Corporate Finance Quiz: Computing And Interpreting Beta
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Computing And Interpreting BetaQuestion 1 of 20

Stock A had a return of +2% in a period when the market's return was -4%. The risk-free rate during this period was 1%. Assuming this single period is representative of the stock's relationship with the market, which of the following is the most accurate conclusion about Stock A's beta?

Beta must be positive, but less than 1, because the stock's return was positive.
Beta must be negative, as the stock's excess return was positive while the market's excess return was negative.
Beta is approximately zero, indicating the stock's movements are independent of the market.
Beta cannot be determined without knowing the standard deviation of the stock and market returns.
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Corporate Finance Quiz

Corporate Finance Quiz: Computing And Interpreting Beta

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

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

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Question 1

Stock A had a return of +2% in a period when the market's return was -4%. The risk-free rate during this period was 1%. Assuming this single period is representative of the stock's relationship with the market, which of the following is the most accurate conclusion about Stock A's beta?

  1. Beta must be positive, but less than 1, because the stock's return was positive.
  2. Beta must be negative, as the stock's excess return was positive while the market's excess return was negative. (correct answer)
  3. Beta is approximately zero, indicating the stock's movements are independent of the market.
  4. Beta cannot be determined without knowing the standard deviation of the stock and market returns.
Explanation: Beta measures the covariance of a stock's excess returns with the market's excess returns. The stock's excess return is RA−Rf=2%−1%=+1%R_A - R_f = 2\% - 1\% = +1\%. The market's excess return is Rm−Rf=−4%−1%=−5%R_m - R_f = -4\% - 1\% = -5\%. Since the stock's excess return was positive when the market's excess return was negative, their covariance is negative, implying a negative beta. Conceptually, β≈Stock Excess ReturnMarket Excess Return=+1%−5%=−0.2\beta \approx \frac{\text{Stock Excess Return}}{\text{Market Excess Return}} = \frac{+1\%}{-5\%} = -0.2.

Question 2

A technology firm is currently all-equity financed and has a beta of 1.2. The company plans to change its capital structure to a debt-to-equity ratio of 0.5 by issuing debt and repurchasing shares. If the corporate tax rate is 30%, what will be the firm's new equity beta after the recapitalization?

  1. 0.89
  2. 1.20
  3. 1.62 (correct answer)
  4. 1.80
Explanation: This is a two-step process. First, determine the firm's asset beta (unlevered beta), which is unaffected by leverage. Since the firm is currently all-equity, its asset beta βU\beta_U is equal to its equity beta, 1.2. Second, relever this asset beta using the new capital structure with the Hamada formula: βL=βU[1+(1−t)(D/E)]\beta_L = \beta_U [1 + (1-t)(D/E)]. Plugging in the values: βL=1.2[1+(1−0.30)(0.5)]=1.2[1+(0.7)(0.5)]=1.2[1+0.35]=1.2(1.35)=1.62\beta_L = 1.2 [1 + (1 - 0.30)(0.5)] = 1.2 [1 + (0.7)(0.5)] = 1.2 [1 + 0.35] = 1.2(1.35) = 1.62.

Question 3

An investor's portfolio is currently valued at $100,000 and is fully invested in a market index fund with a beta of 1.2. The investor wants to achieve an overall portfolio beta of exactly 1.0 by investing additional funds in risk-free Treasury bills (which have a beta of 0). How much money must the investor invest in Treasury bills?

  1. $16,667
  2. $20,000 (correct answer)
  3. $25,000
  4. $120,000
Explanation: Let VTV_T be the total value of the new portfolio, and xx be the amount invested in Treasury bills. The total value will be \100,000 + x.Theweightoftheindexfundwillbe. The weight of the index fund will be w_{fund} = \frac{100,000}{100,000+x},andtheweightoftheT−billswillbe, and the weight of the T-bills will be w_{bills} = \frac{x}{100,000+x}.Theportfoliobetaequationis. The portfolio beta equation is \beta_p = w_{fund} \beta_{fund} + w_{bills} \beta_{bills}.Weset. We set \beta_p = 1.0:: 1.0 = \frac{100,000}{100,000+x}(1.2) + \frac{x}{100,000+x}(0).Thissimplifiesto. This simplifies to 1.0 = \frac{120,000}{100,000+x}.Solvingfor. Solving for x:: 100,000 + x = 120,000 \implies x = $20,000$.

