Quantitative Methods - Basic concepts Flashcards
1
Q
How much would the following income stream be worth assuming a 12% discount rate?
$100 received today.
$200 received 1 year from today.
$400 received 2 years from today.
$300 received 3 years from today.
A) $721.32.
B) $810.98.
C) $1,112.44.
A
B
2
Q
Nortel Industries has a preferred stock outstanding that pays (fixed) annual dividends of $3.75 a share. If an investor wants to earn a rate of return of 8.5%, how much should he be willing to pay for a share of Nortel preferred stock?
A) $31.88.
B) $44.12.
C) $42.10.
A
B
3
Q
Perpetuities present value = ?
A
pmt / interest rate
4
Q
The First State Bank is willing to lend $100,000 for 4 years at a 12% rate of interest, with the loan to be repaid in equal semi-annual payments. Given the payments are to be made at the end of each 6-month period, how much will each loan payment be?
A) $32,925.
B) $16,104.
C) $25,450.
A
N = 4 × 2 = 8; I/Y = 12/2 = 6; PV = -100,000; FV = 0; CPT → PMT = 16,103.59.
5
Q
Optimal Insurance is offering a deferred annuity that promises to pay 10% per annum with equal annual payments beginning at the end of 10 years and continuing for a total of 10 annual payments. For an initial investment of $100,000, what will be the amount of the annual payments?
A) $42,212.
B) $38,375.
C) $25,937.
A
B
- To get the PV of the series payments:
Using a financial calculator: N = 10, I = 10, PV = $100,000, PMT = 0, Compute FV = $259,374.25.
- Using a financial calculator and solving for a 10-year annuity due because the payments are made at the beginning of each period (you need to put your calculator in the “begin” mode), with a present value of $259,374.25, a number of payments equal to 10, an interest rate equal to ten percent, and a future value of $0.00, the resultant payment amount is $38,374.51. Alternately, the same payment amount can be determined by taking the future value after nine years of deferral ($235,794.77), and then solving for the amount of an ordinary (payments at the end of each period) annuity payment over 10 years.
!! remember to set the payment to begin!!
6
Q
If 10 equal annual deposits of $1,000 are made into an investment account earning 9% starting today, how much will you have in 20 years?
A) $42,165.
B) $39,204.
C) $35,967.
A
B
Switch to BGN mode. PMT = -1,000; N = 10, I/Y = 9, PV = 0; CPT → FV = 16,560.29. Remember the answer will be one year after the last payment in annuity due FV problems. Now PV10 = 16,560.29; N = 10; I/Y = 9; PMT = 0; CPT → FV = 39,204.23. Switch back to END mode.
!! remember to set the payment to begin!!
7
Q
What is the maximum an investor should be willing to pay for an annuity that will pay out $10,000 at the beginning of each of the next 10 years, given the investor wants to earn 12.5%, compounded annually?
A) $52,285.
B) $55,364.
C) $62,285.
A
C
Using END mode, the PV of this annuity due is $10,000 plus the present value of a 9-year ordinary annuity: N=9; I/Y=12.5; PMT=-10,000; FV=0; CPT PV=$52,285; $52,285 + $10,000 = $62,285.
Or set your calculator to BGN mode then N=10; I/Y=12.5; PMT=-10,000; FV=0; CPT PV= $62,285.
8
Q
What is the maximum price an investor should be willing to pay (today) for a 10 year annuity that will generate $500 per quarter (such payments to be made at the end of each quarter), given he wants to earn 12%, compounded quarterly?
A) $6,440.
B) $11,557.
C) $11,300.
A
B
Using a financial calculator: N = 10 × 4 = 40; I/Y = 12 / 4 = 3; PMT = -500; FV = 0; CPT → PV = 11,557.
9
Q
Compute the present value of a perpetuity with $100 payments beginning four years from now. Assume the appropriate annual interest rate is 10%.
A) $1000.
B) $683.
C) $751.
A
C
(first time picked B, draw a timeline will help identify N)
Compute the present value of the perpetuity at (t = 3). Recall, the present value of a perpetuity or annuity is valued one period before the first payment. So, the present value at t = 3 is 100 / 0.10 = 1,000. Now it is necessary to discount this lump sum to t = 0. Therefore, present value at t = 0 is 1,000 / (1.10)3 = 751.
