NASAA Series 66 — All Questions

A portfolio holds 60% in Stock A (expected return 12%) and 40% in Bond B (expected return 5%). The portfolio's expected return is:

• a.9.2%✓
• b.17%
• c.11.2%
• d.8.5%

Portfolio expected return is a weighted average: 0.60 x 12% + 0.40 x 5% = 7.2% + 2.0% = 9.2%. Multiply each weight by its return and sum.

A portfolio is 70% in a fund with a beta of 1.4 and 30% in a fund with a beta of 0.6. The portfolio's beta is:

• a.2.00
• b.1.00
• c.0.98
• d.1.16✓

Portfolio beta is a weighted average of the component betas: 0.70 x 1.4 + 0.30 x 0.6 = 0.98 + 0.18 = 1.16.

Using CAPM, if the risk-free rate is 3%, the expected market return is 10%, and a stock's beta is 1.2, the stock's required return is:

• a.8.4%
• b.13.0%
• c.15.0%
• d.11.4%✓

CAPM: required return = Rf + beta x (Rm - Rf) = 3% + 1.2 x (10% - 3%) = 3% + 1.2 x 7% = 3% + 8.4% = 11.4%.

A portfolio's CAPM-expected return is 11%, but it actually returned 13%. Its alpha is:

• a.+2%✓
• b.0%
• c.-2%
• d.+24%

Alpha = actual return - CAPM-expected return = 13% - 11% = +2%. A positive alpha indicates outperformance versus the risk-adjusted expectation.

A portfolio returns 12%, the risk-free rate is 2%, and the portfolio's standard deviation is 8%. Its Sharpe ratio is:

• a.10.0
• b.1.25✓
• c.0.17
• d.1.50

Sharpe ratio = (Rp - Rf) / standard deviation = (12% - 2%) / 8% = 10 / 8 = 1.25. It measures excess return per unit of total risk.

Fund A has a Sharpe ratio of 0.9; Fund B has a Sharpe ratio of 0.6. This indicates that:

• a.Fund A necessarily carries a higher standard deviation than Fund B
• b.The two funds are equally attractive on a risk-adjusted basis
• c.Fund B produced a higher total return
• d.Fund A delivered more return per unit of total risk✓

A higher Sharpe ratio means more excess return per unit of total risk (standard deviation). Fund A is more efficient on a risk-adjusted basis than Fund B.

A portfolio has an expected return of 8% and a standard deviation of 10%. Assuming returns are normally distributed, about 68% of annual outcomes should fall between:

• a.0% and 16%
• b.-2% and 18%✓
• c.-12% and 28%
• d.6% and 10%

About 68% of outcomes lie within plus or minus one standard deviation: 8% +/- 10% = -2% to 18%. Roughly 95% lie within two standard deviations.

A U.S. Treasury bill used as the risk-free asset has a beta of:

• a.-1
• b.0✓
• c.1
• d.Greater than 1

The risk-free asset has zero systematic risk, so its beta is 0: its return does not move with the market. A beta of 1 belongs to the market portfolio, a beta above 1 means more volatile than the market, and a negative beta means moving opposite the market, which a Treasury bill does not do.

Under CAPM, an investor is compensated with a higher expected return for bearing:

• a.Unsystematic risk, which diversification eliminates
• b.Liquidity risk from securities that are hard to sell quickly
• c.Systematic (market) risk, as measured by beta✓
• d.Total risk

CAPM holds that only systematic (non-diversifiable) risk, measured by beta, is rewarded. Unsystematic risk can be diversified away and therefore earns no risk premium.

Adding a risk-free asset to the risky portfolios on the efficient frontier creates:

• a.A security market line that plots each security's required return against its beta
• b.A straight line from the risk-free rate to the minimum-variance portfolio on the efficient frontier
• c.The capital market line, a straight line from the risk-free rate through the market portfolio✓
• d.A downward-curving line showing that more of the risk-free asset lowers expected return and raises risk

Combining the risk-free asset with the market portfolio produces the capital market line, a straight line from the risk-free rate through the market portfolio that dominates the efficient frontier alone. The security market line plots required return against beta for individual securities. The line touches the frontier at the market (tangency) portfolio, not at the minimum-variance portfolio. The risk-free asset lowers risk, so the combinations do not bend downward.

