NASAA Series 65 — All Questions

The Producer Price Index differs from the Consumer Price Index because the Producer Price Index measures:

• a.The total value of all finished goods and services produced within a nation
• b.Prices received by domestic producers for their output at the wholesale level✓
• c.Prices paid by urban households for a fixed basket of retail goods and services
• d.The average hourly wage paid across the private nonfarm business sector

The PPI tracks selling prices from the producer's point of view, which is why it is often watched as an early warning of consumer inflation still working its way through the supply chain. The CPI tracks what households actually pay at retail. Total output is measured by GDP, and wage data come from separate labor statistics releases.

The fundamental accounting equation reflected on a corporation's balance sheet states that:

• a.Net income equals total revenue minus the cost of the goods sold
• b.Working capital equals current assets plus current liabilities
• c.Total assets equal total liabilities plus total shareholders' equity✓
• d.Total assets equal total revenues minus total operating expenses

A balance sheet balances because everything the company owns was financed either by creditors or by owners: Assets = Liabilities + Shareholders' Equity. Revenue minus expenses produces net income on the income statement, not assets. Working capital is current assets MINUS current liabilities, not the sum of them.

A company reports net sales of $5,000,000 and cost of goods sold of $3,000,000. Its gross profit margin is:

• a.20%
• b.40%✓
• c.60%
• d.167%

Gross profit = $5,000,000 - $3,000,000 = $2,000,000. Gross profit margin = $2,000,000 / $5,000,000 = 0.40, or 40%. The 60% figure is the cost of goods sold as a percentage of sales, which is the complement of the answer, not the margin itself. Gross margin measures production efficiency before operating expenses, interest, and taxes.

A firm earns net income of $600,000 on net sales of $8,000,000. Its net profit margin is closest to:

• a.4.8%
• b.13.3%
• c.0.8%
• d.7.5%✓

Net profit margin = net income / net sales = $600,000 / $8,000,000 = 0.075, or 7.5%. The 13.3% figure inverts the ratio ($8,000,000 / $600,000 = 13.3 times, which is not a margin). Net margin captures what survives after every expense, so it is compared across firms in the same industry rather than across industries.

A common stock trades at $40 per share and pays a quarterly dividend of $0.30. Its current dividend yield is:

• a.3.33%
• b.13.3%
• c.0.75%
• d.3.0%✓

Annualize the dividend first: $0.30 x 4 = $1.20 per year. Dividend yield = $1.20 / $40.00 = 0.03, or 3.0%. Using the quarterly $0.30 without annualizing produces the 0.75% trap. Dividend yield rises when the share price falls, so a suddenly high yield can signal market doubt about the dividend rather than a bargain.

A company's common shares trade at $45 while its book value per share is $30. Its price-to-book ratio is:

• a.15.0
• b.1.5✓
• c.1.15
• d.0.67

Price-to-book = market price per share / book value per share = $45 / $30 = 1.5. The 0.67 figure inverts the ratio. A price-to-book above 1.0 means the market values the company above its accounting net worth, often because of intangible assets or expected growth that the balance sheet does not capture.

An investor deposits $10,000 in an account paying 6% compounded annually. Ignoring taxes, the balance after two years is:

• a.$11,236✓
• b.$11,000
• c.$12,360
• d.$11,200

Year one: $10,000 x 1.06 = $10,600. Year two: $10,600 x 1.06 = $11,236. Equivalently, $10,000 x (1.06)^2 = $11,236. The $11,200 answer applies simple interest of $600 per year and ignores the $36 of interest earned on the first year's interest, which is exactly the compounding effect the question is testing.

Compared with an ordinary annuity that pays the same amount for the same number of periods, an annuity due has:

• a.A higher present value, because each payment arrives at the beginning of the period✓
• b.An unpredictable present value, because the payer chooses the timing each period
• c.An identical present value, because the number of payments does not change
• d.A lower present value, because each payment arrives at the end of the period

In an annuity due each cash flow is received one period sooner than in an ordinary annuity, so each is discounted for one less period and the present value is higher. Rent and insurance premiums are typical annuities due; bond coupons and most loan payments are ordinary annuities. The count of payments is the same in both, which is why timing alone drives the difference.

