NASAA Series 65 — All Questions

A 6% coupon bond is trading at a discount to par. Which ranking of its yields is correct?

• a.Yield to maturity, current yield and coupon rate are all equal
• b.Current yield exceeds yield to maturity, which exceeds the coupon rate
• c.Coupon rate exceeds current yield, which exceeds yield to maturity
• d.Yield to maturity exceeds current yield, which exceeds the coupon rate✓

At a discount, current yield (annual interest divided by the lower price) is above the coupon rate, and yield to maturity is higher still because it adds the gain as the price pulls up to par. The reverse ordering describes a premium bond. Putting current yield above yield to maturity ignores the pull-to-par gain. Equal yields occur only when the bond trades at par.Bond yields

A bond with a 6% coupon and $1,000 par value is bought for $1,200. What is its current yield?

• a.6.0%
• b.20.0%
• c.5%✓
• d.7.2%

Current yield is annual interest divided by market price: $60 / $1,200 = 5%. A 6.0% figure is just the coupon rate on par. A 7.2% figure multiplies the coupon by the price ratio instead of dividing. A 20.0% figure is the premium over par, not a yield.Bond yields

An investor in the 28% federal bracket holds a municipal bond yielding 3.6%. What taxable bond yield would give the same after-tax return?

• a.2.6%
• b.5%✓
• c.4.6%
• d.3.6%

Taxable-equivalent yield equals the tax-free yield divided by (1 - tax rate): 3.6% / 0.72 = 5%. A 3.6% figure ignores the tax on a taxable bond. A 4.6% figure adds 28% of 3.6% instead of dividing. A 2.6% figure multiplies by (1 - tax rate), which is how to find an after-tax yield and not a taxable-equivalent one.Taxable-equivalent yield

The risk-free rate is 3%, the market is expected to return 10%, and a stock's beta is 1.2. Under CAPM, the stock's required return is

• a.8.4%
• b.11.4%✓
• c.10%
• d.12%

CAPM required return = risk-free rate + beta x (market return - risk-free rate) = 3% + 1.2 x 7% = 11.4%. An 8.4% figure applies beta to the market premium without adding the risk-free rate. A 10% figure is the market return, which applies only at a beta of 1.0. A 12% figure multiplies the market return by beta.CAPM

A portfolio has an expected return of 8% and a standard deviation of 10%. Assuming a normal distribution, a return between -2% and 18% in a given year has a probability of about

• a.99.7%
• b.68%✓
• c.50%
• d.95%

The range -2% to 18% is the mean plus or minus one standard deviation, which covers about 68% of outcomes. Fifty percent is not tied to a standard deviation band. Roughly 95% requires two standard deviations (-12% to 28%). Roughly 99.7% requires three (-22% to 38%).Standard deviation

A portfolio returned 11% with a standard deviation of 16% while Treasury bills yielded 3%. What is its Sharpe ratio?

• a.0.19
• b.0.69
• c.0.5✓
• d.1.45

Sharpe ratio is excess return per unit of total risk: (11% - 3%) / 16% = 0.5. A 0.69 result divides the raw return by the standard deviation without subtracting the risk-free rate. A 0.19 result divides the risk-free rate by the standard deviation. A 1.45 result divides the standard deviation into the return in the wrong direction.Sharpe ratio

Unlike the Sharpe ratio, the Treynor ratio measures excess return relative to which risk measure?

• a.Tracking error, the spread against a benchmark's returns
• b.Beta, the portfolio's sensitivity to market movements✓
• c.Standard deviation, the total variability of returns
• d.Duration, the portfolio's sensitivity to interest rates

Treynor divides excess return by beta, so it rewards compensation for systematic risk and suits a portfolio that is one piece of a larger diversified holding. Standard deviation is the Sharpe ratio's denominator. Tracking error is used in the information ratio. Duration measures bond price sensitivity and is not a performance-ratio denominator.Treynor ratio

Given its beta, a fund's CAPM-expected return is 10%, but the fund actually returned 12%. What is the fund's alpha?

