NASAA Series 65 — All Questions

A firm is financed 60% by equity costing 10% and 40% by debt with a 6% pre-tax cost. The tax rate is 25%. Its weighted average cost of capital is:

• a.around 6.3%
• b.8.4%
• c.approximately 7.8%✓
• d.about 8.0%

WACC = 0.60 x 10% + 0.40 x 6% x (1 - 0.25) = 6.0% + 1.8% = 7.8%. Recheck: 0.4 x 6 = 2.4; 2.4 x 0.75 = 1.8. The 8.4% answer omits the debt tax shield (6.0 + 2.4). The 8.0% answer is the simple average of 10% and 6%, ignoring the weights. The 6.3% answer applies the tax adjustment to the entire weighted sum, including equity, whose cost is not tax-deductible.CFA Institute curriculum, Corporate Issuers (cost of capital)

A bond has a modified duration of 6.0. If its yield rises by 50 basis points, what is the approximate percentage change in price?

• a.A decrease of about 0.3%
• b.A decrease of about 12.0%
• c.A decrease of about 3.0%✓
• d.An increase of about 3.0%

Modified duration estimates the percentage price change per 1 percentage point change in yield, with an inverse relationship. A 0.50 point rise times 6.0 gives roughly a 3.0% price decline. Reading 50 basis points as 5 points would yield a far larger move, and a rising yield cannot raise the price.

Fund A returned 12% with a standard deviation of 15%. Fund B returned 10% with a standard deviation of 10%. The risk-free rate is 3%. Which statement is correct?

• a.The two funds have the same Sharpe ratio, because both beat the risk-free rate
• b.Fund A has the higher Sharpe ratio, because its raw return of 12% is higher than 10%
• c.Fund A has the higher Sharpe ratio, because its excess return of 9% exceeds Fund B's 7%
• d.Fund B has the higher Sharpe ratio, 0.70 versus 0.60 for Fund A✓

The Sharpe ratio is excess return divided by standard deviation. Fund A is (12 − 3) / 15 = 0.60 and Fund B is (10 − 3) / 10 = 0.70. Fund B earned more excess return per unit of total risk even though its raw return is lower. Ranking by raw return ignores risk.

A project costs $1,000 today and returns $400, $500, and $600 at the end of years 1 through 3. Using a 10% discount rate, what is the project's NPV, and should it be accepted?

• a.About $228, so accept it because NPV is positive✓
• b.About $500, so accept it because the total inflows exceed the cost
• c.About $228, so reject it because the payback period is longer than two years
• d.About $-228 negative, so reject it because discounting turns the NPV negative

NPV discounts each cash flow: 400/1.1 + 500/1.1² + 600/1.1³ = 1227.65, less the $1,000 cost, is about 227.65. A positive NPV means the project earns more than the 10% required return, so the decision rule says accept. Adding undiscounted inflows ignores the time value of money, and payback length is not the NPV rule.

A portfolio earned a 7.0% nominal return in a year when inflation was 3.0%. What is the real return, computed exactly rather than by simple subtraction?

• a.4.00%
• b.10.00%
• c.3.88%✓
• d.4.12%

The exact real return is (1 + nominal) / (1 + inflation) − 1 = 1.07 / 1.03 − 1 = 3.88%. Simple subtraction gives 4.00%, which is only an approximation. Dividing the 4-point difference by (1 − inflation) gives 4.12%, and adding the two rates, 10.00%, is not a real return at all.

A three-year, 5% annual-pay bond with a $1,000 par value is priced to yield 6%. About what is its price?

• a.$1,150.00
• b.$973.27✓
• c.$1,000.00
• d.$1,027.75

Discount the three $50 coupons and the $1,000 principal at 6%: the present value is about $973.27. A bond whose coupon rate is below its market yield sells at a discount to par. The $1,027.75 figure is the price if the yield were 4%, so it is a premium price and fails the direction test, and $1,150 simply adds the three coupons to par.