Under the net present value method, a proposed capital project should be accepted when:

• a.The total undiscounted inflows exceed the accounting profit reported for the project
• b.The present value of the expected cash inflows exceeds the initial cost of the project✓
• c.The discount rate applied to the project is greater than its internal rate of return
• d.The payback period is longer than the estimated useful life of the new equipment

Net present value discounts every expected future cash flow back to today at the required rate of return and subtracts the outlay. A positive NPV means the project earns more than the required rate and adds value. A discount rate above the internal rate of return produces a negative NPV, and a payback period longer than the asset's life means the outlay is never recovered.

The internal rate of return on an investment is best defined as the discount rate that:

• a.Makes the net present value of all expected cash flows equal to zero✓
• b.A lender charges the investor to finance the purchase of the asset
• c.Reflects the rate of inflation expected over the investment's holding period
• d.Equals the average annual accounting profit divided by the initial outlay

The internal rate of return is the break-even discount rate: apply it to the cash flows and the present value of inflows exactly equals the outflow, so NPV is zero. For a bond held to maturity, the IRR of the cash flows is the yield to maturity. Accounting profit measures, borrowing costs, and inflation expectations are all separate concepts.

A retailer reports cost of goods sold of $6,000,000 and average inventory of $1,500,000. Its inventory turnover ratio is:

• a.9.0 times
• b.4.0 times✓
• c.2.5 times
• d.0.25 times

Inventory turnover = cost of goods sold / average inventory = $6,000,000 / $1,500,000 = 4.0 times per year. That implies roughly 365 / 4 = 91 days of inventory on hand. A falling turnover ratio can warn that merchandise is not selling and that write-downs may follow.

The point in the business cycle at which output stops declining and begins to recover is called the:

• a.Peak, the turning point that ends an expansion
• b.Recession, two consecutive quarters of falling output
• c.Trough, the turning point that ends a contraction✓
• d.Plateau, a period of entirely unchanging real output

The four phases of the business cycle are expansion, peak, contraction, and trough. The trough is the low point where activity bottoms and the next expansion begins. The peak is the opposite turning point. A recession is a phase of decline, not a turning point, and 'plateau' is not a recognized phase of the cycle.

On a corporation's statement of cash flows, cash spent to repurchase the company's own common stock is classified as:

• a.A noncash item, because no funds actually leave the corporation
• b.An operating activity, because it arises from day-to-day business
• c.A financing activity, because it changes the firm's capital structure✓
• d.An investing activity, because it involves a purchase of securities

The statement of cash flows has three sections. Financing activities cover transactions with owners and lenders: issuing or repurchasing stock, paying dividends, and borrowing or repaying debt. Investing activities cover the purchase and sale of long-term assets and of securities of OTHER issuers. Operating activities cover the cash effects of running the business.

In textbook monetary analysis, lowering the reserve requirement ratio (which the Federal Reserve has set at 0% since March 26, 2020) would most likely:

• a.Increase the money supply by allowing banks to lend a larger share of deposits✓
• b.Leave lending unchanged, since banks fund their loans from capital rather than from deposits
• c.Reduce the money supply, because banks would have to hold a larger share of each deposit in reserve
• d.Raise the federal funds rate by reducing the supply of reserves available to banks

A lower reserve requirement frees a larger share of each deposit for lending, so the money multiplier rises, the money supply expands, and interest rates tend to fall. This is an expansionary tool. The Federal Reserve reduced reserve requirement ratios to zero percent effective March 26, 2020, so today it steers rates mainly through other tools, but the textbook effect is unchanged. Claiming no effect ignores that banks lend out deposits beyond the reserves they must hold. Holding more in reserve and shrinking the supply of reserves describe a higher requirement, not a lower one.Federal Reserve Board, Reserve Requirements (federalreserve.gov/monetarypolicy/reservereq.htm)

