Trash Finance Exam

1. A $1,000 par bond has a 6% annual coupon rate and pays interest semiannually. What cash coupon does the investor receive every six months? A. $120 | B. $6 | C. $30 | D. $60

C. $30 Explanation: Annual coupon interest is 0.06 x $1,000 = $60. Each of two semiannual payments is $60/2 = $30.

2. Which expression defines a bond's current yield? A. Annual coupon interest / current market price | B. Annual total return / initial investment | C. Annual coupon interest / yield to maturity | D. Annual coupon interest / par value

A. Annual coupon interest / current market price Explanation: Current yield measures coupon income relative to the current price. It excludes capital gains or losses and differs from the coupon rate, which uses par value.

3. A $1,000 par bond pays annual coupons at 8.25%, matures in four years, and has an 8.64% YTM. What is its current yield, rounded to two decimal places? A. 8.64% | B. 8.45% | C. 8.36% | D. 8.25%

C. 8.36% Explanation: C = $82.50. Discounting four coupons and $1,000 at 8.64% gives P = $987.2646. Current yield = $82.50/$987.2646 = 8.3564%, or 8.36%.

4. For a fixed-rate bond with unchanged promised cash flows, what happens to its market price when its required yield rises? A. It stays at par. | B. It rises. | C. It changes only if the issuer defaults. | D. It falls.

D. It falls. Explanation: A higher discount rate reduces the present value of the same future coupons and principal. Bond prices and yields move inversely.

5. A bond has $1,000 par value, a 12% annual coupon, five years to maturity, and a 10% YTM. What is its price, rounded to the nearest cent? A. $1,200.00 | B. $1,000.00 | C. $1,075.82 | D. $924.16

C. $1,075.82 Explanation: P = 120[1 - (1.10)^(-5)]/0.10 + 1,000/(1.10)^5 = $1,075.8157. The coupon rate exceeds the YTM, so it trades at a premium.

6. You buy a $1,000 par bond with a 10% annual coupon and six years remaining when its YTM is 8%. You sell immediately after receiving the first annual coupon, and YTM is still 8%. What is your one-year holding period return, rounded to two decimal places? A. 8.00% | B. 7.82% | C. 11.95% | D. 10.00%

A. 8.00% Explanation: The initial price is $1,092.4576; the ex-coupon sale price with five years left is $1,079.8542. HPR = (100 + 1,079.8542 - 1,092.4576)/1,092.4576 = 8.00%.

7. Holding other factors constant, which pair of changes each independently reduces a coupon bond's interest rate risk? A. Longer maturity and higher coupon rate | B. Shorter maturity and lower YTM | C. Longer maturity and lower coupon rate | D. Shorter maturity and higher coupon rate

D. Shorter maturity and higher coupon rate Explanation: A shorter maturity moves cash flows closer to the present, and a higher coupon returns more cash earlier. A lower YTM instead increases price sensitivity, other things equal.

8. A zero-coupon bond pays $1,000 in five years. If its annual effective required return is 6%, what is its price, rounded to the nearest cent? A. $943.40 | B. $747.26 | C. $700.00 | D. $1,000.00

B. $747.26 Explanation: A zero-coupon bond has one maturity payment: P = $1,000/(1.06)^5 = $747.2582, or $747.26.

9. A $1,000 par bond has a 6% annual coupon rate, five years to maturity, and a 7% nominal annual YTM compounded semiannually. Which inputs correctly value the bond using six-month periods? A. N = 10; PMT = $60; periodic rate = 7% | B. N = 5; PMT = $60; periodic rate = 3.5% | C. N = 10; PMT = $30; periodic rate = 3.5% | D. N = 5; PMT = $30; periodic rate = 7%

C. N = 10; PMT = $30; periodic rate = 3.5% Explanation: With semiannual payments, double the years, halve the annual coupon dollars, and halve the quoted nominal annual yield: N = 10, PMT = $30, r = 3.5%.

10. What is the price of a $1,000 par bond with a 6% annual coupon rate paid semiannually, five years to maturity, and a 7% nominal annual YTM compounded semiannually? Round to the nearest cent. A. $1,041.58 | B. $1,000.00 | C. $789.29 | D. $958.42

D. $958.42 Explanation: P = 30[1 - (1.035)^(-10)]/0.035 + 1,000/(1.035)^10 = $958.41697. Use ten periods and a 3.5% periodic yield.