A 10-year bond with a 7% coupon trades at 108 and is callable in three years at 102. Which of its yield measures is the lowest?

• a.Current yield, because it is computed on the premium price rather than on par
• b.Nominal yield, because the coupon is always the lowest measure for a bond selling at a premium
• c.Yield to call, because a premium bond is more likely to be called and the investor loses the premium sooner✓
• d.Yield to maturity, because a longer horizon always lowers the yield

For a bond selling at a premium, the price will be pulled down toward par or the call price, and the sooner that happens the greater the capital loss per year. The yield to the earliest call is therefore generally the lowest measure, and investors quote the yield to worst. For these terms the measures rank 7.0% nominal, about 6.5% current, about 5.9% to maturity, and about 4.7% to the call, so the nominal yield is actually the highest.

A portfolio holds two assets in equal weights. Asset X has a standard deviation of 20% and asset Y has 10%. Their returns are uncorrelated. What is the portfolio's standard deviation?

• a.About 11.2%✓
• b.About 15.8%
• c.15.0%
• d.About 22.4%

With zero correlation the portfolio variance is w²σ² for each asset added: 0.25 × 400 + 0.25 × 100 = 125, whose square root is 11.18%. The weighted average of the standard deviations, 15%, would apply only if the assets were perfectly correlated. Using unweighted variances gives 22.4%, and weighting the variances without squaring the weights gives 15.8%; both overstate the risk.

A stock has a 30% chance of returning 20%, a 50% chance of returning 8%, and a 20% chance of returning −10%. What is its expected return?

• a.5.0%
• b.6.0%
• c.10.0%
• d.8.0%✓

Expected return is the probability-weighted average: 0.30 × 20 + 0.50 × 8 + 0.20 × (−10) = 6 + 4 − 2 = 8.0%. The simple average of the three outcomes, 6.0%, treats the scenarios as equally likely, which they are not; 10.0% leaves out the loss scenario and 5.0% averages only the best and worst cases.

What is the Federal Reserve's reserve requirement ratio for depository institutions today?

• a.10 percent on all transaction accounts
• b.3 percent on the first tranche of transaction accounts only
• c.It is set by each Reserve Bank and varies by institution size
• d.Zero percent, in effect since March 26, 2020✓

The Board reduced reserve requirement ratios to zero percent effective March 26, 2020, which eliminated reserve requirements for all depository institutions. The 10% and 3% figures are the old ratios that applied to transaction accounts before that change. Today the Fed works mainly through the interest it pays on reserves and other tools.Federal Reserve Board, Reserve Requirements

The Federal Reserve's discount window offers primary, secondary and seasonal credit. How does the discount rate on secondary credit compare with the rate on primary credit?

• a.Secondary credit carries a lower rate, because those borrowers are smaller
• b.Secondary credit carries a higher rate, and it is available only to institutions in strong financial condition
• c.The two rates are identical, and only the collateral requirements differ
• d.Secondary credit carries a higher rate, and it is available to institutions that are not eligible for primary credit✓

Primary credit is the main program and is for institutions in generally sound financial condition. Secondary credit is for institutions that do not qualify for primary credit and its discount rate is higher than the primary credit rate. Pricing weaker borrowers higher reflects their added risk, and strong borrowers use the primary program.Federal Reserve Board, The Discount Window

Which body specifies the short-term objective that the Federal Reserve's open market operations are conducted to achieve?

• a.The Board of Governors acting alone, with no committee vote
• b.The Treasury Department, through its debt-issuance schedule
• c.The Federal Open Market Committee✓
• d.The Federal Reserve Bank of New York, which sets the federal funds target on its own

Open market operations are the purchase and sale of securities in the open market, and the short-term objective for them is specified by the FOMC. The New York Reserve Bank carries out the trades at the direction of the FOMC but does not set the objective, and the Treasury does not direct monetary policy.Federal Reserve Board, Open Market Operations

A portfolio earned +20%, −10%, and +15% in three consecutive years. What is its geometric mean annual return, and how does it compare with the arithmetic mean of 8.33%?