When the Federal Reserve raises the discount rate, the direct effect is that:

• a.Treasury bill prices rise as the Fed stops buying securities
• b.Borrowing from the Fed's discount window becomes more expensive for banks✓
• c.The rate banks charge one another overnight is fixed by the Fed at the new level
• d.Banks must hold a larger percentage of deposits as required reserves

The discount rate is the rate charged on discount-window loans to depository institutions, so raising it makes that borrowing costlier and signals tighter policy. Reserve requirements are a separate tool and are set at zero. Bill prices do not rise because of it. The federal funds rate is negotiated between banks; the Fed targets a range rather than fixing it.

A worker's nominal wages rise 2.1% over a year while the Consumer Price Index rises 3.2%. The worker's real wage has:

• a.Fallen about 1.1%, so purchasing power declined✓
• b.Risen about 1.1%, because nominal wages went up
• c.Fallen about 3.2%, the full rate of inflation
• d.Risen about 5.3%, the sum of the two rates

Real wage growth is approximately nominal growth minus inflation: 2.1% - 3.2% = -1.1%. Nominal gains do not raise purchasing power when prices rise faster. Only the gap between the rates matters, not inflation alone. Adding the rates would be correct only for a deflation of the same size.

Which combination describes stagflation?

• a.Falling prices together with slow output growth and high unemployment
• b.Rising prices together with strong output growth and low unemployment
• c.Rising prices together with slow output growth and high unemployment✓
• d.Stable prices together with slow output growth and high unemployment

Stagflation pairs inflation with weak growth and high joblessness, which is why tightening policy to cut prices tends to deepen the slowdown. Falling prices with weak output describe deflationary depression. Inflation with strong growth is an overheating economy. With stable prices, a weak economy is an ordinary recession.

A stock trades at a P/E ratio of 24, and analysts expect its earnings per share to grow 12% a year. Its PEG ratio is:

• a.288.0
• b.2.0✓
• c.0.5
• d.12.0

PEG is the P/E ratio divided by the expected annual earnings growth rate expressed in whole percent: 24 / 12 = 2.0. A result of 0.5 comes from inverting the division. Subtracting the growth rate gives 12, and multiplying the two figures gives 288; neither is a PEG ratio.

A company is expected to pay a dividend of $2.40 next year. Dividends are expected to grow 4% a year indefinitely, and investors require a 10% return. Under the constant-growth dividend discount model, the stock's value is:

• a.$17.14
• b.$24.00
• c.$40.00✓
• d.$60.00

Value = D1 / (r - g) = $2.40 / (0.10 - 0.04) = $2.40 / 0.06 = $40.00. Dividing by 10% alone ($24.00) ignores growth. Dividing by r plus g (14%) gives $17.14, and dividing by g alone (4%) gives $60.00; both misuse the denominator.

In the constant-growth dividend discount model, which change by itself would raise the estimated value of a stock?

• a.A wider spread between the required return and the dividend growth rate
• b.A lower expected dividend next year, with growth and required return unchanged
• c.A higher required return, with the expected dividend and growth rate unchanged
• d.A higher expected growth rate in dividends, required return unchanged✓

Value = D1 / (r - g). A higher g narrows the denominator and lifts value. A higher r or a larger r - g spread widens the denominator and lowers value, and a lower D1 shrinks the numerator.

The risk-free rate is 3%, the expected market return is 10%, and a stock has a beta of 1.2. Under the capital asset pricing model, the stock's required return is:

• a.13.0%
• b.8.4%
• c.12.0%
• d.11.4%✓

Required return = Rf + beta x (Rm - Rf) = 3% + 1.2 x 7% = 3% + 8.4% = 11.4%. Multiplying beta by the market return (12.0%) skips the risk-free rate and the premium. Using only beta times the premium (8.4%) omits Rf. Adding Rf and Rm (13.0%) ignores beta.