Question 4

Stock A has a correlation of 0.6 with the market portfolio. The standard deviation of Stock A's returns is 30%, and the standard deviation of the market's returns is 20%. What is the beta of Stock A?

  1. 0.40
  2. 0.60
  3. 0.90 (correct answer)
  4. 1.50
Explanation: The formula for beta based on correlation and standard deviations is βi=Cov(Ri,Rm)σm2=ρi,mσiσmσm2=ρi,mσiσm\beta_i = \frac{\text{Cov}(R_i, R_m)}{\sigma_m^2} = \frac{\rho_{i,m} \sigma_i \sigma_m}{\sigma_m^2} = \rho_{i,m} \frac{\sigma_i}{\sigma_m}. Plugging in the given values: βA=0.6×0.300.20=0.6×1.5=0.90\beta_A = 0.6 \times \frac{0.30}{0.20} = 0.6 \times 1.5 = 0.90.

Question 5

A project has a beta of 0.5. The market risk premium is 6% and the risk-free rate is 2%. The project's own internal forecast predicts an expected return of 5.5%. What is the project's alpha, and what does it signify about the project's value?

  1. The project's alpha is +0.5%, indicating it is expected to generate a return above the level required for its systematic risk. (correct answer)
  2. The project's alpha is -0.5%, indicating that it is an undesirable investment that will destroy value.
  3. The project's required return is 5.5%, meaning its alpha is zero and it is a fairly priced investment.
  4. The project's alpha is +3.5%, indicating it is significantly undervalued relative to its risk.
Explanation: First, calculate the required rate of return for the project using the Capital Asset Pricing Model (CAPM): E[R]=Rf+β(E[Rm]−Rf)=2%+0.5(6%)=2%+3%=5.0%E[R] = R_f + \beta (E[R_m] - R_f) = 2\% + 0.5(6\%) = 2\% + 3\% = 5.0\%. Alpha is the difference between the project's expected return and its required return: α=Expected Return−Required Return=5.5%−5.0%=+0.5%\alpha = \text{Expected Return} - \text{Required Return} = 5.5\% - 5.0\% = +0.5\%. A positive alpha indicates that the project is expected to earn more than is required to compensate for its systematic risk, suggesting it is a value-creating (undervalued) investment.

Question 6

A financial analyst is tasked with estimating the cost of equity for a privately held software company. Which of the following approaches is the most appropriate method for determining the company's equity beta?

  1. Regress the private company's historical accounting earnings against historical S&P 500 returns to estimate a beta.
  2. Assume a beta of 1.0, as the company's specific risk is undiversifiable for its concentrated owners and best proxied by the market.
  3. Use the average equity beta of a group of publicly traded, comparable software companies without any adjustments.
  4. Unlever the equity betas of comparable public companies, average the resulting asset betas, and then relever this average using the private company's specific capital structure. (correct answer)
Explanation: Since the private company's stock is not traded, its beta cannot be estimated directly via regression. The standard 'pure-play' method is to identify publicly traded comparable firms, remove the effect of their financial leverage by calculating their asset (unlevered) betas, average these asset betas to get an estimate of the industry's business risk, and then apply the private company's own financial leverage (D/E ratio and tax rate) to this asset beta to find its appropriate equity beta.

Question 7

An analyst observes that a particular stock's returns consistently plot below the Security Market Line (SML). Which of the following statements is the most accurate description of this stock based on the Capital Asset Pricing Model?

  1. The stock has a positive alpha and is considered undervalued for its level of systematic risk.
  2. The stock has a negative alpha and is considered overvalued for its level of systematic risk. (correct answer)
  3. The stock is more volatile than the market, but its price is considered fair by the market.
  4. The stock's beta must be less than 1, indicating it is a defensive investment.
Explanation: The Security Market Line (SML) plots the required rate of return for an asset as a function of its beta. Assets that are fairly priced lie on the SML. Assets whose expected returns plot above the SML have a positive alpha and are considered undervalued. Assets whose expected returns plot below the SML have a negative alpha, meaning their expected return is insufficient to compensate for their level of systematic risk. Therefore, they are considered overvalued.