10
Q
A $500 investment offers a 7.5% annual rate of return. How much will it be worth in four years?
A) $668.
B) $650.
C) $892.
A
A
N = 4; I/Y = 7.5; PV = -500; PMT = 0; CPT → FV = 667.73.
or: 500(1.075)4 = 667.73
11
Q
Wei Zhang has funds on deposit with Iron Range bank. The funds are currently earning 6% interest. If he withdraws $15,000 to purchase an automobile, the 6% interest rate can be best thought of as a(n):
A) financing cost.
B) opportunity cost.
C) discount rate.
A
B
Since Wei will be foregoing interest on the withdrawn funds, the 6% interest can be best characterized as an opportunity cost - the return he could earn by postponing his auto purchase until the future.
12
Q
A local bank offers an account that pays 8%, compounded quarterly, for any deposits of $10,000 or more that are left in the account for a period of 5 years. The effective annual rate of interest on this account is:
A) 8.24%.
B) 9.01%.
C) 4.65%.
A
A
(1 + periodic rate)^m − 1 = (1.02)^4 − 1 = 8.24%.
(first time used the financial calculator, but using the geometric mean method is much faster)
13
Q
Justin Banks just won the lottery and is trying to decide between the annual cash flow payment option or the lump sum option. He can earn 8% at the bank and the annual cash flow option is $100,000/year, beginning today for 15 years. What is the annual cash flow option worth to Banks today?
A) $1,080,000.00.
B) $924,423.70.
C) $855,947.87.
A
B
First put your calculator in the BGN.
N = 15; I/Y = 8; PMT = 100,000; CPT → PV = 924,423.70.
Alternatively, do not set your calculator to BGN, simply multiply the ordinary annuity (end of the period payments) answer by 1 + I/Y. You get the annuity due answer and you don’t run the risk of forgetting to reset your calculator back to the end of the period setting.
OR N = 14; I/Y = 8; PMT = 100,000; CPT → PV = 824,423.70 + 100,000 = 924,423.70.
14
Q
If $2,000 a year is invested at the end of each of the next 45 years in a retirement account yielding 8.5%, how much will an investor have at retirement 45 years from today?
A) $100,135.
B) $90,106.
C) $901,060.
A
C
N = 45; PMT = -2,000; PV = 0; I/Y = 8.5%; CPT → FV = $901,060.79.
15
Q
T-bill yields can be thought of as:
A)
nominal risk-free rates because they do not contain an inflation premium.
B)
nominal risk-free rates because they contain an inflation premium.
C)
real risk-free rates because they contain an inflation premium.
A
B
T-bills are government issued securities and are therefore considered to be default risk free. More precisely, they are nominal risk-free rates rather than real risk-free rates since they contain a premium for expected inflation.
16
Q
The required rate of return on a security = ?
A
real risk-free rate + expected inflation + default risk premium + liquidity premium + maturity risk premium.
17
Q
Nominal risk-free rate = ?
A
real risk-free rate + expected inflation rate.
18
Q
_____ = _______ - inflation rate
A
Real risk-free rate = Nominal risk free rate - inflation rate
19
Q
If an investor puts $5,724 per year, starting at the end of the first year, in an account earning 8% and ends up accumulating $500,000, how many years did it take the investor?
A) 26 years.
B) 27 years.
C) 87 years.
A
B
I/Y = 8; PMT = -5,724; FV = 500,000; CPT → N = 27.
Remember, you must put the pmt in as a negative (cash out) and the FV in as a positive (cash in) to compute either N or I/Y.
20
Q
As the number of compounding periods increases, what is the effect on the annual percentage rate (APR) and the effective annual rate (EAR)?
A) APR increases, EAR increases.
B) APR increases, EAR remains the same.
C) APR remains the same, EAR increases.
A
C
The APR remains the same since the APR is computed as (interest per period) × (number of compounding periods in 1 year). As the frequency of compounding increases, the interest rate per period decreases leaving the original APR unchanged. However, the EAR increases with the frequency of compounding.
21
Q
What is the effective annual rate if the stated rate is 12% compounded quarterly?
A) 12.55%.
B) 12.00%.
C) 57.35%.
A
A
EAR = (1 + 0.12 / 4)4 - 1 = 12.55%
22
Q
Marc Schmitz borrows $20,000 to be paid back in four equal annual payments at an interest rate of 8%. The interest amount in the second year’s payment would be:
A) $1116.90.