The correlation coefficient between two assets can range:

• a.From 0 to 100
• b.From -1.0 to +1.0✓
• c.From 0 to +1.0 only, since assets can never move in opposite directions
• d.From negative infinity to positive infinity

Correlation ranges from -1.0 (perfectly opposite) to +1.0 (perfectly together), with 0 meaning no linear relationship. Lower correlation improves diversification.

Two investors both choose portfolios on the efficient frontier but pick different points on it. The best explanation is that they:

• a.Are measured against different benchmarks
• b.Must have different time horizons
• c.Have different risk tolerances✓
• d.Hold different amounts of wealth

Every portfolio on the efficient frontier is efficient, and where an investor sits depends on personal risk tolerance and utility. More risk-averse investors choose lower-risk points and less risk-averse investors choose higher-risk points. Benchmarks are used to measure results, not to choose a point on the frontier. Time horizon may influence risk tolerance but does not by itself fix the point. Wealth does not restrict which frontier portfolio an investor can hold.

A criticism of standard deviation as a risk measure is that it:

• a.Measures only market risk, so it ignores a security's company-specific risk
• b.Counts only whether returns were positive or negative, not how far they were from the average
• c.Is calculated only for individual securities, so it cannot describe the total variability of a whole portfolio
• d.Treats upside and downside volatility the same, though investors mainly fear the downside✓

Standard deviation penalizes upside and downside movements equally, while investors chiefly fear downside. Measures such as the Sortino ratio use downside deviation instead. It measures total risk, not just market risk, which is what beta captures. It is based on how far returns deviate from their average, not simply on their sign. It can be computed for a portfolio as readily as for a single security.

Which bond has the GREATEST interest-rate (price) risk, all else equal?

• a.A 5-year floating-rate bond that resets quarterly
• b.A 1-year Treasury bill
• c.A 2-year note with a high coupon
• d.A 30-year zero-coupon bond✓

Interest-rate risk rises with duration. A long-maturity zero-coupon bond has the highest duration (no interim cash flows) and therefore the greatest price sensitivity to rate changes.

Purchasing-power (inflation) risk is MOST damaging to which holding?

• a.A diversified portfolio of common stocks
• b.A long-term fixed-rate bond✓
• c.A commodity fund
• d.A Treasury Inflation-Protected Security whose principal adjusts with the CPI

Inflation (purchasing-power) risk most harms long-term fixed-rate bonds, whose fixed payments lose real value. Stocks, TIPS, and commodities offer some inflation protection.

Reinvestment risk is the danger that:

• a.Inflation will steadily erode the real purchasing power of the fixed coupon payments
• b.Rising interest rates will cause the price of a long-term bond to fall before maturity
• c.A bond issuer will default and fail to return the investor's principal
• d.Coupon or principal proceeds must be reinvested at lower rates than the original✓

Reinvestment risk is that cash flows (coupons or maturing principal) must be reinvested at lower prevailing rates, reducing total return. Zero-coupon bonds avoid coupon reinvestment risk.

Credit (default) risk is BEST described as the risk that:

• a.Broad stock-market declines reduce the whole portfolio's value
• b.The issuer fails to make timely interest or principal payments✓
• c.The investor cannot sell the security quickly without a price concession
• d.Market interest rates will rise and push the bond's price below par

Credit/default risk is the chance an issuer cannot meet its interest or principal obligations. It is highest for low-rated (junk) issuers, and rating agencies assess it.

An investor in a thinly traded, non-listed limited partnership faces significant:

• a.Market risk
• b.Interest-rate risk requiring daily marking to market
• c.Reinvestment risk
• d.Liquidity risk✓

Liquidity (marketability) risk is the difficulty of selling an asset quickly at a fair price. Non-listed partnerships and private placements are illiquid and hard to exit.

Which of the following is a form of SYSTEMATIC risk?

• a.The risk that one firm's management makes a strategic error
• b.The risk that a single issuer is downgraded
• c.Market risk affecting nearly all securities at once✓
• d.The risk that a specific company's new product launch fails and its shares fall

Systematic risk (market, interest-rate, inflation, currency) affects broad markets and is non-diversifiable. The other choices describe unsystematic, company-specific risks.

A U.S. investor holding unhedged European stocks faces currency risk, meaning returns can fall if:

• a.The euro gains in value relative to the dollar
• b.Dividends are paid in euros
• c.Trading hours differ from U.S. hours
• d.The euro weakens against the U.S. dollar✓

Currency (exchange-rate) risk: when the euro weakens against the dollar, each euro of stock value and dividend converts into fewer dollars, which reduces the U.S. investor's return. A stronger euro raises dollar returns. The currency a dividend is paid in only matters through how the exchange rate moves. Differences in trading hours do not change the dollar value of the holding.