A stock is expected to return 9%, while the capital asset pricing model says it should return 11.4%. On a security market line graph, the stock plots:

• a.Above the line, so it is overpriced
• b.On the line, so it is fairly priced
• c.Below the line, so it is underpriced
• d.Below the line, so it is overpriced✓

A stock whose expected return falls short of the CAPM required return has a negative alpha and plots below the security market line; it offers too little return for its risk, so it is overpriced. Stocks above the line are underpriced. Only a stock whose expected return equals the required return sits on the line.

A portfolio earned 12% with a beta of 1.1. The risk-free rate was 3% and the market returned 9%. The portfolio's Jensen alpha is:

• a.+2.4%✓
• b.+3.0%
• c.-2.4%
• d.+9.6%

CAPM expected return = 3% + 1.1 x (9% - 3%) = 9.6%. Alpha = actual 12% - 9.6% = +2.4%. A +3.0% figure compares the portfolio with the market return and ignores beta. Reversing the subtraction gives -2.4%. The 9.6% is the benchmark return, not the excess over it.

A portfolio returned 11% with a beta of 1.25 when the risk-free rate was 3%. Its Treynor ratio is:

• a.6.4%✓
• b.2.4%
• c.8.8%
• d.10.0%

Treynor = (return - risk-free rate) / beta = 8% / 1.25 = 6.4%. Dividing the raw return by beta (8.8%) skips the risk-free rate. Multiplying the excess return by beta gives 10.0%, and dividing the risk-free rate by beta gives 2.4%; neither measures excess return per unit of systematic risk.

A portfolio on the efficient frontier offers:

• a.A guaranteed return equal to the risk-free rate
• b.The highest expected return available for its level of risk✓
• c.A higher return than every other portfolio at every level of risk
• d.The lowest standard deviation of any possible portfolio

The efficient frontier connects portfolios that give the most expected return for each level of risk. Only the global minimum-variance portfolio has the lowest standard deviation. Frontier portfolios trade off risk and return against one another, so none beats all others at every risk level. Frontier portfolios still carry risk.

Two assets whose returns have a correlation coefficient of +1.0 are combined in a portfolio. The portfolio's standard deviation is:

• a.The weighted average of the two standard deviations✓
• b.Zero, if the two assets are held in equal dollar amounts
• c.Lower than the weighted average, because some offsetting still occurs
• d.Higher than the weighted average, because the risks compound together

With perfect positive correlation the assets move in lockstep, so combining them offers no diversification and the portfolio's risk is exactly the weighted average. Any correlation below +1.0 pulls risk under that average. Risk cannot exceed the weighted average, because that is the maximum. Zero risk would require a correlation of -1.0 and specific weights.

Adding more unrelated stocks to a 20-stock portfolio mainly reduces:

• a.Interest rate risk on its bond holdings
• b.Unsystematic risk specific to individual companies✓
• c.Inflation risk on the portfolio's purchasing power
• d.Systematic risk that affects the whole market

Diversification averages out company-specific events, so unsystematic risk falls as holdings are added. Systematic risk cannot be diversified away within one market. Inflation and interest rate risk are market-wide exposures that more stocks do not remove, and interest rate risk concerns bonds rather than stocks.

Annual returns for a stock are normally distributed with a mean of 8% and a standard deviation of 10%. About 68% of annual returns should fall between:

• a.-12% and 28%
• b.-2% and 18%✓
• c.-22% and 38%
• d.0% and 16%

About 68% of outcomes lie within one standard deviation of the mean: 8% +/- 10% gives -2% to 18%. Two standard deviations (-12% to 28%) cover about 95%, and three (-22% to 38%) cover about 99.7%. The 0% to 16% band uses a deviation of 8%, which is the mean, not the spread.