B) $1244.90.
C) $6038.40.
A
B
With PV = 20,000, N = 4, I/Y = 8, computed Pmt = 6,038.42. Interest (Yr1) = 20,000(0.08) = 1600. Interest (Yr2) = (20,000 − (6038.42 − 1600))(0.08) = 1244.93
23
Q
An investor purchases a 10-year, $1,000 par value bond that pays annual coupons of $100. If the market rate of interest is 12%, what is the current market value of the bond?
A) $950.
B) $1,124.
C) $887.
A
C
Note that bond problems are just mixed annuity problems. You can solve bond problems directly with your financial calculator using all five of the main TVM keys at once. For bond-types of problems the bond’s price (PV) will be negative, while the coupon payment (PMT) and par value (FV) will be positive. N = 10; I/Y = 12; FV = 1,000; PMT = 100; CPT → PV = -886.99.
24
Q
Steve Hall wants to give his son a new car for his graduation. If the cost of the car is $15,000 and Hall finances 80% of the value of the car for 36 months at 8% annual interest, his monthly payments will be:
A) $376.
B) $413.
C) $289.
A
A
PV = 0.8 × 15,000 = -12,000; N = 36; I = 8/12 = 0.667; CPT → PMT = 376.
25
A major brokerage house is currently selling an investment product that offers an 8% rate of return, compounded monthly. Based on this information, it follows that this investment has:
A) an effective annual rate of 8.00%.
B) a periodic interest rate of 0.667%.
C) a stated rate of 0.830%.
B
| Periodic rate = 8.0 / 12 = 0.667. Stated rate is 8.0% and effective rate is 8.30%.
26
An investment offers $100 per year forever. If Peter Wallace's required rate of return on this investment is 10%, how much is this investment worth to him?
A) $10,000.
B) $1,000.
C) $500.
B
| For a perpetuity, PV = PMT ÷ I = 100 ÷ 0.10 = 1,000.
27
An individual borrows $200,000 to buy a house with a 30-year mortgage requiring payments to be made at the end of each month. The interest rate is 8%, compounded monthly. What is the monthly mortgage payment?
A) $1,480.46.
B) $1,467.53.
C) $2,142.39.
B
| With PV = 200,000; N = 30 × 12 = 360; I/Y = 8/12; CPT → PMT = $1,467.53.
28
What is the present value of a 12-year annuity due that pays $5,000 per year, given a discount rate of 7.5%?
A) $36,577.
B) $41,577.
C) $38,676.
B
Using your calculator: N = 11; I/Y = 7.5; PMT = -5,000; FV = 0; CPT → PV = 36,577 + 5,000 = $41,577. Or set your calculator to BGN mode and N = 12; I/Y = 7.5; PMT = -5,000; FV = 0; CPT → PV = $41,577.
!! annuity due : cash happens at beginning of period
29
Ordinary annuity cash flows occur ____ of each time period. Annuity due cash flows occur ____ of each time period.
at the end; at the beginning
30
____ cash flows occur at the end of each time period. ____ cash flows occur at the beginning of each time period.
Ordinary annuity; Annuity due
31
Concerning an ordinary annuity and an annuity due with the same payments and positive interest rate, which of the following statements is most accurate?
A) The present value of the ordinary annuity is less than an annuity due.
B) The present value of the ordinary annuity is greater than an annuity due.
C) There is no relationship.
A
With a positive interest rate, the present value of an ordinary annuity is less than the present value of an annuity due. The first cash flow in an annuity due is at the beginning of the period, while in an ordinary annuity, the first cash flow occurs at the end of the period. Therefore, each cash flow of the ordinary annuity is discounted one period more.
32
An investor makes 48 monthly payments of $500 each beginning today into an account that will have a value of $29,000 at the end of four years. The stated annual interest rate is closest to:
A) 10.00%.
B) 9.50%.
C) 9.00%.
C
Because this is an annuity due (payments at the start of each period) the calculator must first be set to BGN mode.
N = 48; PMT = 500; FV = -29,000; PV = 0; CPT I/Y = 0.7532
This percentage is a monthly rate because the time periods were entered as 48 months. It must be converted to a stated annual percentage rate (APR) by multiplying by the number of compounding periods per year: 0.7532 × 12 = 9.04%.
