CFA Level I Practice: 45 Worked Problems and 15 Formula Flashcards on Time Value of Money, Returns, Statistics, Bond Pricing and Duration

Bond duration

5 cards

01
What is the Macaulay duration of a 5-year zero-coupon bond?
- A
  It depends on the yield
- B
  Exactly 5 years
- C
  More than 5 years
- D
  Less than 5 years
02
A bond has a Macaulay duration of 4.5 years and a yield to maturity of 6% (annual compounding). What is its modified duration?
- A
  4.77
- B
  4.50
- C
  4.00
- D
  4.25
03
A bond has a modified duration of 7. Its yield rises by 50 basis points. What is the approximate percentage change in its price?
- A
  −7.0%
- B
  −3.5%
- C
  −0.35%
- D
  +3.5%
04
Which bond's price is most sensitive to a change in yields?
- A
  A 20-year zero-coupon bond
- B
  A 20-year 8% coupon bond
- C
  A 5-year zero-coupon bond
- D
  A 5-year 8% coupon bond
05
What is modified duration in terms of Macaulay duration, for a yield $y$ paid $m$ times a year?

Future value

3 cards

06
You deposit $1,000 today at 6% per year, compounded annually. How much is in the account after 3 years?
- A
  $1,262.48
- B
  $1,123.60
- C
  $1,180.00
- D
  $1,191.02
07
You save $2,000 at the end of every year for 10 years in an account earning 5%. How much do you have right after the last deposit?
- A
  $25,155.79
- B
  $15,443.47
- C
  $26,413.57
- D
  $20,000.00
08
What is the future value of a single sum $PV$ invested at rate $r$ per period for $N$ periods?

Present value

1 card

09
You will receive $10,000 in 5 years. If the appropriate discount rate is 8%, what is that payment worth today?
- A
  $6,000.00
- B
  $14,693.28
- C
  $7,350.30
- D
  $6,805.83

Effective interest rate

3 cards

10
A loan quotes a stated annual rate of 12% compounded monthly. What is the effective annual rate (EAR)?
- A
  12.55%
- B
  12.00%
- C
  12.68%
- D
  12.75%
11
Same T-bill: $100,000 face, $98,000 price, 180 days to maturity. What is its effective annual yield?
- A
  4.00%
- B
  4.08%
- C
  2.04%
- D
  4.18%
12
What is the effective annual rate for a stated annual rate $r$ compounded $m$ times a year?

Continuous compounding

1 card

13
$1,000 is invested at a stated rate of 5% with continuous compounding. What is its value after 2 years?
- A
  $1,102.50
- B
  $1,105.17
- C
  $1,100.00
- D
  $1,110.00

Annuity

4 cards

14
An investment pays $1,000 at the end of each year for 5 years. At a 7% discount rate, what is it worth today?
- A
  $4,387.21
- B
  $4,100.20
- C
  $5,750.74
- D
  $5,000.00
15
Same investment, but the $1,000 is paid at the beginning of each year for 5 years. At 7%, what is it worth today?
- A
  $3,831.96
- B
  $4,387.21
- C
  $4,100.20
- D
  $4,693.32
16
What is the present value of an ordinary annuity paying $PMT$ at the end of each of $N$ periods, at rate $r$?
17
How does the present value of an annuity due relate to that of an ordinary annuity with the same payments and rate?

Perpetuity

2 cards

18
A preferred share pays a fixed dividend of $50 per year forever. If investors require a 4% return, what is the share worth?
- A
  $2,000
- B
  $1,300
- C
  $500
- D
  $1,250
19
What is the present value of a level perpetuity paying $PMT$ per period, first payment one period from now, at rate $r$?

Dividend discount model

1 card

20
A stock will pay a dividend of $2.00 next year, and dividends grow at 3% per year forever. With a 8% required return, what is the stock worth today?
- A
  $41.20
- B
  $66.67
- C
  $40.00
- D
  $25.00

Rule of 72

1 card

21
An investment earns 9% per year. Roughly how long does it take to double?
- A
  About 8 years
- B
  About 11 years
- C
  About 9 years
- D
  About 7.2 years

Compound annual growth rate

1 card

22
An investment grew from $1,000 to $1,500 over 5 years. What was its compound annual growth rate?
- A
  8.45%
- B
  7.50%
- C
  10.00%
- D
  8.00%