Question 8

An analyst estimates a company's historical beta to be 1.5 using five years of past data. However, the company recently sold a high-risk division (estimated asset beta of 2.0) that represented 20% of its total value and used the cash proceeds to pay down a significant portion of its debt. What adjustment should the analyst make to the historical beta of 1.5 for use in a forward-looking valuation?

  1. The analyst should adjust the beta upward to reflect the greater concentration in the remaining assets.
  2. No adjustment is needed, as the 1.5 historical beta is the most objective measure of the company's risk.
  3. The analyst should adjust the beta downward to reflect both a lower average business risk and reduced financial leverage. (correct answer)
  4. The analyst should adjust beta down for lower business risk but up for the debt paydown, likely resulting in a negligible net change.
Explanation: Historical beta reflects a company's past structure. Significant corporate events require adjustments for forward-looking analysis. Selling a high-risk division lowers the company's overall asset (business) risk. Using the proceeds to pay down debt reduces the debt-to-equity ratio, which lowers financial leverage. Both a decrease in business risk and a decrease in financial leverage will lead to a lower equity beta. Therefore, the analyst must adjust the historical 1.5 beta downward.

Question 9

Analyst A claims Stock X is riskier than Stock Y because Stock X has a standard deviation of returns of 40% while Stock Y's is 25%. Analyst B claims Stock Y is riskier because its beta is 1.5 while Stock X's is 0.8. In the context of the Capital Asset Pricing Model (CAPM) for a well-diversified investor, which statement is more accurate?

  1. Analyst A is more accurate, because standard deviation measures total risk, which is the most comprehensive risk metric.
  2. Analyst B is more accurate, because beta measures the non-diversifiable systematic risk that is priced by the market. (correct answer)
  3. Both analysts are correct, as standard deviation and beta are equally valid measures of the risk that determines expected return.
  4. Neither analyst is correct; the Sharpe ratio is the only definitive measure for comparing the riskiness of two stocks.
Explanation: The CAPM posits that investors are only compensated for bearing systematic risk, which is the risk that cannot be diversified away. Beta is the measure of this systematic risk. Standard deviation measures total risk (systematic + unsystematic). For a well-diversified investor, unsystematic risk has been eliminated, so the only relevant risk is systematic risk. Therefore, Analyst B's focus on beta as the measure of priced risk is the more accurate perspective within the CAPM framework.

Question 10

A firm with a debt-to-equity ratio of 0 is considering a project that will be financed entirely with debt, raising its D/E ratio to 0.4. The firm's current equity beta is 1.1, the project's asset beta is 1.5, and the tax rate is 25%. The project is small and will not materially change the firm's overall asset beta. What is the most appropriate beta to use when calculating the cost of equity for the firm as a whole after it accepts the project?

  1. 1.10, because the project is too small to affect the firm's overall risk profile.
  2. 1.43, based on levering the firm's original asset beta to the new D/E ratio. (correct answer)
  3. 1.50, because the project's risk determines the required return for the new capital raised.
  4. 1.95, based on levering the project's asset beta to the new D/E ratio.
Explanation: The question asks for the cost of equity for the firm as a whole. Since the project is small and does not materially change the firm's overall asset beta, we should use the firm's existing asset beta. The firm's current D/E is 0, so its asset beta (βU\beta_U) is equal to its equity beta, 1.1. After the project, the firm's D/E ratio will be 0.4. We must relever the firm's asset beta to this new D/E ratio to find the new equity beta. βL=βU[1+(1−t)(D/E)]=1.1[1+(1−0.25)(0.4)]=1.1[1+(0.75)(0.4)]=1.1[1+0.3]=1.1(1.3)=1.43\beta_L = \beta_U [1 + (1-t)(D/E)] = 1.1 [1 + (1-0.25)(0.4)] = 1.1 [1 + (0.75)(0.4)] = 1.1 [1 + 0.3] = 1.1(1.3) = 1.43.