A bond with positive convexity and no embedded options will see its price respond to a fall in yield by:

• a.Rising by exactly as much as it would fall for the same rise in yield
• b.Rising only if the issuer has the right to call it
• c.Rising by less than it would fall for a rise in yield of the same size
• d.Rising by more than it would fall for a rise in yield of the same size✓

Positive convexity means the price-yield curve bends upward, so gains from falling yields exceed losses from equal rises. Duration alone would predict equal moves in both directions. A callable bond tends to have negative convexity when yields fall, which is the opposite of the effect here.

A 10-year zero-coupon bond has a Macaulay duration of:

• a.10 years, equal to its time to maturity✓
• b.More than 10 years, because interest compounds
• c.5 years, the midpoint of its life
• d.Zero, because it pays no coupons

A zero-coupon bond's only cash flow comes at maturity, so its Macaulay duration equals its maturity. Coupon bonds have durations below maturity. Having no coupons raises, not lowers, duration. Compounding does not extend duration past the single payment date.

An investor holds a 10-year Treasury bought at par with a 2.5% coupon. Yields on comparable Treasuries have risen to 3.5%. The bond will most likely trade:

• a.At a discount to par, because its 2.5% coupon is below the market yield✓
• b.At a premium to par, because the coupon is locked in for the next ten years
• c.At par, because Treasury principal is backed by the full faith of the government
• d.At a premium to par, because yields rose and bond prices follow yields upward

When market yields exceed a bond's coupon, the price drops below par so the buyer's yield reaches the market rate. A fixed coupon below market is a drawback, not a benefit. Government backing assures repayment at maturity but does not hold the market price at par. Price and yield move in opposite directions.

Under the pure expectations theory, a downward-sloping (inverted) yield curve implies that the market expects short-term rates to:

• a.Stay at today's level
• b.Fall in the future✓
• c.Rise in the future
• d.Rise, because long bonds carry a risk premium

In the pure expectations theory, long-term rates are an average of current and expected future short rates, so a long rate below the short rate means short rates are expected to fall. Expecting a rise would give an upward slope. If rates were expected to stay put, the curve would be flat. A risk premium belongs to liquidity preference theory, not pure expectations.

Inflation expectations rise from 2% to 4% while the real interest rate stays unchanged. The nominal rate will:

• a.Rise about 4 percentage points, matching the new inflation rate
• b.Stay unchanged, because the central bank sets nominal rates
• c.Rise about 2 percentage points, keeping the real rate the same✓
• d.Fall, because higher inflation erodes interest income

By the Fisher relationship, nominal rate is about real rate plus expected inflation, so a 2-point rise in expected inflation adds about 2 points. A 4-point rise would take the full inflation level instead of the change. Lenders raise nominal rates, not cut them, to offset inflation. Market nominal rates move with expectations even though the central bank sets its policy rate.

A bond pays a nominal yield of 6.5% while expected inflation is 2.5%. The approximate real yield is:

• a.9.0%
• b.4.0%✓
• c.6.5%
• d.2.6%

Real yield is about nominal yield minus expected inflation: 6.5% - 2.5% = 4.0%. Adding the two rates gives 9.0%. Dividing 6.5 by 2.5 gives 2.6, which is a ratio, not a rate. A real yield of 6.5% would assume zero inflation.

A company has net profit margin of 5%, asset turnover of 1.6 and an equity multiplier of 2.5. Using the DuPont formula, its return on equity is:

• a.20.0%✓
• b.3.2%
• c.8.0%
• d.12.5%

ROE = margin x turnover x equity multiplier = 0.05 x 1.6 x 2.5 = 0.20 or 20%. Margin times turnover alone (8%) is return on assets. Leaving out turnover gives 12.5%. Dividing by the multiplier instead of multiplying gives 3.2%.