The risk that a change in tax law removes the federal tax exemption on certain municipal bonds is an example of:

• a.Default risk, from the municipality's deteriorating finances
• b.Interest-rate risk, from a broad rise in market yields
• c.Legislative (political) risk✓
• d.Reinvestment risk

Legislative/political risk is the danger that new laws or regulations adversely affect an investment, such as altering the favorable tax treatment of municipal bond interest.

Using the Rule of 72, approximately how long will it take money to double at an 8% annual compound return?

• a.About 9 years✓
• b.About 12 years
• c.About 6 years
• d.About 15 years

Rule of 72: years to double is approximately 72 / rate = 72 / 8 = 9 years. The rule estimates doubling time at a given compound rate of return.

Using the Rule of 72, what approximate annual return is needed to double an investment in 6 years?

• a.About 12%✓
• b.About 18%
• c.About 8%
• d.About 6%

Rule of 72: rate is approximately 72 / years = 72 / 6 = 12%. Rearranging the rule solves for the compound return required to double in a given time.

An investor deposits $10,000 at a 10% annual compound return for 3 years. The approximate future value is:

• a.$13,310✓
• b.$11,000
• c.$30,000
• d.$13,000

Future value = PV x (1 + r)^n = 10,000 x (1.10)^3 = 10,000 x 1.331 = $13,310. Compounding applies the return to the accumulated balance each year.

What is the approximate present value of $20,000 to be received in 2 years, discounted at 5% annually?

• a.$18,000
• b.$22,050
• c.$19,048
• d.$18,141✓

Present value = FV / (1 + r)^n = 20,000 / (1.05)^2 = 20,000 / 1.1025 = $18,141. A higher discount rate or a longer horizon lowers the present value.

For a given stated annual rate, increasing the compounding frequency from annual to monthly will:

• a.Reduce the future value of a deposit
• b.Increase the effective annual yield✓
• c.Leave the effective annual yield unchanged
• d.Decrease the effective annual yield

More frequent compounding raises the effective annual yield (and the future value) because interest starts earning interest sooner. Effective yield exceeds the nominal rate as frequency rises.

An investor contributes $5,000 at the end of each year for 30 years. Compared with contributing the same total amount all at once at year 30, the annual-contribution plan will:

• a.Accumulate more, because earlier contributions compound for longer✓
• b.Accumulate the same amount, since the total dollars contributed are identical
• c.Accumulate less, because spreading contributions out reduces total interest
• d.Produce a guaranteed loss

By the time value of money, earlier contributions compound longer, so a stream of annual contributions accumulates more than a single lump sum deposited at the end of the period.

If inflation averages 3% per year, approximately how long until the purchasing power of a dollar is cut in half?

• a.About 33 years
• b.About 12 years
• c.About 24 years✓
• d.About 48 years

The Rule of 72 applies to inflation: 72 / 3 = 24 years for purchasing power to halve (equivalently, for prices to double). About 12 years is what a 6% rate would give, 48 years corresponds to 1.5%, and 33 years comes from dividing a different constant (100) by 3.

An investment's internal rate of return (IRR) is the discount rate at which:

• a.The net present value of all cash flows equals zero✓
• b.The coupon rate equals the risk-free rate
• c.The undiscounted cash inflows equal twice the initial outflow
• d.The investment's future value equals its par value at maturity

IRR is the discount rate that makes the net present value of an investment's cash flows equal zero. It is compared with the required return to judge whether to accept the investment.

A portfolio earns a nominal 7% while inflation is 3%. The approximate real rate of return is:

• a.About 2%
• b.About 21%
• c.About 10%
• d.About 4%✓

Real return is approximately nominal return minus inflation = 7% - 3% = 4% (the exact Fisher calculation gives about 3.9%). It reflects the true gain in purchasing power.

$1,000 invested at 7% compounded annually grows to about $1,967 after 10 years. After 20 years it will be worth approximately:

• a.$3,934
• b.$3,870✓
• c.$2,400
• d.$1,967

Future value = 1,000 x (1.07)^20 = about 1,000 x 3.87 = $3,870. Doubling the horizon more than doubles the value because compounding accelerates over time.