• a.+10%
• b.+2%✓
• c.-2%
• d.+12%

Alpha is actual return minus the CAPM-expected return: 12% - 10% = +2%, meaning the manager added value beyond the risk taken. Reversing the subtraction gives -2%, which would indicate underperformance. Ten percent is the expected return, not the excess. Twelve percent is the actual return, not the excess.Alpha

If $10,000 is invested at 6% compounded annually, what is the value after two years?

• a.$11,236✓
• b.$11,200
• c.$11,000
• d.$12,000

Future value = $10,000 x 1.06 x 1.06 = $11,236. The $11,200 answer uses simple interest, which ignores interest earned on the first year's interest. The $11,000 answer counts only one year of interest. The $12,000 answer applies 10% per year, which is not the stated rate.Time value of money

Using the rule of 72, about how many years will it take an investment earning 8% annually to double?

• a.6 years
• b.18 years
• c.12 years
• d.9 years✓

The rule of 72 divides 72 by the annual rate: 72 / 8 = 9 years. Six years would correspond to a 12% rate. Twelve years would correspond to a 6% rate. Eighteen years would correspond to a 4% rate.Rule of 72

A CD pays 4.5% and the investor is in the 22% bracket. With 3% inflation, the real after-tax return is approximately

• a.1.5%
• b.0.51%✓
• c.4.5%
• d.3.51%

After-tax yield is 4.5% x (1 - 0.22) = 3.51%; subtracting 3% inflation leaves about 0.51%. A 1.5% figure ignores taxes and takes inflation from the pretax rate. A 3.51% figure is the after-tax return before inflation. A 4.5% figure ignores both taxes and inflation.Real return

To tighten monetary policy, the Federal Reserve would most likely

• a.lower the interest rate paid on reserve balances
• b.sell Treasury securities in open market operations✓
• c.buy Treasury securities in open market operations
• d.lower the discount rate charged on Fed loans

Selling securities drains reserves from banks, which pushes the federal funds rate up and slows lending. Buying securities adds reserves and eases policy. Lowering the rate paid on reserve balances reduces banks' incentive to hold reserves and eases policy. A lower discount rate makes borrowing from the Fed cheaper, which also eases policy.Monetary policy

Which action is an example of expansionary fiscal policy?

• a.The Fed cuts the discount rate to member banks
• b.The Fed buys Treasury notes through open market operations
• c.The Treasury raises interest rates on new Series I bonds
• d.Congress enacts a temporary payroll tax reduction✓

Fiscal policy is set by Congress and the President through taxes and spending, so a payroll tax cut that raises disposable income is expansionary fiscal policy. Open market purchases and a lower discount rate are monetary policy tools controlled by the Fed. Changing the rate on savings bonds is a Treasury pricing decision, not a broad stimulus tool.Fiscal policy

A surge in crude oil prices raises production costs across many industries and pushes the general price level up while output falls. This is best described as

• a.a liquidity trap
• b.cost-push inflation✓
• c.demand-pull inflation
• d.deflationary contraction

Cost-push inflation results from higher input costs that shift aggregate supply inward, raising prices while output declines. Demand-pull inflation comes from spending outrunning supply and normally comes with rising output. Deflation means falling prices, which is the opposite of what happened here. A liquidity trap describes ineffective monetary policy at very low rates, not a cost shock.Inflation

Which combination of conditions defines stagflation?

• a.Rising prices with low unemployment and strong growth
• b.Stable prices with low unemployment and moderate growth
• c.Falling prices with high unemployment and weak growth
• d.Rising prices with high unemployment and weak growth✓

Stagflation pairs persistent inflation with stagnant output and high unemployment, as in the 1970s oil shocks. Falling prices with weak growth describes deflation or a depression. Rising prices with strong growth and low unemployment describes an overheating expansion. Stable prices with low unemployment describes a healthy economy.Stagflation

Which of the following is a lagging economic indicator?