A company retains 60% of its earnings and earns a 15% return on equity. Its sustainable growth rate is:

• a.9.0%✓
• b.6.0%
• c.25.0%
• d.15.0%

Sustainable growth = ROE x retention ratio = 15% x 0.60 = 9.0%. Using ROE alone (15%) assumes everything is retained. Using the payout ratio (40%) instead gives 6.0%. Dividing ROE by retention gives 25%, which inverts the relationship.

A technician sees a stock fail repeatedly at $50, then close above it on heavy volume. A technician would most likely view the move as:

• a.A bullish breakout, with the old resistance at $50 now a likely support✓
• b.A neutral result, because volume says nothing about the strength of a price trend
• c.A false signal, because a stock that failed at $50 several times will fail again
• d.A bearish sign, because the stock now trades above its fair value and should fall

A heavy-volume close above resistance suggests demand has overcome supply, and old resistance often becomes support. Technicians read price and volume, not fair value, so the fair-value argument misses the method. A neutral reading ignores that volume is the confirmation that makes a breakout meaningful. A repeat failure is possible, but the signal here is the opposite.

A U.S. investor owns a British stock that gains 5% in pounds. Over the same period the pound falls 8% against the dollar. The investor's return in dollars is about:

• a.A loss of 3.4%✓
• b.A gain of 13.0%
• c.A gain of 5.0%
• d.A loss of 8.0%

Dollar return = 1.05 x 0.92 - 1 = -3.4%. The local gain alone (5%) ignores currency. The currency loss alone (8%) ignores the stock gain. Adding 5% and 8% treats a falling pound as if it helped.

The Federal Reserve raises the interest rate it pays banks on their reserve balances. This tends to tighten credit because banks:

• a.Lose access to the discount window until market rates have fallen again
• b.Must hold a larger percentage of their deposits in required reserves
• c.Will not lend reserves for less than they can earn at the Fed, so short-term rates rise✓
• d.Earn less on idle reserves and so lend more to businesses

The rate on reserve balances acts as a floor: a bank has no reason to lend reserves to another bank for less than the Fed pays, so market short-term rates move up with it. Reserve requirements are set at zero and are a different tool. Paying more makes holding reserves more attractive, not less, and the discount window stays open to eligible banks.

The Fed lets maturing Treasury securities on its balance sheet run off without reinvesting the proceeds. Over time this tends to:

• a.Shrink bank reserves and tighten financial conditions✓
• b.Expand bank reserves and ease financial conditions
• c.Leave reserves unchanged, because the Treasury repays the Fed in kind
• d.Lower the federal funds target range directly

When a security matures and is not replaced, the Treasury's payment drains reserves from the banking system, which reverses the effect of earlier asset purchases. It does not add reserves and it does not leave them untouched. The target range is a separate policy decision made by the Federal Open Market Committee.

A fund's monthly returns show an R-squared of 0.92 against its benchmark index. This means that:

• a.The fund outperformed the benchmark in 92% of the months measured
• b.The fund earned an alpha of 0.92 percentage point a year
• c.About 92% of the variation in the fund's returns is explained by the benchmark's movements✓
• d.The fund's beta relative to the benchmark equals 0.92

R-squared is the share of a fund's return variation that is explained by movements in the benchmark, so 0.92 means a close fit to the index. It says nothing about how often the fund won, which is a hit rate. Beta measures sensitivity and alpha measures excess return; each is a separate statistic.

Fund X has a mean return of 10% and a standard deviation of 15%. Fund Y has a mean return of 6% and a standard deviation of 6%. Using the coefficient of variation, which fund has less risk per unit of return?

• a.Fund X, because its coefficient of variation of 1.5 is the lower figure
• b.Fund X, because its 10% mean return is the higher return of the two
• c.Fund Y, with a coefficient of variation of 1.0✓
• d.Neither fund, because the two means differ and cannot be compared

Coefficient of variation = standard deviation / mean. Fund X: 15 / 10 = 1.5. Fund Y: 6 / 6 = 1.0. The lower figure means less risk for each unit of return, so Fund Y wins. A higher mean return alone ignores risk, and the statistic exists precisely so funds with different means can be compared.