33
In 10 years, what is the value of $100 invested today at an interest rate of 8% per year, compounded monthly?
A) $180.
B) $216.
C) $222.
C
| N = 10 × 12 = 120; I/Y = 8/12 = 0.666667; PV = -100; PMT = 0; CPT → FV = 221.96.
34
An investor has the choice of two investments. Investment A offers interest at 7.25% compounded quarterly. Investment B offers interest at the annual rate of 7.40%. Which investment offers the higher dollar return on an investment of $50,000 for two years, and by how much?
A) Investment A offers a $122.18 greater return.
B) Investment A offers a $53.18 greater return.
C) Investment B offers a $36.92 greater return.
B
Investment A: I = 7.25 / 4; N = 2 × 4 = 8; PV = $50,000; PMT = 0; CPT → FV = $57,726.98
Investment B: I = 7.40; N = 2; PV = $50,000; PMT = 0; CPT → FV = $57,673.80
Difference = investment A offers a $53.18 greater dollar return.
35
How much should an investor have in a retirement account on his 65th birthday if he wishes to withdraw $40,000 on that birthday and each of the following 14 birthdays, assuming his retirement account is expected to earn 14.5%?
A) $272,977.
B) $234,422.
C) $274,422.
C
This is an annuity due so set your calculator to the BGN mode. N = 15; I/Y = 14.5; PMT = -40,000; FV = 0; CPT → PV = 274,422.50. Switch back to END mode.
36
If $2,500 were put into an account at the end of each of the next 10 years earning 15% annual interest, how much would be in the account at the end of ten years?
A) $27,461.
B) $41,965.
C) $50,759.
C
| N = 10; I = 15; PMT = 2,500; CPT → FV = $50,759.
37
Suppose you are going to deposit $1,000 at the start of this year, $1,500 at the start of next year, and $2,000 at the start of the following year in an savings account. How much money will you have at the end of three years if the rate of interest is 10% each year?
A) $4,000.00.
B) $5,750.00.
C) $5,346.00.
C
Future value of $1,000 for 3 periods at 10% = 1,331
Future value of $1,500 for 2 periods at 10% = 1,815
Future value of $2,000 for 1 period at 10% = 2,200
Total = $5,346
```
N = 3; PV = -$1,000; I/Y = 10%; CPT → FV = $1,331
N = 2; PV = -$1,500; I/Y = 10%; CPT → FV = $1,815
N = 1; PV = -$2,000; I/Y = 10%; CPT → FV = $2,200
```
38
What's the effective rate of return on an investment that generates a return of 12%, compounded quarterly?
A) 12.55%.
B) 12.00%.
C) 14.34%.
A
| (1 + 0.12 / 4)4 − 1 = 1.1255 − 1 = 0.1255.
39
Paul Kohler inherits $50,000 and deposits it immediately in a bank account that pays 6% interest. No other deposits or withdrawals are made. In two years, what will be the account balance assuming monthly compounding?
A) $53,100.
B) $56,400.
C) $50,500.
B
To compound monthly, remember to divide the interest rate by 12 (6%/12 = 0.50%) and the number of periods will be 2 years times 12 months (2 × 12 = 24 periods). The value after 24 periods is $50,000 × 1.00524 = $56,357.99.
The problem can also be solved using the time value of money functions: N = 24; I/Y = 0.5; PMT = 0; PV = 50,000; CPT FV = $56,357.99.
40
Find the future value of the following uneven cash flow stream. Assume end of the year payments. The discount rate is 12%.
```
Year 1: -2,000
Year 2: -3,000
Year 3: 6,000
Year 4: 25,000
Year 5: 30,000
```
A) $65,144.33.
B) $58,164.58.
C) $33,004.15.
B (first time calculated NPV on accident...C)
N = 4; I/Y = 12; PMT = 0; PV = -2,000; CPT → FV = -3,147.04
N = 3; I/Y = 12; PMT = 0; PV = -3,000; CPT → FV = -4,214.78
N = 2; I/Y = 12; PMT = 0; PV = 6,000; CPT → FV = 7,526.40
N = 1; I/Y = 12; PMT = 0; PV = 25,000; CPT → FV = 28,000.00
N = 0; I/Y = 12; PMT = 0; PV = 30,000; CPT → FV = 30,000.00
Sum the cash flows: $58,164.58.