• a.The S&P 500 stock price index
• b.Building permits for new private housing
• c.Average weekly initial claims for unemployment insurance
• d.The average prime rate charged by banks✓

The prime rate follows changes in the economy and in the federal funds rate, so it is a lagging indicator. Building permits are a leading indicator because construction follows approval. Stock prices lead the economy as markets look ahead. Initial jobless claims are a leading indicator of labor market weakness.Economic indicators

Which transaction is counted in this year's gross domestic product?

• a.The government pays monthly Social Security benefits
• b.A family sells a house built in 2015
• c.An investor buys shares on the secondary market
• d.A builder completes a new house this year✓

GDP counts the market value of final goods and services produced in the year, so a newly built house is included. Resale of an existing house is a transfer of an asset produced earlier. Social Security benefits are transfer payments, not payment for current production. Secondary market share purchases move ownership of financial assets and add no output.GDP

A stock is expected to pay a $2.00 dividend next year, with dividends growing 4% per year indefinitely. At a 9% required return, the constant-growth model values the stock at

• a.$22.22
• b.$50.00
• c.$40✓
• d.$30.77

The constant-growth model gives value = next dividend / (required return - growth) = $2.00 / 0.05 = $40. A $22.22 figure divides by the full 9% required return and ignores growth. A $30.77 figure divides by 6.5%, which is not a rate in the problem. A $50.00 figure divides by 4%, the growth rate alone.Dividend discount model

A company reports earnings of $5.00 per share and pays dividends of $2.00 per share. What is its dividend payout ratio?

• a.25%
• b.250%
• c.40%✓
• d.60%

Payout ratio is dividends divided by earnings: $2.00 / $5.00 = 40%. A 25% figure is not derived from the numbers given. A 60% figure is the retention ratio, the share of earnings kept. A 250% figure inverts the division.Financial ratios

A firm has current assets of $400,000, inventory of $150,000, and current liabilities of $200,000. What is its quick ratio?

• a.2.75
• b.0.75
• c.1.25✓
• d.2.00

The quick ratio removes inventory from current assets: ($400,000 - $150,000) / $200,000 = 1.25. A 0.75 result divides inventory by current liabilities. A 2.00 result is the current ratio, which leaves inventory in. A 2.75 result adds the inventory instead of subtracting it.Financial ratios

Evidence that corporate insiders consistently earn abnormal profits on their own company's stock is most inconsistent with which form of market efficiency?

• a.All three forms equally
• b.Strong form✓
• c.Weak form
• d.Semi-strong form

The strong form says prices reflect all information, public and private, so consistent insider profits would contradict it. The weak form holds that prices reflect past trading data, and insider gains do not conflict with it. The semi-strong form says prices reflect all public information, which is consistent with insiders profiting from nonpublic facts. The three forms are nested, so the insider evidence does not contradict them equally.Efficient market hypothesis

Which risk is most reduced by holding stocks of 30 companies across many industries?

• a.Purchasing power risk from rising consumer prices
• b.Business risk specific to any one company✓
• c.Market risk from a broad economic downturn
• d.Interest rate risk from changes in market yields

Company-specific (unsystematic) risk, such as a failed product or a lawsuit, can be diversified away. Market risk, interest rate risk and purchasing power risk are systematic, so they affect nearly all securities and cannot be removed by adding more holdings.Systematic and unsystematic risk

An investment of $10,000 gains 50% in year one and loses 50% in year two. What is its value at the end of year two?

• a.$5,000
• b.$7,500✓
• c.$12,500
• d.$10,000

After a 50% gain the value is $15,000, and a 50% loss on that larger base leaves $7,500. A $5,000 result subtracts 50% from the original amount only. A $10,000 result treats the two returns as offsetting arithmetic averages. A $12,500 result adds a 25% gain with no basis in the returns. Equal percentage gains and losses do not cancel because the base changes.Portfolio returns

Which return measure is best for evaluating a manager who has no control over clients' deposits and withdrawals?

• a.Current yield
• b.Holding period return
• c.Money-weighted return
• d.Time-weighted return✓

Time-weighted return removes the effect of cash flows in and out, so it isolates the manager's decisions. Money-weighted return (internal rate of return) is affected by the timing and size of deposits and withdrawals, which the manager does not control. Holding period return covers one period without adjusting for flows. Current yield measures income only.Performance measurement

Under U.S. GAAP, a corporation pays $2 million of interest on its bonds during the year. Where does the cash paid appear on the statement of cash flows?