Question 11

Company A and Company B operate in the same industry and have identical asset betas. Company A has a debt-to-equity ratio of 1.0, while Company B is debt-free. Both companies are subject to the same tax rate. Which of the following statements about their equity betas (βL\beta_L) is correct?

  1. Company A's equity beta will be higher than Company B's equity beta. (correct answer)
  2. Company B's equity beta will be higher than Company A's equity beta.
  3. The equity betas of both companies will be identical because they are in the same industry.
  4. The relationship between their equity betas cannot be determined without knowing their stock price volatility.
Explanation: Equity beta (βL\beta_L) is a function of asset beta (βU\beta_U) and financial leverage. The formula is βL=βU[1+(1−t)(D/E)]\beta_L = \beta_U [1 + (1-t)(D/E)]. Since both companies have the same asset beta and tax rate, the one with the higher debt-to-equity (D/E) ratio will have the higher equity beta. Company A has a D/E of 1.0, while Company B has a D/E of 0. Therefore, Company A's equity beta will be significantly higher than Company B's equity beta (which is equal to its asset beta).

Question 12

An analyst has forecasted the following returns for Stock J and the Market Portfolio under three economic scenarios.

ScenarioProbabilityStock J ReturnMarket Return
Boom0.325%15%
Normal0.510%8%
Recession0.2-5%-2%

Using the data provided in the passage, calculate the beta of Stock J.

  1. 0.56
  2. 1.41
  3. 1.77 (correct answer)
  4. 1.92
Explanation: To calculate beta, we need the covariance of Stock J with the Market and the variance of the Market. First, calculate expected returns: E[RJ]=.3(25)+.5(10)+.2(−5)=11.5%E[R_J] = .3(25) + .5(10) + .2(-5) = 11.5\%; E[RM]=.3(15)+.5(8)+.2(−2)=8.1%E[R_M] = .3(15) + .5(8) + .2(-2) = 8.1\%. Next, calculate market variance: Var(RM)=.3(15−8.1)2+.5(8−8.1)2+.2(−2−8.1)2=.3(47.61)+.5(0.01)+.2(102.01)=14.283+0.005+20.402=34.69\text{Var}(R_M) = .3(15-8.1)^2 + .5(8-8.1)^2 + .2(-2-8.1)^2 = .3(47.61) + .5(0.01) + .2(102.01) = 14.283 + 0.005 + 20.402 = 34.69. Then, calculate covariance: Cov(RJ,RM)=.3(25−11.5)(15−8.1)+.5(10−11.5)(8−8.1)+.2(−5−11.5)(−2−8.1)=.3(13.5)(6.9)+.5(−1.5)(−0.1)+.2(−16.5)(−10.1)=27.945+0.075+33.33=61.35\text{Cov}(R_J, R_M) = .3(25-11.5)(15-8.1) + .5(10-11.5)(8-8.1) + .2(-5-11.5)(-2-8.1) = .3(13.5)(6.9) + .5(-1.5)(-0.1) + .2(-16.5)(-10.1) = 27.945 + 0.075 + 33.33 = 61.35. Finally, Beta = Cov(RJ,RM)Var(RM)=61.3534.69≈1.77\frac{\text{Cov}(R_J, R_M)}{\text{Var}(R_M)} = \frac{61.35}{34.69} \approx 1.77.

Question 13

Stock XYZ has a beta of -0.3. The risk-free rate is 2% and the expected market return is 8%. According to the CAPM, what is the required return on Stock XYZ, and what does this imply about its role in a diversified portfolio?