11. A fixed-rate bond is selling above par immediately after a coupon payment. Which relationship must hold for its coupon rate and YTM, using matching payment conventions? A. Coupon rate = YTM | B. Coupon rate > YTM | C. Coupon rate = current yield | D. Coupon rate < YTM

B. Coupon rate > YTM Explanation: A premium bond pays a coupon rate above the return currently required by the market. Discounting its payments at the lower YTM produces a price above par.

12. A $1,000 par bond has an 8% annual coupon, ten years to maturity, and a price of $958.73. Which pair gives its annual YTM and current yield, respectively, rounded to two decimal places? A. 8.34% and 8.63% | B. 8.63% and 8.00% | C. 8.00% and 8.34% | D. 8.63% and 8.34%

D. 8.63% and 8.34% Explanation: Solving 958.73 = 80[1 - (1+y)^(-10)]/y + 1,000/(1+y)^10 gives y = 8.6327%. Current yield = 80/958.73 = 8.3444%.

13. A $1,000 par bond is quoted at 112.125 as a percentage of par and has a 9.5% annual coupon rate paid semiannually. Ignoring accrued interest, what are its quoted dollar price and current yield, rounded to the nearest cent and two decimal places? A. $1,121.25 and 8.47% | B. $112.13 and 84.73% | C. $1,121.25 and 4.24% | D. $1,000.00 and 9.50%

A. $1,121.25 and 8.47% Explanation: Price = 1.12125 x $1,000 = $1,121.25. Annual coupons total $95, so current yield = 95/1,121.25 = 8.4727%. Semiannual payments do not halve annual current yield.

14. A bond's quoted nominal annual YTM is 8%, compounded semiannually. What is its effective annual yield, rounded to two decimal places? A. 16.64% | B. 8.16% | C. 8.00% | D. 4.00%

B. 8.16% Explanation: The six-month yield is 4%. Effective annual yield = (1 + 0.08/2)^2 - 1 = 0.0816 = 8.16%.

15. The 10-year Treasury yield is 3.8% and the 2-year yield is 4.4%. What is the 10-year minus 2-year spread, and what does its sign indicate? A. -0.6 percentage point; an inverted spread | B. +0.6 percentage point; a flat spread | C. -0.6 percentage point; a normal spread | D. +0.6 percentage point; an inverted spread

A. -0.6 percentage point; an inverted spread Explanation: The spread is 3.8% - 4.4% = -0.6 percentage point, or -60 basis points. The longer maturity yielding less than the shorter maturity indicates inversion over those maturities.

16. Using the S&P-style ratings discussed in the notes, which is the lowest investment-grade category among these choices? A. BB | B. AAA | C. AA | D. BBB

D. BBB Explanation: BBB is the lowest investment-grade category; BB is speculative grade. Credit ratings assess default risk rather than guaranteeing protection from interest rate changes.

17. An issuer's financial condition deteriorates while the comparable Treasury yield is unchanged. What would normally happen to its credit spread and bond price, other things equal? A. The spread narrows and the price rises. | B. The spread widens and the price falls. | C. The spread stays fixed and the price stays fixed. | D. The spread widens and the price rises.

B. The spread widens and the price falls. Explanation: Greater default risk normally raises the yield premium investors demand over Treasuries. The higher required yield reduces the present value and market price of unchanged promised payments.

18. Which instrument has a coupon rate that generally falls when the reference interest rate rises? A. A zero-coupon bond | B. An indexed bond tied to inflation | C. An ordinary floating-rate bond | D. An inverse floater

D. An inverse floater Explanation: The inverse floater reverses the usual floating-rate relationship: its coupon moves inversely with the reference rate. Zero-coupon bonds have no periodic coupon.

19. An investment earns a 9% nominal annual return while inflation is 3%. What is the exact real annual return, rounded to two decimal places? A. 5.83% | B. 6.00% | C. 8.74% | D. 12.27%

A. 5.83% Explanation: Use (1 + nominal) = (1 + real)(1 + inflation). Real return = 1.09/1.03 - 1 = 5.8252%, or 5.83%. Subtracting 3% from 9% gives only an approximation.