Two zero-coupon bonds both pay $1,000 at maturity in 10 years. Bond X is discounted at 4% and Bond Y at 8%. Which has the higher present value (price) today?

• a.Bond Y
• b.Bond X✓
• c.Neither can be valued without a coupon rate
• d.They have identical present values

A lower discount rate produces a higher present value, so Bond X (4%) is worth more today than Bond Y (8%). Present value and the discount rate move inversely.

A client wants a quick estimate of how many years it takes to double at a 9% annual return. The best estimate is:

• a.About 12 years
• b.About 8 years✓
• c.About 4 years
• d.About 6 years

Rule of 72: 72 / 9 = 8 years to double. The rule provides a fast mental estimate of the compound doubling time at a given return.

A bond has a modified duration of 6. If interest rates rise by 1%, the bond's price will approximately:

• a.Remain unchanged
• b.Rise by about 6%
• c.Fall by about 6%✓
• d.Fall by about 1%

Approximate price change is roughly minus modified duration times the change in yield = -6 x 1% = -6%. Prices fall as rates rise, scaled by duration.

A bond portfolio has a duration of 8. If interest rates fall by 0.5%, the portfolio's value will approximately:

• a.Rise by about 4%✓
• b.Remain flat
• c.Rise by about 0.5%
• d.Fall by about 4%

Price change is roughly minus duration times the change in yield = -8 x (-0.5%) = +4%. Falling rates raise bond prices, magnified by the portfolio's duration.

A barbell bond strategy concentrates holdings in:

• a.Intermediate maturities clustered around a single duration target
• b.Only floating-rate notes that reset every ninety days
• c.Short-term and long-term maturities, with little in between✓
• d.A single long-term maturity chosen to maximize yield to maturity

A barbell concentrates in short and long maturities while avoiding intermediates, blending the liquidity and lower rate risk of short bonds with the higher yield of long bonds.

A bullet bond strategy involves:

• a.Spreading maturities evenly across many consecutive years so an equal portion matures every year
• b.Concentrating maturities around a single target date to fund a known future liability✓
• c.Holding only very short and very long maturities, with nothing in the intermediate range
• d.Buying bonds that can all be called on one date, so the issuer decides when the portfolio matures

A bullet strategy clusters maturities around a single target date, which suits funding a specific future obligation. Spreading maturities evenly is a ladder. Holding only the shortest and longest maturities is a barbell. Callable bonds put the redemption timing in the issuer's hands, so they do not let the investor target a liability date.

Portfolio immunization seeks to protect a bond portfolio from interest-rate risk by:

• a.Matching the portfolio's average coupon rate to the investor's required return
• b.Matching the portfolio's duration to the investor's time horizon✓
• c.Trading bonds frequently to time rate changes
• d.Holding only long-term bonds to lock in the highest yield

Immunization matches portfolio duration to the investment horizon so that price risk and reinvestment risk offset each other, locking in a target return over that horizon. Matching the coupon rate to a required return ignores duration. Frequent trading is market timing, which does not protect against rate risk. Long bonds carry the most price risk, so holding only them does the opposite.

Positive convexity in a bond is desirable because, for a large change in yields, it means:

• a.The bond's duration stays constant no matter how far rates move
• b.The issuer can call the bond at a premium whenever rates decline
• c.Prices fall more when rates rise than they gain when rates fall equally
• d.Prices rise more when rates fall than they fall when rates rise by the same amount✓

Positive convexity means the price-yield curve bends favorably: price gains from a fall in yields exceed price losses from an equal rise. It also means duration changes as yields move, so duration alone is only a linear estimate. A call feature is the source of negative convexity, and negative convexity is the reverse pattern, with larger losses than gains.

'Riding the yield curve' is a strategy in which an investor, in an upward-sloping yield-curve environment:

• a.Buys a longer bond and sells it before maturity as it 'rolls down' to a lower yield and a higher price✓
• b.Buys only the shortest-term Treasury bills and rolls them over as each one matures
• c.Holds each bond to maturity and collects the coupons, with no sale before then
• d.Sells short-term bonds and buys longer ones as the curve steepens, betting that yields keep rising

Riding the yield curve buys a longer-maturity bond and sells it later, after its remaining maturity has shortened and its yield has dropped along an upward-sloping curve, capturing the price gain. Rolling over bills never captures that roll-down. Holding to maturity earns only the coupons and the par value. Betting that yields keep rising is a rate bet that loses on price if it is right.