Amortization calculator

1 card

23
A $200,000 mortgage is repaid over 30 years with equal monthly payments. The rate is 6% per year, compounded monthly. What is the monthly payment?
- A
  $1,073.64
- B
  $1,330.60
- C
  $1,000.00
- D
  $1,199.10

Net present value

2 cards

24
A project costs $10,000 today and returns $4,000 at the end of each of the next 3 years. The required return is 10%. What is its NPV, and should the firm accept it?
- A
  +$52.59: accept
- B
  −$52.59: reject
- C
  +$9,947.41: accept
- D
  +$2,000: accept
25
Two mutually exclusive projects: A has NPV $50,000 and IRR 18%; B has NPV $70,000 and IRR 14%. Both use the same required return. Which should the firm choose, and why?
- A
  B, because NPV measures the value added to shareholders
- B
  A, because a higher IRR means a higher return
- C
  A, because IRR does not depend on the discount rate
- D
  Either: NPV and IRR always agree

Internal rate of return

3 cards

26
A project costs $1,000 today and pays back a single $1,210 at the end of year 2. What is its IRR?
- A
  10.5%
- B
  10%
- C
  21%
- D
  11%
27
You buy one share for $100. A year later you buy a second share for $120. A year after that you sell both for $130 each. No dividends are paid. What is your money-weighted return?
- A
  15.00% per year
- B
  30.00% per year
- C
  12.05% per year
- D
  14.02% per year
28
The internal rate of return is the discount rate at which which quantity equals zero?

Holding period return

2 cards

29
You buy a share for $50, receive a $2 dividend during the year, and sell it for $55 at year-end. What is your holding period return?
- A
  10%
- B
  14%
- C
  4%
- D
  12%
30
What is the holding period return on a share bought at $P_0$, sold at $P_1$, that paid a dividend $D$ in between?

Time-weighted return

3 cards

31
A fund returns +20% in year 1 and −10% in year 2. What is its annualised time-weighted return?
- A
  3.92%
- B
  8.00%
- C
  5.00%
- D
  4.00%
32
A portfolio manager cannot control when clients add or withdraw money. Which return measure is the appropriate one for judging the manager's skill?
- A
  Holding period return, because it is simplest
- B
  Time-weighted return, because it removes the effect of cash-flow timing
- C
  Money-weighted return, because it is the investor's actual IRR
- D
  Arithmetic mean return, because it is unbiased
33
Which portfolio return measure is unaffected by the size and timing of the investor's deposits and withdrawals?

Discount yield

2 cards

34
A 180-day US Treasury bill with a $100,000 face value sells for $98,000. What is its bank discount yield?
- A
  4.00%
- B
  4.08%
- C
  4.18%
- D
  2.04%
35
What is the bank discount yield of a T-bill with face value $F$, priced at a discount $D$, with $t$ days to maturity?

Geometric mean

2 cards

36
A fund returns +50% in one year and −50% the next. Its arithmetic mean return is 0%. What did an investor who stayed in for both years actually earn per year?
- A
  −13.4% per year
- B
  0% per year
- C
  −25% per year
- D
  +6.25% per year
37
What is the geometric mean return over $n$ periods with returns $R_1, \dots, R_n$?

Harmonic mean

1 card

38
An investor buys $100 of a fund every month. In month 1 the price is $10 per unit; in month 2 it is $20. What is the average price paid per unit?
- A
  $15.00
- B
  $12.50
- C
  $13.33
- D
  $14.14

Variance

2 cards

39
A sample of four annual returns is 2%, 4%, 6% and 8%. What is the sample variance?
- A
  2.24 (%²)
- B
  6.67 (%²)
- C
  2.58 (%²)
- D
  5.00 (%²)
40
What is the sample variance of $n$ observations $x_i$ with sample mean $\bar{x}$?