A bond has a Macaulay duration of 5.4 years and a yield to maturity of 8%, compounded annually. Its modified duration is:

• a.4.3 years
• b.5.0 years✓
• c.5.4 years
• d.5.8 years

Modified duration = Macaulay duration / (1 + yield) = 5.4 / 1.08 = 5.0. Multiplying by 1.08 gives 5.83, and leaving duration unchanged gives 5.4. Multiplying by 0.8 gives 4.32, which misreads the 8% yield as a factor.

A savings account pays 12% nominal annual interest, compounded monthly. The effective annual rate is closest to:

• a.12.36%
• b.12.55%
• c.12.68%✓
• d.12.00%

Effective annual rate = (1 + 0.12/12)^12 - 1 = 1.01^12 - 1 = 12.68%. The 12.00% figure ignores compounding. Semiannual compounding gives 12.36% and quarterly compounding gives 12.55%, both of which compound less often than the account does.

A firm's cost of goods sold is $900,000 and its average inventory is $150,000. Using a 365-day year, it takes about how many days to sell its inventory?

• a.61 days✓
• b.30 days
• c.122 days
• d.6 days

Inventory turnover = $900,000 / $150,000 = 6.0 times a year, so days to sell = 365 / 6 = about 61. The figure 6 is the turnover itself, not a number of days. The 122-day and 30-day answers do not follow from the data given.

A company has total liabilities of $600,000 and shareholders' equity of $400,000. Its debt-to-equity ratio is:

• a.0.6
• b.2.5
• c.1.5✓
• d.0.67

Debt-to-equity = total liabilities / shareholders' equity = $600,000 / $400,000 = 1.5. Inverting the fraction gives 0.67. Dividing liabilities by the $1,000,000 of total capital gives 0.6, and dividing total assets by equity gives 2.5, the equity multiplier.

Under the expenditure approach to GDP, a manufacturer's purchase of new machinery for its plant is counted in which component?

• a.Gross private domestic investment✓
• b.Personal consumption expenditures
• c.Government purchases
• d.Net exports

The expenditure approach adds consumption, investment, government purchases and net exports. Business purchases of new capital goods such as machinery are gross private domestic investment. Household spending is consumption, purchases by governments are government spending, and exports minus imports make up net exports.GDP expenditure approach

Heavy federal borrowing to finance a deficit raises market interest rates and reduces private investment. Economists call this effect:

• a.A liquidity trap
• b.Stagflation
• c.Crowding out✓
• d.The wealth effect

Crowding out describes government borrowing competing for savings and pushing up rates, which discourages private investment. A liquidity trap describes a state where lower rates fail to stimulate spending. Stagflation pairs inflation with weak growth, and the wealth effect links asset values to consumer spending.

A bond has a modified duration of 7. If market yields fall by 0.5 percentage point, the bond's price should rise by approximately

• a.0.5%
• b.7%
• c.3.5%✓
• d.14%

Price change is roughly modified duration times the yield change: 7 x 0.5% = 3.5%. A 0.5% price change would confuse the yield move with the price move. A 7% gain would apply the duration to a full 1-point drop. A 14% gain would multiply duration by 2 for no reason.Bond duration

For a bond with positive convexity, an equal-sized change in yield produces which price effect?

• a.The loss from a yield rise exceeds the gain from a yield decline
• b.The gain and loss are equal because price moves linearly
• c.The price falls in both cases because convexity adds risk
• d.The gain from a yield decline exceeds the loss from a yield rise✓

Positive convexity means the price-yield curve is convex, so price rises more when yields fall than it drops when yields rise by the same amount. A larger loss describes negative convexity, as in callable bonds near the call price. Equal gains and losses would make the relationship linear, which duration alone assumes. Price cannot fall in both directions, because yield and price still move inversely.Bond convexity