20. Which valuation method treats inflation consistently? A. Add inflation to both real and nominal cash flows. | B. Discount nominal cash flows at a nominal rate. | C. Discount real cash flows at a nominal rate. | D. Discount nominal cash flows at a real rate.

B. Discount nominal cash flows at a nominal rate. Explanation: Match cash-flow units and discount-rate units. Nominal cash flows require a nominal rate; equivalently, consistently measured real cash flows require a real rate.

21. A two-year bond pays annual coupons of $100 and repays $1,000 principal at the end of year 2. Its annual YTM is 10% and its price is $1,000. What is its Macaulay duration, rounded to two decimal places? A. 1.74 years | B. 1.00 year | C. 1.91 years | D. 2.00 years

C. 1.91 years Explanation: D = [1(100/1.10) + 2(1,100/1.10^2)]/1,000 = 1.90909 years. Weight each payment time by that payment's share of the bond's present value.

22. A bond has a Macaulay duration of 6 years and an annual YTM of 5%, with annual payments. If YTM rises by 0.50 percentage point, what percentage price change does modified duration predict, rounded to two decimal places? A. -28.57% | B. -2.86% | C. +2.86% | D. -3.00%

B. -2.86% Explanation: Dmod = 6/1.05 = 5.714286 years. Delta P/P approximately equals -Dmod x delta y = -5.714286 x 0.005 = -0.028571, or -2.86%.

23. What is the Macaulay duration of a zero-coupon bond with eight years remaining to maturity? A. Exactly eight years | B. Zero because there are no coupons | C. Greater than eight years because there are no coupons | D. Less than eight years because the bond sells at a discount

A. Exactly eight years Explanation: All of the present-value weight is on the single payment eight years from now, so its Macaulay duration equals its remaining maturity.

24. A bond has modified duration 5 and convexity 40, measured consistently for annual yields. Using delta P/P approximately equal to -Dmod x delta y + 0.5 x convexity x (delta y)^2, what is the estimated price change if YTM rises by 1 percentage point? A. -5.20% | B. -4.80% | C. +5.20% | D. -5.00%

B. -4.80% Explanation: The duration term is -5 x 0.01 = -0.05. The convexity correction is 0.5 x 40 x 0.01^2 = +0.002. The total is -0.048, or -4.80%.

25. Under the basic duration immunization approach for a single future obligation, what combination provides a starting point for limiting exposure to small parallel yield changes? A. Hold only long-duration bonds regardless of the obligation date. | B. Match the present values and durations of assets and the obligation. | C. Choose assets with the highest current yield regardless of maturity. | D. Match coupon rates while ignoring present values and durations.

B. Match the present values and durations of assets and the obligation. Explanation: Begin with assets sufficient in present value to fund the obligation, then match duration to balance price and reinvestment effects near the horizon. This is a local approximation and requires monitoring.

26. Why does a duration-immunized bond portfolio usually need periodic rebalancing? A. A matching portfolio must always maintain the same number of bonds. | B. A bond's coupon rate resets whenever market yields change. | C. Matching duration removes every future cash flow. | D. Asset and liability durations change with time and yields.

D. Asset and liability durations change with time and yields. Explanation: Time passes, coupons are paid, and yields change; the asset portfolio's duration and the obligation's duration need not move identically. Rebalance to restore the intended match.

27. A bank funds long-duration fixed-rate securities with short-term deposits. What is a central risk when interest rates rise and depositors demand withdrawals? A. Deposit liabilities automatically fall more than asset values. | B. Asset values can fall while withdrawals force sales at depressed prices. | C. Holding government securities eliminates withdrawal risk. | D. The securities must increase in value before any sale.

B. Asset values can fall while withdrawals force sales at depressed prices. Explanation: Long-duration securities lose market value when rates rise. Short-term deposit withdrawals can force liquidation, turning market-value losses into realized losses and intensifying a liquidity problem.