Alternative calculation solution: -2,000 × 1.124 − 3,000 × 1.123 + 6,000 × 1.122 + 25,000 × 1.12 + 30,000 = $58,164.58.
41
Given: an 11% annual rate compounded quarterly for 2 years; compute the future value of $8,000 today.
A) $9,939.
B) $8,962.
C) $9,857.
A
Divide the interest rate by the number of compound periods and multiply the number of years by the number of compound periods. I = 11 / 4 = 2.75; N = (2)(4) = 8; PV = 8,000.
42
An investor deposits $4,000 in an account that pays 7.5%, compounded annually. How much will this investment be worth after 12 years?
A) $5,850.
B) $9,358.
C) $9,527.
C
| N = 12; I/Y = 7.5; PV = -4,000; PMT = 0; CPT → FV = $9,527.
43
An investor wants to receive $1,000 at the beginning of each of the next ten years with the first payment starting today. If the investor can earn 10 percent interest, what must the investor put into the account today in order to receive this $1,000 cash flow stream?
A) $6,759.
B) $6,145.
C) $7,145.
A
This is an annuity due problem. There are several ways to solve this problem.
Method 1:
PV of first $1,000 = $1,000
PV of next 9 payments at 10% = 5,759.02
Sum of payments = $6,759.02
Method 2:
Put calculator in BGN mode.
N = 10; I = 10; PMT = -1,000; CPT → PV = 6,759.02
Note: make PMT negative to get a positive PV. Don't forget to take your calculator out of BGN mode.
Method 3:
You can also find the present value of the ordinary annuity $6,144.57 and multiply by 1 + k to add one year of interest to each cash flow. $6,144.57 × 1.1 = $6,759.02.
44
A certain investment product promises to pay $25,458 at the end of 9 years. If an investor feels this investment should produce a rate of return of 14%, compounded annually, what's the most he should be willing to pay for it?
A) $9,426.
B) $7,618.
C) $7,829.
C
N = 9; I/Y = 14; FV = -25,458; PMT = 0; CPT → PV = $7,828.54.
or: 25,458/1.149 = 7,828.54
45
Which one of the following statements best describes the components of the required interest rate on a security?
A)
The nominal risk-free rate, the expected inflation rate, the default risk premium, a liquidity premium and a premium to reflect the risk associated with the maturity of the security.
B)
The real risk-free rate, the default risk premium, a liquidity premium and a premium to reflect the risk associated with the maturity of the security.
C)
The real risk-free rate, the expected inflation rate, the default risk premium, a liquidity premium and a premium to reflect the risk associated with the maturity of the security.
C
The required interest rate on a security is made up of the nominal rate which is in turn made up of the real risk-free rate plus the expected inflation rate. It should also contain a liquidity premium as well as a premium related to the maturity of the security.
46
Sarah Parker is buying a new $25,000 car. Her trade-in is worth $5,000 so she needs to borrow $20,000. The loan will be paid in 48 monthly installments and the annual interest rate on the loan is 7.5%. If the first payment is due at the end of the first month, what is Sarah's monthly car payment?
A) $480.57.
B) $483.58.
C) $416.67.
B
| N = 48; I/Y = 7.5 / 12 = 0.625; PV = 20,000; FV = 0; CPT → PMT = 483.58.
47
Given investors require an annual return of 12.5%, a perpetual bond (i.e., a bond with no maturity/due date) that pays $87.50 a year in interest should be valued at:
A) $70.
B) $1,093.
C) $700.
C
| 87.50 ÷ 0.125 = $700.
48
The real risk-free rate can be thought of as:
A)
approximately the nominal risk-free rate plus the expected inflation rate.
B)
exactly the nominal risk-free rate reduced by the expected inflation rate.
C)
approximately the nominal risk-free rate reduced by the expected inflation rate.
C
The approximate relationship between nominal rates, real rates and expected inflation rates can be written as:
Nominal risk-free rate = real risk-free rate + expected inflation rate.
Therefore we can rewrite this equation in terms of the real risk-free rate as:
Real risk-free rate = Nominal risk-free rate - expected inflation rate
The exact relation is: (1 + real)(1 + expected inflation) = (1 + nominal)
49
An investor deposits $10,000 in a bank account paying 5% interest compounded annually. Rounded to the nearest dollar, in 5 years the investor will have:
A) $12,500.
