19 Analytical Methods & Types of Risk Practice Questions & Answers

1. 1. An adviser is valuing a stream of fixed future cash flows. If the required rate of return used to discount those cash flows rises while the cash flows themselves are unchanged, what happens to the net present value of the investment?

   • A.The net present value is unchanged, because only the size of the cash flows determines the result.
   • B.The net present value turns into the internal rate of return, because the two converge as rates rise.
   • C.The net present value falls, because each future dollar is discounted more heavily at a higher rate.✓ Answer
   • D.The net present value rises, because a higher required return increases the worth of future dollars.

   Present value moves inversely with the discount rate: dividing each future cash flow by a larger (1 + r) raised to the number of periods produces a smaller present value, so net present value — the present value of inflows minus outflows — declines. The internal rate of return is a separate figure entirely: it is the one discount rate at which net present value equals zero.

   Source: NASAA Series 65 Test Specifications (June 12, 2023), Analytical Methods: time value of money (net present value, internal rate of return, future value)Report a problem with this question

2. 2. A corporate bond is quoted at a price that produces a yield to maturity of 6.2%. The client's required rate of return for bonds of that credit quality and maturity is 5.5%. Using discounted cash flow analysis, which conclusion about this bond is correct?

   • A.Its net present value is zero at any market price, so the required return matters only for bonds bought at par.
   • B.Its current yield replaces the internal rate of return here, so the client's required return does not affect the decision.
   • C.Its internal rate of return exceeds the required return, so net present value is positive and it is attractive.✓ Answer
   • D.Its internal rate of return is below the required return, so net present value is negative and it should be rejected.

   A bond's yield to maturity is its internal rate of return: the discount rate that sets the present value of all coupons plus par equal to the market price. When that internal rate of return of 6.2% exceeds the investor's required return of 5.5%, discounting the same cash flows at 5.5% gives a present value above the market price, so net present value is positive and the purchase adds value.

   Source: NASAA Series 65 Test Specifications (June 12, 2023), Analytical Methods: time value of money (net present value, internal rate of return, future value)Report a problem with this question

3. 3. A client asks approximately how long a single deposit would take to double in value if it earns an assumed 8% compounded annually and nothing is withdrawn. Using the rule of 72, the best estimate is:

   • A.About 6 years.
   • B.About 9 years.✓ Answer
   • C.About 12 years.
   • D.About 18 years.

   The rule of 72 estimates how long a sum takes to double at a compound rate by dividing 72 by the rate: 72 divided by 8 is 9 years. The relationship also works in reverse, so dividing 72 by the number of years available gives the approximate compound rate a client would need to double the money in that time.

   Source: NASAA Series 65 Test Specifications (June 12, 2023), Analytical Methods: time value of money (future value and compounding)Report a problem with this question

4. 4. An adviser reviews ten years of annual returns for a strategy. Nine of the ten fall between 4% and 8%, while one year returned 140%. Which measure of central tendency best describes the typical annual result, and why?

   • A.The mean, because averaging every observation gives each year, including the extreme one, equal weight.
   • B.The mode, because the value occurring most often in the set is what a typical year actually produced.
   • C.The range, because the spread between the highest and the lowest return summarizes the strategy's results.
   • D.The median, because the middle value of the ordered set is not distorted by a single extreme year.✓ Answer

   The mean is pulled upward by outliers, so one 140% year lifts the ten-year average well above anything the strategy delivered in nine of those years. The median, the middle value of the ordered data, ignores how far an extreme observation lies from the rest and therefore represents skewed data better. The range measures dispersion rather than central tendency.

   Source: NASAA Series 65 Test Specifications (June 12, 2023), Analytical Methods: descriptive statistics (mean, median, mode, range)Report a problem with this question

5. 5. A portfolio's returns are approximately normally distributed, with a mean annual return of 9% and a standard deviation of 6%. Approximately 95% of annual returns would be expected to fall within which range?

   • A.From 3% to 15%.
   • B.From -9% to 27%.
   • C.From -3% to 21%.✓ Answer
   • D.From 0% to 18%.

   In a normal distribution roughly 68% of observations lie within one standard deviation of the mean, about 95% within two and about 99.7% within three. Two standard deviations here is 12 percentage points, so the 95% band runs from 9% minus 12% to 9% plus 12%, that is from -3% to 21%.

   Source: NASAA Series 65 Test Specifications (June 12, 2023), Analytical Methods: descriptive statistics (standard deviation)Report a problem with this question

6. 6. An adviser wants one statistic showing how widely a fund's annual returns have varied around their own average, capturing both market-driven and issuer-specific swings. Which statistic fits, and what does it measure?