Coefficient of variation

1 card

41
Asset A: mean return 10%, standard deviation 5%. Asset B: mean return 20%, standard deviation 8%. Which asset has less risk per unit of return?
- A
  B, with a coefficient of variation of 0.40
- B
  They are equal
- C
  A, because its standard deviation is lower
- D
  A, with a coefficient of variation of 0.50

Sharpe ratio

1 card

42
A portfolio returned 12% with a standard deviation of 15%. The risk-free rate was 3%. What is its Sharpe ratio?
- A
  0.60
- B
  0.75
- C
  0.09
- D
  0.80

Correlation

1 card

43
The covariance between two stocks' returns is 0.006. Stock A has a standard deviation of 10% and stock B of 20%. What is their correlation coefficient?
- A
  0.60
- B
  0.12
- C
  0.30
- D
  0.03

Expected value

1 card

44
An analyst assigns a 30% probability to a 20% return, 50% to a 10% return and 20% to a −10% return. What is the expected return?
- A
  10%
- B
  6.67%
- C
  7%
- D
  9%

Bayes' theorem

2 cards

45
Recessions occur in 20% of years. A leading indicator flashes a warning in 80% of recession years but also gives a false warning in 10% of non-recession years. The indicator has just flashed. What is the probability of a recession?
- A
  66.7%
- B
  16%
- C
  80%
- D
  20%
46
What is Bayes' theorem for the probability of $A$ after observing $B$?

Binomial distribution

1 card

47
A stock rises on any given day with probability 0.6, independently of other days. What is the probability it rises on exactly 2 of the next 3 days?
- A
  64.8%
- B
  43.2%
- C
  36.0%
- D
  21.6%

68–95–99.7 rule

1 card

48
A portfolio's annual returns are normally distributed with a mean of 8% and a standard deviation of 10%. Roughly what is the probability of a return below −12%?
- A
  About 2.5%
- B
  About 16%
- C
  About 0.15%
- D
  About 5%

Confidence interval

1 card

49
A sample of 64 monthly returns has a mean of 5% and a standard deviation of 8%. What is the 95% confidence interval for the population mean?
- A
  4.00% to 6.00%
- B
  3.36% to 6.64%
- C
  3.04% to 6.96%
- D
  −10.68% to 20.68%

Type I and type II errors

1 card

50
An analyst tests whether a fund's alpha is zero at a 5% significance level. What does the 5% represent?
- A
  The probability of rejecting a true null hypothesis (a Type I error)
- B
  The power of the test
- C
  The probability of failing to reject a false null hypothesis (a Type II error)
- D
  The probability that the null hypothesis is true

Bond valuation

3 cards

51
A 3-year bond pays a 5% annual coupon on a $1,000 par value. The market yield for similar bonds is 6%. What is the bond's price?
- A
  $950.00
- B
  $1,000.00
- C
  $973.27
- D
  $1,027.75
52
A 2-year bond pays a 6% coupon semiannually on $1,000 par. The yield to maturity is 8% (a semiannual bond-equivalent yield). What is the price?
- A
  $964.33
- B
  $928.57
- C
  $963.70
- D
  $1,000.00
53
A bond's coupon rate is 7% and its yield to maturity is 5%. Without calculating, what can you say about its price?
- A
  It trades at a discount to par
- B
  It trades at a premium to par
- C
  It trades at par
- D
  Nothing without knowing the maturity

Zero-coupon bond

1 card

54
A 5-year zero-coupon bond has a $1,000 face value. Its yield is 4%, quoted on the usual semiannual bond-equivalent basis. What is its price?
- A
  $800.00
- B
  $821.93
- C
  $820.35
- D
  $900.00

Current yield

1 card

55
A bond with a $60 annual coupon trades at $950. What is its current yield?
- A
  6.00%
- B
  6.32%
- C
  5.70%
- D
  6.50%

Bond convexity

2 cards

56
A bond has a modified duration of 7 and a convexity of 60. Yields rise by 100 basis points. Including the convexity adjustment, what is the approximate price change?
- A
  −7.0%
- B
  −6.4%
- C
  −7.3%
- D
  −6.7%
57
What is the approximate percentage price change of a bond for a yield change $\Delta y$, using modified duration $D_{\text{mod}}$ and convexity $C$?

Accrued interest

1 card

58
A bond pays a $40 coupon every 180 days. Sixty days after the last coupon, its quoted (clean) price is $980. How much does the buyer actually pay?
- A
  $993.33
- B
  $980.00
- C
  $1,020.00
- D
  $986.67

Forward rate

2 cards

59
The 1-year spot rate is 4% and the 2-year spot rate is 5%. What is the implied 1-year rate one year from now?
- A
  5.00%
- B
  4.50%
- C
  6.01%
- D
  5.50%
60
What is the implied one-year rate one year from now, given the one-year and two-year spot rates $S_1$ and $S_2$?

End of deck · 60 cards