B) $10,210.
C) $12,763.
C
PV = 10,000; I/Y = 5; N = 5; CPT → FV = 12,763.
or: 10,000(1.05)5 = 12,763.
50
What will $10,000 become in 5 years if the annual interest rate is 8%, compounded monthly?
A) $14,693.28.
B) $14,802.44.
C) $14,898.46.
```
C
FV(t=5) = $10,000 × (1 + 0.08 / 12)^60 = $14,898.46
```
N = 60 (12 × 5); PV = -$10,000; I/Y = 0.66667 (8% / 12months); CPT → FV = $14,898.46
51
A 10% coupon bond was purchased for $1,000. One year later the bond was sold for $915 to yield 11%. The investor's holding period yield on this bond is closest to:
A) 1.5%.
B) 9.0%.
C) 18.5%.
A
HPY = [(interest + ending value) / beginning value] − 1
= [(100 + 915) / 1,000] − 1
= 1.015 − 1 = 1.5%
52
Given a $1,000 T-bill with 100 days to maturity and a discount of $10 (price of $990):
What is bank discount yield? (formula is fine)
bank discount yield = discount/coupon value * 360/days to maturity
10/1000 * 360/100 = 3.6%
53
Given a $1,000 T-bill with 100 days to maturity and a discount of $10 (price of $990):
What is holding period yield? (formula is fine)
HPY = [(interest + ending value) / beginning value] − 1
(1000-990)/990 = 1.01%
54
Given a $1,000 T-bill with 100 days to maturity and a discount of $10 (price of $990):
What is effective annual yield? (formula is fine)
EAY = (1 + holding period yield)^365/t − 1.
1.0101^(365/100)-1 = 3.74%
55
Given a $1,000 T-bill with 100 days to maturity and a discount of $10 (price of $990):
What is money market yield? (formula is fine)
holding period yield * 365/holding period
1.01% x 360/100 = 3.636%
56
An investment with a cost of $5,000 is expected to have cash inflows of $3,000 in year 1, and $4,000 in year 2. The internal rate of return (IRR) for this investment is closest to:
A) 25%.
B) 15%.
C) 30%.
A
The IRR is the discount rate that makes the net present value of the investment equal to 0.
This means -$5,000 + $3,000 / (1 + IRR) + $4,000 / (1 + IRR)2 = 0
One way to compute this problem is to use trial and error with the existing answer choices and choose the discount rate that makes the PV of the cash flows closest to 5,000.
$3,000 / (1.25) + $4,000 / (1.25)2 = 4,960.
Alternatively: CFO = -5,000; CF1 = 3,000; CF2 = 4,000; CPT → IRR = 24.3%. **this is what i used
57
Sarah Kelley, CFA, is analyzing two mutually exclusive investment projects. Kelley has calculated the net present value (NPV) and internal rate of return (IRR) for each project:
Project 1: NPV = $230; IRR = 15%
Project 2: NPV = $4,000; IRR = 6%
Kelley should make which of the following recommendations concerning the two projects?
A) Accept Project 2 only.
B) Accept both projects.
C) Accept Project 1 only.
A
(this question is similar to the ones in capital budgeting)
Because the investment projects are mutually exclusive, only one project can be chosen. The NPV and IRR criteria are giving conflicting project rankings. When decision criteria conflict, always use the NPV criteria because NPV evaluates projects using an appropriate discount rate, the weighted average cost of capital. The IRR may not be a market rate, therefore future cash flows associated with the project may not be capable of earning a rate of return equal to the IRR.
58
A stock is currently worth $75. If the stock was purchased one year ago for $60, and the stock paid a $1.50 dividend over the course of the year, what is the holding period return?
A) 24.0%.
B) 22.0%.
C) 27.5%.
C
HPY = [(interest + ending value) / beginning value] − 1
(75 − 60 + 1.50) / 60 = 27.5%.
59
A Treasury bill has 40 days to maturity, a par value of $10,000, and is currently selling for $9,900. Its effective annual yield is closest to:
A) 9.00%.
B) 1.00%.
C) 9.60%.