• a.Within financing activities, because the interest is a cost of borrowed capital
• b.Within investing activities, because the bonds fund long-term asset purchases
• c.It is excluded, because interest is shown only on the income statement
• d.Within operating activities, because interest expense is part of net income✓

U.S. GAAP classifies interest paid (and interest received) as an operating cash flow because the expense flows through net income. Classifying it as financing is a common mistake: principal borrowed and repaid is financing, but the interest cost is not. Investing covers purchases and sales of long-term assets and investments, not the cost of funding them. Every cash flow, including interest, is reported on the cash flow statement; the income statement does not replace it.FASB ASC 230-10-45 (Statement of Cash Flows classification)

A company reports net income of $300,000, depreciation of $90,000, and an increase in accounts receivable of $40,000. It spent $120,000 on new equipment. Using cash from operations less capital expenditures, its free cash flow is:

• a.$310,000
• b.$230,000✓
• c.$350,000
• d.$180,000

Cash from operations = 300,000 + 90,000 (non-cash depreciation added back) - 40,000 (receivables rose, so sales not yet collected are subtracted) = 350,000. Free cash flow = 350,000 - 120,000 = 230,000. Rechecking: 300 + 90 - 40 - 120 = 230. The $310,000 figure adds the receivables increase instead of subtracting it. The $180,000 figure forgets the depreciation add-back and the receivables change. The $350,000 figure is operating cash flow before capital spending.CFA Institute curriculum, Financial Statement Analysis (free cash flow)

A firm has current assets of $600,000 and current liabilities of $400,000. It uses $100,000 of cash to pay off accounts payable. Its current ratio after the payment is closest to:

• a.about 1.25
• b.1.50
• c.1.67✓
• d.roughly 1.20

Before: 600,000 / 400,000 = 1.50. Paying a $100,000 payable with cash lowers both sides: (600,000 - 100,000) / (400,000 - 100,000) = 500,000 / 300,000 = 1.67. When the ratio starts above 1.0, removing equal amounts from numerator and denominator raises it. The ratio does not stay at 1.50 just because one current item replaced another. A result of 1.25 reduces assets but forgets to reduce liabilities. A result of 1.20 (600,000 / 500,000) leaves assets alone and adds the payment to liabilities instead of subtracting it.CFA Institute curriculum, Financial Statement Analysis (liquidity ratios)

An issuer's annual report includes an auditor's report with an unqualified (unmodified) opinion. This opinion states that the financial statements:

• a.Are guaranteed by the auditing firm to be free of any fraud or material error
• b.Were prepared by independent accountants without any management estimates
• c.Present fairly the position and results in all material respects✓
• d.Show the company is a sound investment compared with its industry peers and rivals

An unqualified or unmodified opinion is the cleanest audit opinion: the statements fairly present the company's financial position, results and cash flows in all material respects in conformity with GAAP. It is reasonable assurance, not a guarantee against fraud or error. Auditors do not opine on investment merit or peer comparisons. Management prepares the statements and makes the estimates; the auditor tests them rather than replacing them.PCAOB AS 3101 (auditor's report on financial statements); AICPA AU-C 700

A client owns bonds of a manufacturer. The latest annual report contains an auditor's explanatory paragraph raising going-concern doubt. This most nearly means the auditor believes:

• a.The auditor resigned before finishing the examination of the year-end books
• b.The statements violate GAAP, so the audit opinion is automatically adverse
• c.There is substantial doubt the company can meet obligations for about a year✓
• d.The company has already filed for bankruptcy protection under Chapter 11

A going-concern paragraph signals that conditions raise substantial doubt about the entity's ability to continue operating and meet its obligations as they come due within one year after the financial statements are issued. It is a warning, not a bankruptcy filing. It can accompany an otherwise unqualified opinion, so it does not mean the statements violate GAAP (that would point to an adverse opinion). It also differs from an auditor withdrawing or a disclaimer of opinion.FASB ASC 205-40 (going concern); PCAOB AS 2415

