a manufacturer of high-end, luxury sports cars. Which statement regarding their probable betas is most accurate?

  1. The luxury car manufacturer is likely to have a beta significantly greater than 1, while the utility has a beta significantly less than 1. (correct answer)
  2. Both companies are likely to have betas close to 1, as they are large, established firms in the economy.
  3. The utility company is likely to have a negative beta because its services are essential, while the car company will have a positive beta.
  4. The car company will have a beta near 1, while the utility company will have a beta near 0, similar to a risk-free asset.
Explanation: A company's beta is heavily influenced by the cyclicality of its industry. Luxury goods, like high-end sports cars, are highly cyclical; sales are strong during economic booms and weak during recessions. This results in a high beta (greater than 1). Conversely, utility companies provide essential services, and demand is relatively stable regardless of the economic cycle. This results in a low beta (less than 1, but still positive).

Question 12

Portfolio A and Portfolio B are both well-diversified. Portfolio A has a beta of 1.3 and an expected return of 12%. Portfolio B has a beta of 0.7 and an expected return of 8%. The risk-free rate is 4%. According to the Capital Asset Pricing Model (CAPM), which conclusion is most appropriate?

  1. Both portfolios are correctly priced relative to the market.
  2. Both portfolios are underpriced relative to the market.
  3. Portfolio A is overpriced, and Portfolio B is underpriced.
  4. Portfolio A is underpriced, and Portfolio B is overpriced. (correct answer)
Explanation: When you encounter CAPM questions comparing portfolio pricing, you need to calculate what each portfolio's expected return should be according to the model, then compare that to the actual expected returns given. The CAPM formula is: E(R)=Rf+β[E(Rm)−Rf]E(R) = R_f + \beta[E(R_m) - R_f] First, you need to find the market risk premium. Since both portfolios should be correctly priced if they're on the Security Market Line, you can use either portfolio to solve for the market return. Using Portfolio A: 12%=4%+1.3[E(Rm)−4%]12\% = 4\% + 1.3[E(R_m) - 4\%]. Solving: 8%=1.3[E(Rm)−4%]8\% = 1.3[E(R_m) - 4\%], so E(Rm)=10.15%E(R_m) = 10.15\%. Now check what each portfolio's return should be:
  • Portfolio A: E(R)=4%+1.3(10.15%−4%)=12%E(R) = 4\% + 1.3(10.15\% - 4\%) = 12\% (matches actual)
  • Portfolio B: E(R)=4%+0.7(10.15%−4%)=8.31%E(R) = 4\% + 0.7(10.15\% - 4\%) = 8.31\% (actual is only 8%)
Portfolio A offers exactly what CAPM predicts, so it's correctly priced. Portfolio B offers less return (8%) than CAMP requires (8.31%), making it overpriced—you're paying too much for the returns you'll receive. However, this creates an arbitrage opportunity, so Portfolio A is actually underpriced relative to this mispricing. Answer A is wrong because Portfolio B isn't correctly priced. Answer B is wrong because Portfolio B is overpriced, not underpriced. Answer C incorrectly identifies Portfolio A as overpriced when it's actually underpriced. Remember: when a portfolio's actual return is below its CAPM-required return, it's overpriced (expensive for what you get). Always solve for the implied market return first when comparing multiple assets.

Question 13

An investment fund is designed to perfectly replicate the S&P 500 index by holding all constituent stocks in their exact market-capitalization weights. If an analyst uses the S&P 500 index as the proxy for the overall market portfolio, what is the expected beta of this investment fund?

  1. Exactly 1.0. (correct answer)
  2. Approximately 1.0, but it will fluctuate based on daily market volatility.
  3. Exactly 0, because its unsystematic risk has been completely diversified away.
  4. Greater than 1.0, because it is a managed fund with expenses.
Explanation: Beta measures the volatility of an asset or portfolio in relation to the market. The market portfolio itself serves as the benchmark. By definition, the beta of the market portfolio relative to itself is 1.0. Since the fund perfectly replicates the market proxy (the S&P 500), its movements will be identical to the market's movements, and its beta will be exactly 1.0.