  1. 0.2%; the stock provides a hedge against market downturns and is thus valuable in a portfolio. (correct answer)
  2. 3.8%; the stock is very safe and offers a return higher than the risk-free rate.
  3. 0.2%; this indicates a market inefficiency, as no rational investor would accept a return below the risk-free rate.
  4. -1.8%; the stock is expected to have a negative return but is held for its hedging properties.
Explanation: The required return is calculated using the CAPM formula: E[R]=Rf+β(E[Rm]−Rf)E[R] = R_f + \beta (E[R_m] - R_f). Plugging in the values: E[R]=2%+(−0.3)×(8%−2%)=2%−0.3×6%=2%−1.8%=0.2%E[R] = 2\% + (-0.3) \times (8\% - 2\%) = 2\% - 0.3 \times 6\% = 2\% - 1.8\% = 0.2\%. A negative beta indicates that the stock tends to move in the opposite direction of the market. Because of this hedging property, which reduces overall portfolio risk, investors are willing to accept an expected return that is below the risk-free rate. This is a rational outcome within the CAPM framework, not an inefficiency.

Question 14

A company operates in a highly cyclical industry, such as automotive manufacturing, and also maintains a high degree of operating leverage (high fixed costs relative to variable costs). How do these two characteristics independently affect the company's equity beta?

  1. The cyclical industry increases beta, but the high operating leverage decreases beta by making costs more predictable.
  2. The cyclical industry is a form of unsystematic risk and has little effect on beta, whereas high operating leverage increases beta.
  3. Both the cyclical nature of the industry and the high operating leverage contribute to an equity beta greater than 1.0. (correct answer)
  4. The cyclical industry increases beta, but high operating leverage is a component of financial risk, not systematic business risk.
Explanation: A company's equity beta is influenced by both its business risk and its financial leverage. Business risk itself is composed of sales cyclicality and operating leverage. A highly cyclical industry means revenues are very sensitive to the overall economy, which increases the company's asset beta. High operating leverage magnifies the effect of revenue fluctuations on operating income, further increasing the asset beta. Therefore, both factors increase the systematic risk of the firm's assets, leading to a higher equity beta.

Question 15

A company with an equity beta of 1.4 announces a 2-for-1 stock split. Assuming no other new information is released and the market interprets the split as a neutral signal about the company's future prospects, what will be the company's approximate equity beta immediately after the split is completed?

  1. 0.7
  2. 1.4 (correct answer)
  3. 2.8
  4. Cannot be determined without knowing the post-split stock price.
Explanation: A stock split is a cosmetic change that increases the number of shares outstanding while decreasing the price per share proportionally. It does not alter the company's underlying assets, operations, earnings power, or financial leverage. Since beta is a measure of the systematic risk of the company's equity (based on percentage returns, not price levels), a stock split has no theoretical effect on beta. Therefore, the beta will remain 1.4.

Question 16

An analyst is evaluating two stocks. Stock P has a beta of 1.5 and an R-squared of 0.70 from its regression against the market. Stock Q has a beta of 1.5 and an R-squared of 0.25. Assuming a well-diversified investor holds both stocks, which statement is most accurate?

  1. Stock Q is a better investment because it has lower total risk for the same level of systematic risk.
  2. Both stocks should have the same required rate of return according to the CAPM. (correct answer)
  3. Stock P has a higher required rate of return because its high R-squared indicates greater sensitivity to market moves.
  4. Stock Q has a higher required rate of return because its low R-squared implies high unsystematic risk which requires compensation.
Explanation: According to the Capital Asset Pricing Model (CAPM), the required rate of return on a stock is determined only by its systematic risk, as measured by beta. Unsystematic risk, which is captured by 1−R21 - R^2, is assumed to be diversified away by the investor and therefore does not command a risk premium. Since both Stock P and Stock Q have the same beta (1.5), the CAPM would predict the same required rate of return for both, despite their different levels of firm-specific (unsystematic) risk.

Question 17

A mature utility company has a historically stable beta of 0.6. The company announces a major, debt-financed acquisition of a volatile biotechnology startup. From a theoretical standpoint, what is the most likely immediate impact on the company's equity beta?