   • A.Standard deviation, which measures dispersion around the mean and serves as the proxy for total risk.✓ Answer
   • B.Alpha, which measures the return earned above the return that the fund's risk level would predict.
   • C.Beta, which measures volatility relative to the overall market and captures systematic risk only.
   • D.R-squared, which measures how much of a fund's price movement is explained by its benchmark index.

   Standard deviation quantifies how far returns have scattered from their own mean, and because it reflects every source of variation it is the accepted proxy for total risk, systematic plus unsystematic. Beta isolates only the portion of volatility that comes from market movements, so it would miss the issuer-specific swings the adviser wants to see.

   Source: NASAA Series 65 Test Specifications (June 12, 2023), Analytical Methods: descriptive statistics and risk measures (standard deviation, beta, alpha)Report a problem with this question

7. 7. Given a fund's beta, the risk-free rate and the market return, the capital asset pricing model predicted a 9% return for the year. The fund actually returned 11%. What does the 2% difference represent?

   • A.A beta of 2.0, showing the fund moved twice as much as the broad market did during the year.
   • B.A positive alpha, showing the manager produced more return than the risk assumed would justify.✓ Answer
   • C.A Sharpe ratio of 2.0, showing two units of return were earned for each unit of total risk taken.
   • D.The market risk premium, showing how much the market returned above the risk-free rate that year.

   Jensen's alpha is actual return minus the return the capital asset pricing model expected for the risk taken. An 11% result against a 9% expectation gives a positive alpha of 2%, which is read as evidence of manager skill: return beyond what the fund's systematic risk exposure alone would have produced.

   Source: NASAA Series 65 Test Specifications (June 12, 2023), Analytical Methods: risk measures (alpha, beta); Jensen's alpha derived from the capital asset pricing modelReport a problem with this question

8. 8. A client's entire investable net worth sits in a single balanced portfolio. The adviser compares it with a second portfolio that produced the same return, to see which delivered that return with less risk per unit taken. Which statistic is appropriate here?

   • A.The alpha figure, which subtracts the return predicted by the capital asset pricing model from actual return.
   • B.The Sharpe ratio, which divides return above the risk-free rate by the portfolio's standard deviation.✓ Answer
   • C.The R-squared figure, which reports the share of a portfolio's movement traced to its benchmark index.
   • D.The Treynor ratio, which divides return above the risk-free rate by the portfolio's beta coefficient.

   When a portfolio is the investor's entire holding, its unsystematic risk has not been diversified away somewhere else, so total risk is the right denominator. The Sharpe ratio measures excess return per unit of total risk as measured by standard deviation; the Treynor ratio uses beta and suits a single holding sitting inside an already diversified portfolio.

   Source: NASAA Series 65 Test Specifications (June 12, 2023), Analytical Methods: risk-adjusted performance measures (Sharpe ratio, standard deviation, beta)Report a problem with this question

9. 9. Two equity funds a client owns have a correlation coefficient of +0.30 with each other. Which statement about holding both of them is correct?

   • A.Holding both lowers the combined standard deviation, since any correlation under +1.0 diversifies to a degree.✓ Answer
   • B.Holding both produces no risk reduction, since a negative correlation coefficient is required to diversify.
   • C.Holding both means that 30% of each fund's price movement is explained by the other fund's movement.
   • D.Holding both produces maximum risk reduction, since +0.30 is near the most favorable pairing available.

   Correlation runs from -1.0 to +1.0. Only a perfect +1.0 removes every diversification benefit; anything below it means the two funds do not move in lockstep, so combining them reduces the portfolio's standard deviation. Maximum reduction occurs at -1.0, and the proportion of one series explained by another is R-squared, not the correlation coefficient itself.

   Source: NASAA Series 65 Test Specifications (June 12, 2023), Analytical Methods: correlation and portfolio risk reductionReport a problem with this question

10. 10. An adviser analyzing a manufacturer that carries large, slow-moving inventory wants the most conservative test of its ability to pay obligations coming due within one year. Which measure should be used, and how is it computed?

    • A.The current ratio, computed as current assets including inventory, divided by current liabilities.
    • B.Working capital, computed as current assets minus current liabilities, expressed as a dollar amount.
    • C.The debt-to-equity ratio, computed as long-term debt divided by total shareholders' equity.
    • D.The quick ratio, computed as current assets minus inventory, divided by current liabilities.✓ Answer

    The quick ratio, also called the acid-test ratio, strips inventory out of current assets because inventory is the least liquid current asset and may not convert to cash quickly at full value, which is exactly the concern with slow-moving stock. The current ratio leaves inventory in, working capital is a dollar figure rather than a ratio, and debt-to-equity measures leverage rather than liquidity.