In December a consulting firm delivers $80,000 of services and bills the clients, but collects only $30,000 by year end. It pays $45,000 of expenses, all incurred in December. Under accrual accounting, December results are:

• a.A profit of $35,000✓
• b.A profit of $80,000
• c.A loss of $15,000
• d.A profit of $5,000

Accrual accounting recognizes revenue when earned and expenses when incurred, regardless of cash timing: 80,000 - 45,000 = 35,000 profit. The cash-basis result would be 30,000 collected - 45,000 paid = a $15,000 loss. The $80,000 figure ignores expenses. The $5,000 figure takes the uncollected 50,000 (80,000 - 30,000) and subtracts the expenses, which treats the receivable as the revenue instead of the full amount earned.CFA Institute curriculum, Financial Statement Analysis (accrual accounting)

Which statement about a listed company's Form 10-Q is accurate?

• a.It is filed only after a material event and within four business days of that event
• b.It is filed once a year and replaces the annual report for smaller reporting companies
• c.It covers the first three fiscal quarters and carries unaudited statements✓
• d.It is filed for all four fiscal quarters and carries fully audited financial statements

Form 10-Q is the quarterly report. It covers the first three fiscal quarters (the fourth quarter is captured in the Form 10-K) and its financial statements are unaudited. The annual report on Form 10-K contains audited statements. The four-business-day filing belongs to the Form 8-K current report, not the 10-Q. No company replaces the annual report with a 10-Q.Securities Exchange Act Rule 13a-13; SEC Form 10-Q

A listed company's chief financial officer unexpectedly resigns. Which SEC filing is generally required and how soon?

• a.A Form 10-K amendment, within thirty days of the resignation
• b.A Form 10-Q, at the end of the next calendar quarter
• c.A Form 8-K, generally within four business days of the event✓
• d.A Form 4, within two business days by the departing officer

Form 8-K is the current report for material events such as the departure of certain officers (Item 5.02), and the general deadline is four business days after the event. Form 10-Q is a scheduled quarterly report and does not give timely notice. A 10-K amendment is not the vehicle for a mid-year event. Form 4 reports insider transactions in the company's securities, not the departure of the officer.Securities Exchange Act Rule 13a-11; Form 8-K, General Instruction B.1

A U.S. investor converts $110,000 into euros at $1.10 per euro and buys a euro bond. One year later the bond is worth EUR 104,000 including interest, and the euro has fallen to $1.05. The investor's return in dollars is closest to:

• a.about +4.0%
• b.around +0.7%
• c.-4.5%
• d.approximately -0.7%✓

Start: 110,000 / 1.10 = EUR 100,000. End: 104,000 x 1.05 = $109,200. Return = (109,200 - 110,000) / 110,000 = -0.73%. Cross-check: 1.04 x (1.05 / 1.10) - 1 = 1.04 x 0.9545 - 1 = -0.73%. The 4.0% figure is the euro-denominated return only. The -4.5% figure is the currency loss alone, ignoring the 4% earned on the bond. The positive 0.7% is a sign error.CFA Institute curriculum, Economics (exchange rates and returns)

A basket of goods costs $200 in the United States and EUR 160 in the euro area. The spot rate is $1.10 per euro. Absolute purchasing power parity implies a rate of:

• a.$1.25 per euro, which suggests the euro is overvalued at $1.10
• b.$0.80 per euro, which suggests the euro is undervalued against the dollar
• c.$1.25 per euro, which suggests the euro is undervalued at $1.10✓
• d.$1.10 per euro, which suggests the euro is fairly valued against the dollar today

Absolute PPP sets the exchange rate so the same basket costs the same: $200 / EUR 160 = $1.25 per euro. The actual rate of $1.10 buys fewer dollars per euro than PPP implies, so the euro is undervalued against the dollar under this measure. Calling it overvalued reads the gap backwards. The $0.80 figure inverts the ratio (160/200). Saying $1.10 is fair ignores that the basket costs more in the United States when converted at the spot rate.CFA Institute curriculum, Economics (purchasing power parity)