C
The effective annual yield (EAY) is based on a 365-day year and accounts for compound interest. EAY = (1 + holding period yield)^365/t − 1. The holding period yield formula is (price received at maturity − initial price + interest payments) / (initial price) = (10,000 − 9,900 + 0) / (9,900) = 1.01%. EAY = (1.0101)365/40 − 1 = 9.60%.
60
Which of the following is NOT a problem with the internal rate of return (IRR)?
A) Sometimes the IRR exceeds the cost of capital.
B) A higher IRR does not necessarily indicate a more-profitable project.
C) Non-normal cash flow patterns may result in multiple IRRs.
A
If the IRR exceeds the cost of capital, that merely indicates that the project is acceptable-this is not a problem associated with IRR. Non-normal cash flow patterns such as cash outflows during the project's life can result in multiple IRRs, leaving open the question as to which one is valid. A higher IRR will only be realized if the project's cash flows can be reinvested at the IRR, and the true profitability of a project also depends on project size, not just IRR.
61
The ______ rate of return is the IRR calculated using periodic cash flows into and out of an account and is the discount rate that makes the PV of cash inflows equal to the PV of cash outflows.
money-weighted
62
The money-weighted rate of return is the IRR calculated using periodic cash flows into and out of an account and is the discount rate that makes the ______ equal to the ____.
PV of cash inflows; PV of cash outflows
63
The ______ of return measures compound growth.
time-weighted rate
64
_____ is the rate at which $1 compounds over a specified performance horizon.
time-weighted rate of return
65
The _____ return is the preferred measure of a manager's ability to select investments. If the manager controls the money flows into and out of an account, the _____ return is the more appropriate performance measure.
time-weighted; money-weighted
66
If ______, the money-weighted return is the more appropriate performance measure.
the manager controls the money flows into and out of an account
67
If funds are added to a portfolio ______, the money-weighted return will be lower than the time-weighted return. If funds are added ______, the money-weighted return will be higher than the time-weighted return.
just before a period of poor performance; just prior to a period of high returns
68
If funds are added to a portfolio just before a period of poor performance, the money-weighted return will be _____ (higher/lower) than the time-weighted return. If funds are added just prior to a period of high returns, the money-weighted return return will be ____ (higher/lower) than the time-weighted
lower; higher
69
A T-bill with a face value of $100,000 and 140 days until maturity is selling for $98,000. What is its holding period yield?
A) 5.14%.
B) 2.04%.
C) 5.25%.
The holding period yield is the return the investor will earn if the T-bill is held to maturity. HPY = (100,000 - 98,000) / 98,000 = 0.0204, or 2.04%.
70
Williams Warehousing currently has a warehouse lease that calls for five annual payments of $120,000. The warehouse owner, who needs cash, is offering Williams a deal wherein Williams will pay $200,000 this year and then pay only $80,000 each of the remaining 4 years. (Assume that all lease payments are made at the beginning of the year.) Should Williams Warehousing accept the offer if its required rate of return is 9%, and why?
A) No, there is an additional $80,000 payment in this year.
B) Yes, there is a savings of $45,494 in present value terms.
C) Yes, there is a savings of $49,589 in present value terms.
C
The present value of the current lease is $508,766.38, while the present value of the lease being offered is $459,177.59; a savings of 49,589. Alternatively, the present value of the extra $40,000 at the beginning of each of the next 4 years is $129,589 which is $49,589 more than the extra $80,000 added to the payment today.
71
A Treasury bill with a face value of $1,000,000 and 45 days until maturity is selling for $987,000. The Treasury bill's bank discount yield is closest to:
A) 7.90%.
B) 10.40%.
C) 10.54%.
B (first time picked A, that's when you don't calculate the actual discount first)
The actual discount is 1.3%, 1.3% × (360 / 45) = 10.4%
The bank discount yield is computed by the following formula, r = (dollar discount / face value) × (360 / number of days until maturity) = [(1,000,000 − 987,000) / (1,000,000)] × (360 / 45) = 10.40%.
72
If the holding period yield on a Treasury bill (T-bill) with 197 days until maturity is 1.07%, what is the effective annual yield?
A) 0.58%.
B) 1.07%.
C) 1.99%.
C
To calculate the EAY from the HPY, the formula is: (1 + HPY)^(365/t) − 1. Therefore, the EAY is: (1.0107)^(365/197) − 1 = 0.0199, or 1.99%.