    Source: NASAA Series 65 Test Specifications (June 12, 2023), Analytical Methods: financial ratio interpretation (current ratio, quick ratio, debt-to-equity ratio)Report a problem with this question

11. 11. A company's balance sheet shows current assets of $6,000,000, of which $2,000,000 is inventory, and current liabilities of $3,000,000. What is the company's current ratio?

    • A.1.33 to 1.
    • B.3.00 to 1.
    • C.2.00 to 1.✓ Answer
    • D.0.50 to 1.

    The current ratio is current assets divided by current liabilities, with inventory left in: $6,000,000 divided by $3,000,000 equals 2.00 to 1. Removing the $2,000,000 of inventory first would give the quick ratio of 1.33 to 1, which answers a different question about the same balance sheet.

    Source: NASAA Series 65 Test Specifications (June 12, 2023), Analytical Methods: financial ratio calculation (current ratio)Report a problem with this question

12. 12. A company's debt-to-equity ratio has climbed sharply over the past three years. What does that tell an adviser who is reviewing the company's stock for a client?

    • A.The firm has stronger short-term liquidity, because the ratio weighs current assets against current debts.
    • B.The firm is more leveraged and owes larger fixed interest payments, which raises its financial risk.✓ Answer
    • C.The firm now carries less systematic risk, because borrowing shifts risk from the market onto its lenders.
    • D.The firm must report lower earnings per share, because interest always exceeds the return on borrowed funds.

    Debt-to-equity compares borrowed capital with shareholders' equity and is a leverage measure drawn from the balance sheet, not a liquidity measure. More leverage means larger fixed interest obligations that must be paid before shareholders receive anything, which magnifies swings in earnings and increases financial risk, an issuer-specific and therefore diversifiable risk.

    Source: NASAA Series 65 Test Specifications (June 12, 2023), Analytical Methods: financial ratio interpretation (debt-to-equity ratio); Types of Risk: unsystematic risk (financial risk)Report a problem with this question

13. 13. Two companies in the same industry report similar earnings and similar book values, but one trades at 34 times earnings and the other at 9 times earnings. Which one is the value manager's candidate, and on what reasoning?

    • A.The one at 9 times earnings, because a low price-to-earnings multiple is the classic value screen.✓ Answer
    • B.The one at 9 times earnings, because a low price-to-earnings multiple assures a higher dividend payout.
    • C.The one at 34 times earnings, because price-to-earnings compares share price with book value per share.
    • D.The one at 34 times earnings, because a high price-to-earnings multiple marks a bargain on earnings.

    The price-to-earnings ratio is market price per share divided by earnings per share, so it shows what the market pays for each dollar of earnings. Value managers look for low multiples relative to industry peers, while high multiples characterize growth stocks whose future expectations are already reflected in the price. The multiple says nothing directly about dividends, and comparing price with book value is a separate ratio.

    Source: NASAA Series 65 Test Specifications (June 12, 2023), Analytical Methods: valuation ratios (price-to-earnings, price-to-book)Report a problem with this question

14. 14. An adviser computes the price-to-book ratio for a company whose balance sheet carries a large goodwill entry. Which statement about that calculation is correct?

    • A.Goodwill is excluded, so book value per share rests on tangible assets less liabilities and preferred stock.✓ Answer
    • B.Book value per share is total assets divided by common shares, with the company's liabilities disregarded.
    • C.Goodwill is included, so intangible assets lift the reported book value per share and lower the ratio.
    • D.A ratio above 1.0 shows the shares trade below their net asset backing, the usual signal of a value stock.

    Book value per share is computed from tangible net worth: tangible assets minus liabilities minus the value of preferred stock, divided by the common shares outstanding, so intangibles such as goodwill are stripped out. A price-to-book ratio below 1.0, not above it, means the shares trade beneath their net asset backing, which is the classic value screen.

    Source: NASAA Series 65 Test Specifications (June 12, 2023), Analytical Methods: valuation ratios (price-to-book, book value per share)Report a problem with this question

15. 15. A 62-year-old client with a 30-year time horizon holds only bank certificates of deposit and short-term Treasury bills, refusing any fluctuation in principal. Which risk most threatens this plan, and how is it classified?

    • A.Business risk, an unsystematic risk arising from the operating decisions made by each of the issuers.
    • B.Liquidity risk, an unsystematic risk arising when no ready resale market exists for a given holding.
    • C.Credit risk, an unsystematic risk reduced by spreading the deposits across many separate issuers.
    • D.Purchasing power risk, a systematic risk that spreading money among such instruments cannot remove.✓ Answer

    Over a 30-year horizon the real danger to a portfolio of cash-equivalent instruments is that its returns fail to keep pace with inflation, eroding the buying power of the client's money and income. Purchasing power risk is market-wide and non-diversifiable, and it is precisely the risk that refusing to accept principal fluctuation does not avoid.