Question 14

An investor has constructed a portfolio containing 40 different stocks across a variety of economic sectors. A colleague remarks, 'Because your portfolio is so well-diversified, you have effectively eliminated the risk of your investment.' Which of the following provides the most accurate critique of this statement?

  1. The statement is largely correct, as holding more than 30 stocks is generally sufficient to eliminate nearly all investment risk.
  2. The statement is incorrect because diversification increases a portfolio's exposure to systematic risk.
  3. The statement is incorrect because only portfolios managed by professionals can truly eliminate risk.
  4. The statement is incorrect; while diversification greatly reduces unsystematic risk, the portfolio is still exposed to systematic, or market, risk. (correct answer)
Explanation: This question addresses a common misconception about diversification. Diversification is highly effective at reducing or eliminating unsystematic (firm-specific) risk. However, it cannot eliminate systematic (market) risk, which affects all assets in the market to some degree. Events like recessions, interest rate changes, or geopolitical crises will still impact the value of the diversified portfolio.

Question 15

An investor holds a single, highly volatile stock with a beta of 0.8 and a standard deviation of 50%. The investor then adds 29 other stocks from a wide range of industries to create a well-diversified portfolio. Which of the following statements most accurately describes the risk characteristics of the new portfolio compared to the original single-stock investment?

  1. The portfolio's beta will be significantly lower than 0.8 due to the reduction of unsystematic risk.
  2. The portfolio's total risk will be substantially lower, primarily due to the reduction of unsystematic risk. (correct answer)
  3. The portfolio's total risk will be approximately equal to the average standard deviation of the 30 individual stocks.
  4. The portfolio's systematic risk will increase as more assets are added to the portfolio.
Explanation: Diversification's primary benefit is the reduction of firm-specific (unsystematic) risk. By adding 29 other stocks, the high unsystematic risk component of the original stock (evidenced by its high standard deviation) is averaged out with the others, leading to a much lower total portfolio risk (standard deviation). The portfolio's beta will be the weighted average of the 30 stocks' betas and is not necessarily lower than 0.8; it could be higher or lower depending on the betas of the added stocks. Systematic risk is not reduced by diversification.

Question 16

An investor wishes to construct a portfolio with a target beta of 1.2. The investor has access to two assets: a broad market index fund with a beta of 1.0, and a risk-free asset (e.g., Treasury bills) with a beta of 0. To achieve the target beta, the investor must:

  1. invest 80% in the market index and 20% in the risk-free asset.
  2. invest 120% in the risk-free asset and short the market index by 20%.
  3. invest 20% in the market index and 80% in the risk-free asset.
  4. invest 120% in the market index and borrow 20% at the risk-free rate. (correct answer)
Explanation: When you encounter portfolio beta questions, you're working with weighted averages. The portfolio beta equals the sum of each asset's weight multiplied by its beta: βp=w1β1+w2β2\beta_p = w_1\beta_1 + w_2\beta_2. To achieve a beta of 1.2 with a market index (beta = 1.0) and risk-free asset (beta = 0), you need: 1.2=wmarket(1.0)+wrisk−free(0)1.2 = w_{market}(1.0) + w_{risk-free}(0). This simplifies to 1.2=wmarket1.2 = w_{market}, meaning you need 120% in the market index. Since portfolio weights must sum to 100%, if you invest 120% in the market index, you must have -20% in the risk-free asset. A negative weight means borrowing money at the risk-free rate to invest more in the market index. This confirms answer D is correct. Answer A (80% market, 20% risk-free) gives a beta of 0.8, which is too low. Answer B makes no mathematical sense—you can't invest 120% in an asset with zero beta and expect any positive beta outcome. Answer C (20% market, 80% risk-free) produces a beta of only 0.2, far below the 1.2 target. Remember this key principle: to achieve a portfolio beta above 1.0 using a market index (beta = 1.0), you must use leverage by borrowing at the risk-free rate. Any combination that includes positive weights in risk-free assets will always produce a beta below 1.0, making it impossible to reach higher target betas.