  1. Beta will decrease because the acquisition provides diversification benefits that lower the company's total risk.
  2. Beta will remain unchanged at 0.6 because historical beta is the best estimate of a firm's long-term risk profile.
  3. Beta will increase due to both the higher systematic business risk of the new assets and the increased financial leverage. (correct answer)
  4. Beta will increase due to higher business risk from biotech, but the new debt's tax shield will partially offset this increase.
Explanation: A firm's equity beta is determined by its asset (business) risk and its financial leverage. The acquisition of a volatile biotech firm increases the average business risk of the company's assets. Financing the acquisition with debt increases the company's debt-to-equity ratio, which increases its financial leverage. Both of these factors will increase the equity beta. Diversification at the firm level does not reduce the systematic risk that beta measures.

Question 18

A conglomerate has two divisions: a manufacturing division valued at $300 million with an asset beta of 1.4, and a services division valued at $200 million with an asset beta of 0.8. The company maintains a debt-to-equity ratio of 0.25 and has a corporate tax rate of 20%. What is the equity beta of the conglomerate?

  1. 1.16
  2. 1.32
  3. 1.39 (correct answer)
  4. 1.45
Explanation: First, calculate the conglomerate's overall asset beta by taking a weighted average of the divisional asset betas. The total value is $500M. The weights are wmfg=300/500=0.6w_{mfg} = 300/500 = 0.6 and wsvc=200/500=0.4w_{svc} = 200/500 = 0.4. The firm's asset beta is βU=(0.6)(1.4)+(0.4)(0.8)=0.84+0.32=1.16\beta_U = (0.6)(1.4) + (0.4)(0.8) = 0.84 + 0.32 = 1.16. Second, lever this asset beta to find the equity beta using the firm's D/E ratio and tax rate: βL=βU[1+(1−t)(D/E)]=1.16[1+(1−0.20)(0.25)]=1.16[1+(0.8)(0.25)]=1.16[1+0.20]=1.16(1.2)=1.392\beta_L = \beta_U [1 + (1-t)(D/E)] = 1.16 [1 + (1-0.20)(0.25)] = 1.16 [1 + (0.8)(0.25)] = 1.16 [1 + 0.20] = 1.16(1.2) = 1.392.

Question 19

A regression of the monthly excess returns of Apex Corp. against the monthly excess returns of a market index produced the following statistics: slope coefficient (beta) = 0.85, intercept (alpha) = 0.001, and R-squared = 0.30. Which of the following is the most accurate interpretation of these results?

  1. Apex Corp.'s systematic risk is lower than the market average, and 70% of its total risk is unsystematic. (correct answer)
  2. Apex Corp. is 15% less volatile than the market, and its returns are highly correlated with market returns.
  3. Approximately 85% of the variation in Apex Corp.'s returns can be explained by movements in the market.
  4. The stock has a beta of 0.30, and its expected excess return due to market risk is 85% of the market risk premium.
Explanation: The slope coefficient of the regression is the stock's beta (0.85), which measures systematic risk. Since β<1\beta < 1, its systematic risk is lower than the market average. R-squared (0.30) represents the proportion of the stock's total variance (risk) that is explained by market variance (systematic risk). Therefore, 1−R2=1−0.30=0.701 - R^2 = 1 - 0.30 = 0.70, or 70%, of the total risk is unsystematic (firm-specific).

Question 20

An analyst calculates a stock's beta using 60 monthly returns and obtains a value of 1.4. When recalculating using the same 60 months but with weekly returns instead, the beta estimate changes to 1.2. Assuming both calculations use the same market index, what is the most likely explanation for this difference?

  1. Weekly data provides more observations, leading to a more accurate beta estimate that reflects true systematic risk
  2. Monthly data captures longer-term relationships better, making the higher beta estimate more reliable for investment decisions
  3. The difference suggests nonsynchronous trading effects, where the stock doesn't trade as frequently as the index (correct answer)
  4. Calculation error occurred because beta should be identical regardless of the frequency of return measurement
Explanation: Nonsynchronous trading (thin trading) causes systematic underestimation of beta when using higher-frequency data. If a stock doesn't trade every day, weekly returns may not capture the full comovement with the market, leading to lower beta estimates. Choice A incorrectly assumes more data points always improve accuracy. Choice B ignores the statistical bias from nonsynchronous trading. Choice D is wrong because return frequency does affect beta estimation in practice due to microstructure effects.