• a.About 7.49%, which is lower than the arithmetic mean✓
• b.About 24.2%, the cumulative three-year return, which is higher than the arithmetic mean
• c.About 8.07%, which is the cumulative return divided by three and is only slightly below the arithmetic mean
• d.About 8.33%, the same as the arithmetic mean

The geometric mean compounds the returns: (1.20 × 0.90 × 1.15)^(1/3) − 1 = 7.49%. It is below the 8.33% arithmetic mean whenever returns vary, and the more volatile the returns the wider the gap. The geometric mean is the measure of the actual compound growth an investor earned.

Investment A has an expected return of 10% and a standard deviation of 15%. Investment B has an expected return of 8% and a standard deviation of 10%. Using the coefficient of variation, which is the better risk-adjusted choice?

• a.Investment B, with a coefficient of variation of 0.80 versus 0.67 for A
• b.Investment B, with a coefficient of variation of 1.25 versus 1.50 for A✓
• c.Investment A, with a coefficient of variation of 1.50 versus 1.25 for B
• d.Investment A, because it has the higher expected return

The coefficient of variation is standard deviation divided by expected return, or risk per unit of return. A is 15 / 10 = 1.50 and B is 10 / 8 = 1.25. The lower figure means less risk per unit of expected return, so B is better on this measure. The 0.80 and 0.67 figures invert the ratio, which would mean higher is better.

A zero-coupon bond with a $1,000 par value matures in 10 years. If it is priced to yield 5% with semiannual compounding, what is its approximate price?

• a.About $610.27✓
• b.About $613.91
• c.About $500.00
• d.About $781.20

A zero pays only par at maturity, so its price is the present value of $1,000 over 20 half-year periods at 2.5%: 1,000 / 1.025²⁰ = $610.27. Discounting annually at 5% for 10 years gives $613.91, which ignores semiannual compounding. Using only 10 half-year periods gives $781.20, and $500 treats the yield as simple interest.

A project requires an initial investment of $2,000, and the present value of its expected cash inflows at the required return is $2,300. What is its profitability index, and what does it indicate?

• a.0.15, which indicates that the project earns a 15% internal rate of return
• b.1.15, which indicates that the project adds value and should be accepted✓
• c.0.87, which indicates that the project destroys value and should be rejected
• d.1.15, which indicates that the project should be rejected because the ratio exceeds 1

The profitability index is the present value of future cash flows divided by the initial investment: 2,300 / 2,000 = 1.15. An index above 1.0 means the NPV is positive ($300), so the project is acceptable on this test. The 0.87 figure inverts the ratio, and the 0.15 figure is the NPV per dollar invested, not an internal rate of return.

A price-weighted index holds three stocks priced at $90, $50, and $10, with a divisor of 3, so the index is 50. The $90 stock splits 3-for-1 and now trades at $30. To keep the index at 50, what is the new divisor?

• a.1.8✓
• b.1.2
• c.3.0
• d.0.6

After the split the prices sum to 30 + 50 + 10 = 90, and keeping the index at 50 requires a divisor of 90 / 50 = 1.8. Leaving the divisor at 3 would drop the index to 30 even though nothing about the companies' value changed. Dropping the split stock from the sum gives 1.2, and the 0.6 figure divides the split price by the index.

An investor puts $500 into a fund at the end of each of three months, when the share price is $25, $20, and then $50. What is her average cost per share over the three purchases?

• a.$27.27✓
• b.$31.67
• c.$25.00
• d.$35.00

She buys 20 + 25 + 10 = 55 shares for $1,500, so her average cost is 1,500 / 55 = $27.27. This is below the $31.67 average of the three prices because a fixed dollar amount buys more shares when the price is low. The $35.00 figure is the midpoint of the high and the low, and $25.00 is just the first purchase price.