A U.S. investor owns shares of a foreign company. The foreign government suddenly forbids converting local currency to dollars and sending dividends abroad. This risk is best described as:

• a.Call risk, a form of issuer-specific business risk
• b.Transfer (capital control) risk, a form of political risk✓
• c.Reinvestment risk, a form of interest rate risk
• d.Liquidity risk, a form of exchange trading risk

Restrictions on converting and repatriating funds are capital controls, and the chance of them is transfer risk within political (country) risk. Reinvestment risk is about having to reinvest cash flows at lower rates. Call risk applies to bonds the issuer can redeem early. Liquidity risk concerns the ability to trade without moving the price; the investor's problem here is access to the proceeds, not the ability to find a buyer.CFA Institute curriculum, Economics (country and political risk)

Why is a government's debt denominated in a foreign currency generally considered riskier for default than the same government's debt in its own currency?

• a.The government cannot create the foreign currency and must earn or hold it✓
• b.Foreign-currency bonds are never rated by the major credit rating agencies
• c.Foreign courts automatically seize the government's assets upon any late payment
• d.Local-currency bonds carry no inflation risk because the central bank backs them

A government that borrows in its own currency can, in principle, always create more of it to pay (at the cost of inflation or currency weakness), so rating agencies often rate local-currency debt higher. Foreign-currency debt must be serviced from export earnings, reserves or new borrowing. It is false that such bonds are unrated. Local-currency bonds do carry inflation risk. Courts do not automatically seize assets on a late payment; sovereign immunity makes enforcement difficult.CFA Institute curriculum, Fixed Income (sovereign credit risk)

A skilled worker loses a job when software permanently replaces the task, and no local employer needs the worker's remaining skills. This is best classified as:

• a.Cyclical unemployment
• b.Frictional unemployment
• c.Structural unemployment✓
• d.Seasonal unemployment

Structural unemployment results from a mismatch between workers' skills or location and available jobs, often after technological change. Cyclical unemployment rises in recessions and falls in expansions as demand changes. Frictional unemployment is the short search time between jobs even when skills match. Seasonal unemployment follows predictable calendar patterns, such as harvest or holiday work.BLS Current Population Survey definitions (unemployment categories)

A survey of 1,000 civilian adults finds 600 employed, 40 actively looking for work, and 360 neither working nor searching. The unemployment rate is:

• a.64.0%
• b.6.67%
• c.4.0%
• d.6.25%✓

The labor force is employed plus unemployed = 600 + 40 = 640. The unemployment rate = 40 / 640 = 6.25%. Dividing by all 1,000 adults gives 4.0%, which wrongly includes people outside the labor force. Dividing by the 600 employed gives 6.67%. The 64% figure is the labor force participation rate (640 / 1,000), a different statistic.BLS Current Population Survey definitions (labor force measures)

The one-year spot rate is 3.0%, and the market expects the one-year rate a year from now to be 5.0%. Under the pure expectations theory, the two-year annualized spot rate is closest to:

• a.around 3.0%
• b.about 5.0%
• c.8.2%
• d.roughly 4.0%✓

Under pure expectations, the two-year spot rate is the geometric average of the expected one-year rates: sqrt(1.03 x 1.05) - 1 = sqrt(1.0815) - 1 = 3.995%, about 4.0%. The 8.2% figure is the two-year cumulative return (1.0815 - 1), not an annualized rate. The 5.0% figure is only the expected forward rate for year two. The 3.0% figure is only the first year's rate.CFA Institute curriculum, Fixed Income (expectations theory)

Suppose investors expect short-term interest rates to stay flat for the next ten years. According to the liquidity preference (liquidity premium) theory, the yield curve will most likely be:

• a.Flat, because long yields equal the average of the expected short rates
• b.Humped, because demand clusters in the intermediate maturity range
• c.Upward sloping, because lenders require extra yield for committing funds longer✓
• d.Downward sloping, because investors expect to profit from falling rates