    Source: NASAA Series 65 Test Specifications (June 12, 2023), Types of Risk: systematic (non-diversifiable) risk, including purchasing power (inflation) riskReport a problem with this question

16. 16. A client's account holds the bonds and the common stock of one corporation and nothing else. Adding many unrelated issuers to the account would substantially reduce which risk, and why?

    • A.Interest rate risk, because a change in market rates reprices each issuer's bonds in a different direction.
    • B.Geopolitical risk, because international events reach only the particular issuers named in a portfolio.
    • C.Purchasing power risk, because inflation erodes the cash flows of some issuers but not those of others.
    • D.Credit risk, because one issuer's failure to pay interest or principal affects only its own securities.✓ Answer

    Credit or default risk is issuer-specific: it is the chance that this particular borrower cannot make its payments, so holding many unrelated issuers means no single default can impair much of the account. Interest rate, geopolitical and purchasing power risks are market-wide forces that act on securities generally, so adding more issuers does not remove them.

    Source: NASAA Series 65 Test Specifications (June 12, 2023), Types of Risk: unsystematic (diversifiable) risk, including credit risk and issuer-specific riskReport a problem with this question

17. 17. A client holds 30 different common stocks, every one of them a regional bank, and tells her adviser that the account is fully diversified. What should the adviser explain?

    • A.Holding issuers from a single industry removes sector risk and leaves only issuer-specific risk in the account.
    • B.Holding 30 issuers of any kind removes both the systematic and the unsystematic risk from an equity account.
    • C.Holding 30 issuers from one industry is concentration, not diversification, since one industry event hits every position.✓ Answer
    • D.Holding 30 bank issuers drives the account's beta toward zero, since averaging many betas cancels them out.

    Diversification works only when holdings respond differently to the same events, and 30 regional banks share exposure to interest rates, credit conditions and bank regulation, so one industry-wide shock reaches every position at once. Diversification also never removes systematic risk, and averaging the betas of many holdings produces the portfolio's weighted-average beta rather than a beta of zero.

    Source: NASAA Series 65 Test Specifications (June 12, 2023), Types of Risk: systematic risk (including sector risk) and the limits of diversificationReport a problem with this question

18. 18. A client has kept a large balance in a non-interest-bearing checking account for two years while alternatives of comparable safety paid a positive return. How should the adviser characterize what that decision has cost the client?

    • A.Financial risk, the loss taken when an issuer becomes unable to service its debt obligations as they come due.
    • B.Opportunity cost, the return on the next-best alternative that was given up by leaving the funds idle.✓ Answer
    • C.Reinvestment risk, the loss taken when proceeds of a maturing investment must be put to work at lower rates.
    • D.Liquidity risk, the loss taken when an asset cannot be sold promptly at a price close to fair value.

    Opportunity cost is the value of the next-best alternative forgone when capital is committed one way rather than another, and on this exam the risk-free rate, conventionally the 91-day Treasury bill, is the benchmark opportunity cost and the floor for any required return. The other three choices name risks of loss on an investment actually held, not the cost of failing to invest at all.

    Source: NASAA Series 65 Test Specifications (June 12, 2023), Types of Risk: opportunity costReport a problem with this question

19. 19. A corporation is liquidated. After unpaid wages, taxes and the administrative costs of the bankruptcy have been satisfied, in what order are the remaining claimants paid?

    • A.Secured bondholders, general creditors, subordinated debenture holders, preferred stockholders, common stockholders.✓ Answer
    • B.Preferred stockholders, secured bondholders, general creditors, subordinated debenture holders, common stockholders.
    • C.General creditors, secured bondholders, preferred stockholders, subordinated debenture holders, common stockholders.
    • D.Secured bondholders, subordinated debenture holders, general creditors, common stockholders, preferred stockholders.

    All debt outranks all equity, and within the debt layer seniority follows the collateral and the contract: creditors holding pledged collateral are paid first, then general unsecured creditors including debenture holders and trade creditors, then holders of subordinated debentures who agreed by contract to rank behind other unsecured debt. Only after every creditor is satisfied do preferred stockholders receive anything, and common stockholders hold the residual claim and are paid last.

    Source: NASAA Series 65 Test Specifications (June 12, 2023), Types of Risk: capital structure and liquidation priority of debt, preferred stock and common stockReport a problem with this question

Practice questions written from the NASAA Series 65 Test Specifications and the Uniform Securities Act. Not affiliated with or endorsed by NASAA, FINRA or Prometric. Dollar thresholds, fee figures and contribution limits change; where one matters the question supplies it. Confirm current requirements with NASAA before testing. NASAA exam content outline →