28. You buy a $1,000 par bond for $985. It pays an $80 annual coupon. One year later, immediately after receiving the coupon, 14 years remain and annual YTM is 7%. What is your one-year holding period return, rounded to two decimal places? A. 7.18% | B. 8.18% | C. 18.52% | D. 8.12%

C. 18.52% Explanation: With 14 years left, P1 = 80[1 - (1.07)^(-14)]/0.07 + 1,000/(1.07)^14 = $1,087.4547. HPR = (80 + 1,087.4547 - 985)/985 = 18.5233%, or 18.52%.

29. A $1,000 par bond pays a 6.25% annual coupon rate in semiannual installments, trades at $950, and has a 7% nominal annual required return compounded semiannually. What remaining maturity solves the valuation equation, rounded to two decimal places? A. 18.27 years | B. 7.00 years | C. 4.57 years | D. 9.14 years

D. 9.14 years Explanation: Use PMT = $31.25 and periodic yield = 3.5%. Solve 950 = 31.25[1 - (1.035)^(-N)]/0.035 + 1,000/(1.035)^N to obtain N = 18.27275 six-month periods, or 9.13637 years.

30. For a coupon-bond investor, what two effects generally follow a rise in market interest rates? A. Lower bond prices and lower reinvestment rates | B. Lower bond prices and higher reinvestment rates | C. Higher bond prices and higher reinvestment rates | D. Higher bond prices and lower reinvestment rates

B. Lower bond prices and higher reinvestment rates Explanation: Rising yields reduce the market value of existing fixed cash flows, creating price risk, while allowing coupons to be reinvested at higher rates. Duration immunization balances these offsetting effects near a target horizon.

31. What is the price paid to acquire an option called? A. The strike price | B. The expiration price | C. The exercise value | D. The premium

D. The premium Explanation: The premium is the option price. The strike is the fixed price used when the option is exercised.

32. An American call option gives its holder which contractual right? A. To buy the underlying at the strike on or before expiration | B. To sell the underlying at the strike only at expiration | C. To buy the underlying at the strike only at expiration | D. To require the writer to buy the option back at its original premium

A. To buy the underlying at the strike on or before expiration Explanation: An American call permits the holder to buy the underlying at the strike on or before expiration. A put gives a right to sell.

33. Which statement accurately describes a European option? A. It can be exercised only at expiration, although it may be sold before then if a market exists | B. It can be exercised at any time before expiration | C. It must be exercised even when out of the money | D. It can only have a European underlying asset

A. It can be exercised only at expiration, although it may be sold before then if a market exists Explanation: European refers to exercise timing: exercise is allowed only at expiration. This does not require an investor to keep the option until expiration.

34. A stock is priced at $50 and its call has a $45 strike. What are the call's moneyness and intrinsic value per share? A. In the money; $5 | B. Out of the money; $5 | C. In the money; $45 | D. At the money; $0

A. In the money; $5 Explanation: A call is in the money when S exceeds K. Its intrinsic value is max(50 - 45, 0) = $5 per share.

35. At expiration, a put has a $50 strike while the stock price is $55. What is its payoff per share? A. $50 | B. -$5 | C. $5 | D. $0

D. $0 Explanation: The put is out of the money and can expire unexercised. Its payoff is max(50 - 55, 0) = $0; the payoff is never negative for the holder.

36. A call premium is $7 per share. The stock price is $50 and the strike is $45. How much of the premium is extrinsic value? A. $7 | B. $12 | C. $2 | D. $5

C. $2 Explanation: Intrinsic value is $50 - $45 = $5. Extrinsic value is the $7 premium minus $5 intrinsic value = $2.

37. You buy a call for $3 per share with a $40 strike. At expiration, the stock is $48. What are payoff and profit per share, ignoring fees and financing? A. Payoff $8; profit $11 | B. Payoff $0; profit -$3 | C. Payoff $5; profit $8 | D. Payoff $8; profit $5

D. Payoff $8; profit $5 Explanation: Call payoff is max(48 - 40, 0) = $8. Profit subtracts the $3 premium, leaving $5 per share.

38. What is the potential maximum loss from writing an uncovered call on a stock, ignoring fees? A. The stock price when the call was written | B. The strike price times the number of shares | C. Unlimited as the stock price rises | D. The premium received

C. Unlimited as the stock price rises Explanation: A short call owes max(S_T - K, 0). With no offsetting stock position, the loss can grow without bound as the stock price rises.