Liquidity preference theory adds a term (liquidity) premium that rises with maturity to the average of expected short rates. With flat expectations the curve therefore slopes upward. A flat curve is what pure expectations theory would predict in this situation. Inversion would require expected falling rates, which the question rules out. A hump is the type of shape associated with other theories or changing rate expectations, not a premium for maturity.CFA Institute curriculum, Fixed Income (term structure theories)

The 2-year Treasury yields 4.60% and the 10-year Treasury yields 4.25%. The 10-year minus 2-year spread and the curve shape are:

• a.-35 basis points; the curve is inverted between those maturities✓
• b.+35 basis points; the curve is upward sloping
• c.-350 basis points; the curve is inverted between those maturities
• d.+0.35 basis points; the curve is essentially flat between those maturities

Spread = 4.25% - 4.60% = -0.35 percentage points = -35 basis points (one basis point is 0.01%, so 0.35% = 35 bp; recomputed: 0.35 / 0.01 = 35). Long yields below short yields mean an inverted curve. A positive 35 reverses the subtraction order. The -350 figure shifts the decimal two places too far. The 0.35 basis-point figure confuses percentage points with basis points.U.S. Treasury yield curve conventions (CFA Institute, Fixed Income)

An investor deposits $10,000 at 8% nominal annual interest compounded semiannually for 3 years. The ending balance is closest to:

• a.about $12,653✓
• b.$12,597
• c.approximately $12,682
• d.roughly $12,400

Semiannual compounding: 4% per period for 6 periods. 1.04^6 = 1.265319, so the balance is $12,653. Recheck by steps: 1.04^2 = 1.0816, 1.0816^3 = 1.2653. The $12,597 figure compounds only annually (1.08^3). The $12,400 figure uses simple interest (10,000 + 3 x 800). The $12,682 figure compounds quarterly (1.02^12), which the question does not state.CFA Institute curriculum, Quantitative Methods (time value of money)

A retiree will receive $2,000 at the beginning of each of the next 4 years. At a 5% discount rate, the present value of these payments is closest to:

• a.roughly $7,092
• b.around $8,000
• c.approximately $6,754
• d.about $7,446✓

Present value of an ordinary annuity = 2,000 x [1 - 1.05^-4] / 0.05 = 2,000 x 3.5460 = $7,092. Payments at the beginning of each year form an annuity due, so multiply by 1.05: $7,092 x 1.05 = $7,446. Check: 2,000 + 2,000/1.05 + 2,000/1.05^2 + 2,000/1.05^3 = 2,000 + 1,904.76 + 1,814.06 + 1,727.68 = 7,446.50. The $7,092 answer treats the payments as end-of-year. The $8,000 total ignores discounting. The $6,754 answer divides by 1.05 instead of multiplying.CFA Institute curriculum, Quantitative Methods (annuity due)

A client wants $500,000 in 20 years and will invest a level amount at the end of each year in an account earning 7% annually. The required annual contribution is closest to:

• a.$25,000
• b.$12,196✓
• c.$35,000
• d.$11,399

Future value annuity factor = (1.07^20 - 1) / 0.07 = (3.8697 - 1) / 0.07 = 40.995. Payment = 500,000 / 40.995 = $12,196. Check: 12,196 x 40.995 = 499,980, about 500,000. The $11,399 figure (12,196 / 1.07) assumes deposits at the start of each year, but the question says year end. The $25,000 answer divides the goal by 20 and ignores growth. The $35,000 answer takes 7% of the goal, which is a single year of interest on the target.CFA Institute curriculum, Quantitative Methods (future value of an annuity)

Three annual returns for a fund are 4%, 8% and 12%. Treated as a sample, the standard deviation is:

• a.16.0%
• b.3.3%
• c.4.0%✓
• d.8.0%

Mean = 8%. Deviations: -4, 0, +4. Squares: 16, 0, 16 = 32. Sample variance divides by n - 1 = 2, giving 16; the square root is 4.0%. Dividing by n = 3 gives 10.67 and a population standard deviation of 3.3%, which is not the sample statistic. The 16.0% figure is the variance, not the standard deviation. The 8.0% figure is the mean.CFA Institute curriculum, Quantitative Methods (dispersion)

A stock rises 50% in year one and falls 50% in year two. Which statement describes its performance?