A bond with a 5% coupon and $1,000 par is trading at $800. Its current yield is:

• a.6.25%✓
• b.5.00%
• c.4.00%
• d.8.00%

Current yield = annual coupon / market price = $50 / $800 = 6.25%. Buying a bond below par raises its current yield above the stated coupon rate.

For a bond trading at a premium above par, the correct ordering of yields from lowest to highest is:

• a.Yield to maturity, then current yield, then nominal coupon yield, arranged from the very lowest up to the highest
• b.All three yields are exactly equal to one another whenever a bond happens to trade at any price other than par
• c.Yield to maturity, current yield, nominal (coupon) yield✓
• d.Current yield, then nominal coupon yield, then yield to maturity, arranged from the very lowest up to the highest

For a premium bond: yield to maturity is less than current yield, which is less than the nominal (coupon) yield. For a discount bond, this ordering reverses.

To fund a child's college tuition due in exactly 12 years, which bond choice best eliminates reinvestment risk?

• a.A money market fund rolled over continuously
• b.A zero-coupon bond maturing in 12 years✓
• c.High-coupon corporate bonds
• d.A bond ladder that staggers maturities over twelve years

A zero-coupon bond pays no interim coupons, so there is nothing to reinvest, eliminating reinvestment risk and locking in a known maturity value for the target date.

During the year a client realizes $8,000 of long-term capital gains and $3,000 of long-term capital losses. The net capital gain is:

• a.$0
• b.$5,000 long-term gain✓
• c.$3,000, the maximum annual capital-loss deduction
• d.$11,000

Gains and losses of the same character net against each other: $8,000 - $3,000 = $5,000 net long-term capital gain, which is taxed at the preferential long-term rate.

A client has a net capital loss of $9,000 for the year and no capital gains. On this year's return the client may deduct against ordinary income:

• a.The full $9,000, since a net capital loss is fully deductible
• b.$3,000, carrying the remaining $6,000 forward to future years✓
• c.$4,500, one-half of the net capital loss
• d.$0, because capital losses can offset only capital gains and never ordinary income

Net capital losses offset ordinary income up to $3,000 per year, and the excess ($6,000) carries forward indefinitely to offset future gains or income.

A municipal bond yields 4% tax-free. For an investor in the 25% federal tax bracket, the taxable-equivalent yield is:

• a.3.00%
• b.5.00%
• c.5.33%✓
• d.4.25%

Taxable-equivalent yield = tax-free yield / (1 - tax rate) = 4% / (1 - 0.25) = 4% / 0.75 = 5.33%. It lets a muni be compared with taxable bonds.

A municipal bond yields 3.5% tax-free. For an investor in the 32% bracket, the taxable-equivalent yield is approximately:

• a.2.38%
• b.3.82%
• c.4.20%
• d.5.15%✓

Taxable-equivalent yield = 3.5% / (1 - 0.32) = 3.5% / 0.68 = 5.15%. A higher tax bracket raises the taxable-equivalent yield, making munis more attractive.

A corporate bond yields 6%. For an investor in the 30% bracket, the after-tax yield is:

• a.2.00%
• b.6.00%
• c.7.80%
• d.4.20%✓

After-tax yield = taxable yield x (1 - tax rate) = 6% x (1 - 0.30) = 6% x 0.70 = 4.20%. This can then be compared with a municipal bond's tax-free yield.

An investor in the 35% bracket compares a 4% municipal bond with a 6% corporate bond. Which is better after tax, and why?

• a.The corporate bond, because its stated 6% yield is higher than the muni's 4%
• b.The muni, because its taxable-equivalent yield of about 6.15% exceeds the corporate's 6%✓
• c.They are identical after tax, because both provide the same after-tax income
• d.The corporate bond is better, because municipal bond interest is fully taxable at ordinary income rates

The muni's taxable-equivalent yield = 4% / (1 - 0.35) = 6.15%, which beats the 6% corporate. Bonds must be compared on an equivalent after-tax basis.

Which action would trigger the wash-sale rule and disallow a loss?

• a.Selling a stock at a loss and buying a different company in an unrelated industry
• b.Selling a bond at a loss and buying an unrelated stock two months later
• c.Buying the same stock 20 days BEFORE selling other shares of it at a loss✓
• d.Selling a stock at a loss and waiting 45 days before repurchasing the same shares

The wash-sale rule applies to purchases of substantially identical securities within 30 days before or after the loss sale, including a purchase made before the sale.