39. You buy one call contract covering 100 shares for a $3 per-share premium. What is the maximum possible loss, ignoring fees? A. Unlimited | B. $3,000 | C. $300 | D. $100

C. $300 Explanation: A call buyer can let the option expire and loses at most the premium paid: $3 x 100 = $300.

40. You buy one September $50 put contract covering 100 shares for a $2 per-share premium. What is the maximum profit at expiration, ignoring fees and financing? A. $5,000 | B. $4,800 | C. $200 | D. $5,200

B. $4,800 Explanation: The stock cannot fall below zero. At zero, payoff is $50 x 100 = $5,000, and profit is $5,000 - $200 premium = $4,800.

41. You buy a put with a $50 strike for $2 per share. At which stock price at expiration does the position break even, ignoring fees and financing? A. $2 | B. $50 | C. $52 | D. $48

D. $48 Explanation: A long put breaks even at K - p = $50 - $2 = $48. Payoff then equals the premium.

42. You write a put with a $50 strike and receive $2 per share. The stock finishes at $43 at expiration. What is your profit per share, ignoring fees and financing? A. $5 | B. $7 | C. -$5 | D. -$7

C. -$5 Explanation: The short put owes $50 - $43 = $7 per share and keeps the $2 premium. Profit is $2 - $7 = -$5.

43. Which position is a covered call? A. Long stock and short call | B. Long stock and long put | C. Short stock and long call | D. Long stock and long call

A. Long stock and short call Explanation: A covered call combines ownership of the underlying stock with writing a call on that stock.

44. You buy stock at $50 and write a $55 call for $3 per share. What is the maximum profit per share at expiration, ignoring dividends, fees, and financing? A. $8 | B. $3 | C. Unlimited | D. $5

A. $8 Explanation: Above $55, the stock gain is capped at $55 - $50 = $5. Adding the $3 call premium gives maximum profit of $8 per share.

45. You buy stock at $50 and write a $55 call for $3 per share. If the stock becomes worthless at expiration, what is the position's loss per share, ignoring dividends, fees, and financing? A. $53 | B. $50 | C. $3 | D. $47

D. $47 Explanation: The stock loses $50, but the call expires worthless and the writer keeps $3. Net loss is $50 - $3 = $47 per share.

46. You own one share and buy a put on that share with a $48 strike. What is the minimum combined terminal payoff of the stock and put, before subtracting the initial costs? A. $50 | B. $0 | C. $48 | D. The put premium

C. $48 Explanation: The combined payoff is S_T + max(48 - S_T, 0) = max(S_T, 48). The put guarantees a $48 floor on terminal proceeds per share.

47. You buy stock at $50 and a put with a $48 strike for $2 per share. What is the maximum loss per share at expiration, ignoring dividends, fees, and financing? A. $2 | B. $48 | C. $4 | D. $52

C. $4 Explanation: Total initial cost is $52, while the protective put guarantees at least $48 in terminal proceeds. Maximum loss is $52 - $48 = $4.

48. Which trade creates a bull call vertical spread on the same stock with the same expiration? A. Buy a $50 call and buy a $50 put | B. Buy a $50 call and sell a $60 call | C. Buy a $60 call and sell a $50 call | D. Sell a $50 call and sell a $50 put

B. Buy a $50 call and sell a $60 call Explanation: A bull call spread buys the lower-strike call and sells the higher-strike call, producing a limited bullish payoff.

49. You buy a $50 call for $7 and sell a $60 call for $3, both per share and with the same expiration. What is the maximum profit per share, ignoring fees and financing? A. $10 | B. $14 | C. $4 | D. $6

D. $6 Explanation: The net premium paid is $7 - $3 = $4. The maximum payoff is the $60 - $50 = $10 strike difference, so maximum profit is $10 - $4 = $6.

50. Two call options on the same stock have the same expiration but different strike prices. A position using one long call and one short call is which type of spread? A. Long straddle | B. Diagonal spread | C. Vertical spread | D. Calendar spread

C. Vertical spread Explanation: A vertical spread uses different strikes and the same expiration. Calendar spreads vary expiration; diagonal spreads vary both.