• a.The geometric mean is about -25% per year, and the investor ends with 50%
• b.The geometric mean is about +25% per year because the first year's gain is larger
• c.The geometric mean is about -13.4% per year, and the investor ends with 75% of the start✓
• d.The arithmetic and geometric means are both 0%, and the investor breaks even

Growth factors: 1.50 x 0.50 = 0.75, so the investor ends with 75% of the starting value, a 25% total loss. The geometric mean is sqrt(0.75) - 1 = -13.4% per year. The arithmetic mean is (50% - 50%) / 2 = 0%, which overstates results; breaking even is wrong. No positive 25% average applies. The -25% figure is the two-year cumulative loss, not an annual rate, and the investor ends with 75%, not 50%.CFA Institute curriculum, Quantitative Methods (geometric mean return)

A company has a market capitalization of $800 million, debt of $300 million, cash of $100 million, and EBITDA of $125 million. Its EV/EBITDA multiple is:

• a.about 6.4x
• b.roughly 5.6x
• c.8.0x✓
• d.around 8.8x

Enterprise value = market cap + debt - cash = 800 + 300 - 100 = $1,000 million. EV / EBITDA = 1,000 / 125 = 8.0x. Recheck: 125 x 8 = 1,000. The 6.4x answer divides market cap alone by EBITDA. The 8.8x answer adds debt but forgets to subtract cash (1,100 / 125). The 5.6x answer subtracts both debt and cash from market cap (700 / 125), which is the reverse of the correct treatment of debt.CFA Institute curriculum, Equity Valuation (enterprise value multiples)

A company reports total equity of $500 million, of which $100 million is preferred stock, and has 20 million common shares outstanding. The shares trade at $30. Its price-to-book ratio is:

• a.0.67
• b.1.5✓
• c.1.2
• d.2.0

Book value attributable to common = 500 - 100 (preferred) = $400 million. Book value per share = 400 / 20 = $20. Price-to-book = 30 / 20 = 1.5. The 1.2 answer uses total equity of $500 million (25 per share, 30 / 25). The 0.67 answer inverts the ratio (20 / 30). The 2.0 answer has no basis in the data given.CFA Institute curriculum, Equity Valuation (price-to-book)

A portfolio has a beta of 1.25 and a total standard deviation of 24%. The market's standard deviation is 16%. Treating total variance as systematic plus nonsystematic variance, the nonsystematic standard deviation is closest to:

• a.20.0%
• b.24.0%
• c.13.3%✓
• d.4.0%

Systematic risk = beta x market standard deviation = 1.25 x 16% = 20%. Variances: total 24^2 = 576, systematic 20^2 = 400, so nonsystematic variance = 176 and the standard deviation = sqrt(176) = 13.3%. The 4.0% answer simply subtracts standard deviations (24 - 20), but variances, not standard deviations, add. The 20.0% answer is the systematic component. The 24.0% answer is the total.CFA Institute curriculum, Portfolio Management (systematic and nonsystematic risk)

A client's employer stock makes up 70% of her portfolio. Her adviser says most of that exposure is company-specific. How can that risk best be reduced?

• a.Spread holdings across many issuers and industries rather than one company✓
• b.Shorten the average maturity, since the exposure is mainly rate risk
• c.Hedge the market's direction, since the exposure is mainly market risk
• d.Move to inflation-linked bonds, since the exposure is mainly inflation risk

Concentration in one issuer creates unsystematic (company-specific) risk, which diversification across issuers and industries largely eliminates. Hedging the market addresses systematic risk, which would remain even in a well-diversified portfolio. Shortening maturity reduces interest rate sensitivity of bonds and does not change employer-stock risk. Inflation-linked bonds address inflation risk, not the risk that one company's results disappoint.CFA Institute curriculum, Portfolio Management (diversification)