Question 17

An analyst is comparing two stocks. Stock A has a beta of 1.4 and a standard deviation of 35%. Stock B has a beta of 0.9 and a standard deviation of 40%. Which of the following statements is the most accurate?

  1. Stock B has higher systematic risk and higher total risk.
  2. Stock A has higher systematic risk, while Stock B has higher total risk. (correct answer)
  3. For a well-diversified investor, Stock B is the riskier investment.
  4. Stock A has higher total risk and higher unsystematic risk.
Explanation: Systematic risk is measured by beta. Stock A's beta (1.4) is higher than Stock B's (0.9), so Stock A has higher systematic risk. Total risk is measured by standard deviation. Stock B's standard deviation (40%) is higher than Stock A's (35%), so Stock B has higher total risk. A well-diversified investor is primarily concerned with systematic risk, making Stock A riskier in a portfolio context.

Question 18

An analyst is comparing the expected systematic risk of a large, publicly-owned water utility company and a manufacturer of high-end, luxury sports cars. Which statement regarding their probable betas is most accurate?

  1. The luxury car manufacturer is likely to have a beta significantly greater than 1, while the utility has a beta significantly less than 1. (correct answer)
  2. Both companies are likely to have betas close to 1, as they are large, established firms in the economy.
  3. The utility company is likely to have a negative beta because its services are essential, while the car company will have a positive beta.
  4. The car company will have a beta near 1, while the utility company will have a beta near 0, similar to a risk-free asset.
Explanation: A company's beta is heavily influenced by the cyclicality of its industry. Luxury goods, like high-end sports cars, are highly cyclical; sales are strong during economic booms and weak during recessions. This results in a high beta (greater than 1). Conversely, utility companies provide essential services, and demand is relatively stable regardless of the economic cycle. This results in a low beta (less than 1, but still positive).

Question 19

A publicly traded technology firm announces that its primary supplier has unexpectedly declared bankruptcy, causing major disruptions to its production line. Assuming the overall market conditions remain stable, what is the most likely immediate impact on the technology firm's systematic and unsystematic risk?

  1. Systematic risk will increase, while unsystematic risk will remain largely unchanged.
  2. Unsystematic risk will increase, while systematic risk will remain largely unchanged. (correct answer)
  3. Both systematic and unsystematic risk will increase significantly.
  4. Both systematic and unsystematic risk will decrease due to investor flight to safety.
Explanation: The supplier bankruptcy is a company-specific event. Such events increase the firm's idiosyncratic, or unsystematic, risk. Systematic risk, which is measured by beta, reflects the firm's sensitivity to broad market movements (e.g., economic cycles, interest rate changes). A supplier issue does not fundamentally alter this sensitivity to market-wide factors, so systematic risk remains largely unchanged.

Question 20

An analyst observes that for a particular stock, the covariance of its returns with the market's returns has recently increased. Simultaneously, the variance of the market's returns has decreased. Assuming no other changes, what is the net effect on the stock's beta?

  1. The beta will decrease.
  2. The beta will increase. (correct answer)
  3. The beta will remain unchanged.
  4. The effect on beta is indeterminate without knowing the magnitudes of the changes.
Explanation: The formula for beta is βi=Cov(Ri,Rm)Var(Rm)\beta_i = \frac{\text{Cov}(R_i, R_m)}{\text{Var}(R_m)}. The question states that the numerator (covariance) has increased, and the denominator (market variance) has decreased. Both of these changes will cause the value of the fraction to increase. Therefore, the stock's beta will unambiguously increase.