51. You buy one June $60 call and one June $60 put on the same stock. What is this strategy called? A. A long straddle | B. A covered call | C. A short straddle | D. A bull call spread

A. A long straddle Explanation: A long straddle purchases both a call and a put with the same strike and expiration.

52. A long straddle has a $60 strike, a $5 call premium, and a $3 put premium, all per share. What are its expiration breakeven stock prices, ignoring fees and financing? A. $60 and $68 | B. $52 and $68 | C. $55 and $63 | D. $57 and $65

B. $52 and $68 Explanation: The total premium is $5 + $3 = $8. Breakevens are $60 - $8 = $52 and $60 + $8 = $68.

53. You buy a $60 call for $5 and a $60 put for $3, all per share and with the same expiration. The stock finishes at $75. What is the combined profit per share, ignoring fees and financing? A. $7 | B. $15 | C. $8 | D. -$8

A. $7 Explanation: The call pays $75 - $60 = $15; the put pays zero. Subtract the total $8 premium to get $7 profit per share.

54. For European options on a non-dividend-paying stock with the same strike K and expiration, which relation is put-call parity? A. C - P = PV(K) - S_0 | B. S_0 + P = C + PV(K) | C. C + P = S_0 + PV(K) | D. S_0 + C = P + PV(K)

B. S_0 + P = C + PV(K) Explanation: A protective put (stock plus put) has the same terminal payoff as a call plus a risk-free investment that pays K. Equal payoffs imply equal current values.

55. A non-dividend-paying stock costs $50. A European put with a $52 strike and one year to expiration costs $4. The effective annual risk-free rate is 4%. What is the matching European call price under put-call parity? A. $8 | B. $2 | C. $4 | D. $6

C. $4 Explanation: PV(K) = $52/1.04 = $50. Therefore C = S_0 + P - PV(K) = $50 + $4 - $50 = $4 per share.

56. Under European put-call parity for a non-dividend-paying stock, which portfolio replicates a long call with strike K? A. Long stock, long put, and borrow PV(K) | B. Long stock, short put, and lend PV(K) | C. Short stock, long put, and lend PV(K) | D. Long stock, short put, and borrow PV(K)

A. Long stock, long put, and borrow PV(K) Explanation: Rearranging C = S_0 + P - PV(K) gives long stock plus long put financed partly by borrowing PV(K), which requires repaying K at expiration.

57. What does an option's implied volatility represent? A. The option's guaranteed future return | B. The stock's realized return over the previous year | C. The probability the option will be exercised | D. The volatility level consistent with its market price in an option pricing model

D. The volatility level consistent with its market price in an option pricing model Explanation: Implied volatility is inferred from the observed option price using a pricing model. It is not a guaranteed realized volatility or return.

58. Two options on the same stock have the same expiration. One has 25% implied volatility and the other has 35%. In volatility terms, which is relatively more expensive? A. Neither, because implied volatility does not reflect option pricing | B. The 35% option because its price implies higher volatility | C. The 25% option because its volatility estimate is lower | D. Both must have the same dollar premium

B. The 35% option because its price implies higher volatility Explanation: Higher implied volatility means a higher price in volatility terms. This comparison alone does not establish the higher-IV option is mispriced or guarantee equal dollar premiums.

59. In the simplified corporate option model, debt of $800 is due at a single future date and shareholders have limited liability. Equity at that date is equivalent to which claim? A. A short call on firm assets with a strike of $800 | B. A risk-free bond paying $800 | C. A call on firm assets with a strike of $800 | D. A put on firm assets with a strike of $800

C. A call on firm assets with a strike of $800 Explanation: Equity receives max(V_T - $800, 0), the payoff of a call on the firm's assets with strike equal to the promised debt payment.

60. In a simplified firm with a single debt payment of $800 due now, asset value is $600 and equity has limited liability. Ignoring bankruptcy costs, what do debt and equity holders receive? A. Debt $600; equity $0 | B. Debt $0; equity $600 | C. Debt $600; equity $200 | D. Debt $800; equity -$200

A. Debt $600; equity $0 Explanation: Debt receives min(V_T, D) = min($600, $800) = $600. Equity receives max(V_T - D, 0) = $0. Debt is equivalent to firm assets minus the equity call.