73
The bank discount of a $1,000,000 T-bill with 135 days until maturity that is currently selling for $979,000 is:
A) 5.6%.
B) 5.8%.
C) 6.1%.
A
($21,000 / 1,000,000) × (360 / 135) = 5.6%.
bank discount yield = discount/coupon value * 360/days to maturity
**coupon, not selling price
74
The two properties of probability are:
- The sum of the probabilities of all _____ is 1.
- The probability of any event cannot be _____.
possible mutually exclusive events;
| greater than 1 or less than 0.
75
____ probability measures predetermined probabilities based on well-defined inputs
Priori
76
____ probability measures probability from observations or experiments
Empirical
77
____ probability is an informed guess.
Subjective
78
A priori probability measures ____ based on ____
predetermined probabilities; well-defined inputs
79
Empirical probability measures probability from _____
observations or experiments
80
Subjective probability is ______
an informed guess.
81
```
An investor has two stocks, Stock R and Stock S in her portfolio. Given the following information on the two stocks, the portfolio's standard deviation is closest to:
σR = 34%
σS = 16%
rR,S = 0.67
WR = 80%
WS = 20%
```
A) 7.8%.
B) 29.4%.
C) 8.7%.
B
The formula for the standard deviation of a 2-stock portfolio is:
s = [WA^2sA^2 + WB^2sB^2 + 2WAWBsAsB(rA,B)]^1/2
s = [(0.8^2 × 0.34^2) + (0.2^2 × 0.16^2) + (2 × 0.8 × 0.2 × 0.34 × 0.16 × 0.67)]^1/2 = [0.073984 + 0.001024 + 0.0116634]^1/2 = 0.0866714^1/2 = 0.2944, or approximately 29.4%.
82
Data shows that 75 out of 100 tourists who visit New York City visit the Empire State Building. It rains or snows in New York City one day in five. What is the joint probability that a randomly choosen tourist visits the Empire State Building on a day when it neither rains nor snows?
A) 60%.
B) 15%.
C) 95%.
A
A joint probability is the probability that two events occur when neither is certain or a given. Joint probability is calculated by multiplying the probability of each event together. (0.75) × (0.80) = 0.60 or 60%.
83
For a stock, which of the following is least likely a random variable? Its:
A) most recent closing price.
B) stock symbol.
C) current ratio.
B
A random variable must be a number. Sometimes there is an obvious method for assigning a number, such as when the random variable is a number itself, like a P/E ratio. A stock symbol of a randomly selected stock could have a number assigned to it like the number of letters in the symbol. The symbol itself cannot be a random variable.
84
Assume two stocks are perfectly negatively correlated. Stock A has a standard deviation of 10.2% and stock B has a standard deviation of 13.9%. What is the standard deviation of the portfolio if 75% is invested in A and 25% in B?
A) 0.00%.
B) 4.18%.
C) 0.17%.
B (not C, C did not do 1/2次方)
[W1^2 σ1^2 + W2^2 σ2^2 + 2W1W2σ1σ2r1,2]^0.5
= [(0.75)2(0.102)2 + (0.25)^2(0.139)^2 + (2)(0.75)(0.25)(0.102)(0.139)(-1.0)]^0.5
= 0.0418, or 4.18%.
85
A portfolio manager wants to eliminate four stocks from a portfolio that consists of six stocks. How many ways can the four stocks be sold when the order of the sales is important?
A) 180.
B) 360.
C) 24.
B
This is a choose four from six problem where order is important. Thus, it requires the permutation formula: n! / (n − r)! = 6! / (6 − 4)! = 360.
With TI calculator: 6 [2nd][nPr] 4 = 360.
86
For a given corporation, which of the following is an example of a conditional probability? The probability the corporation's:
A) inventory improves.
B) dividend increases given its earnings increase.
C) earnings increase and dividend increases.
B
A conditional probability involves two events. One of the events is a given, and the probability of the other event depends upon that given.
87
In a given portfolio, half of the stocks have a beta greater than one. Of those with a beta greater than one, a third are in a computer-related business. What is the probability of a randomly drawn stock from the portfolio having both a beta greater than one and being in a computer-related business?
A) 0.333.
B) 0.667.
C) 0.167.
C
This is a joint probability. From the information: P(beta > 1) = 0.500 and P(comp. stock | beta > 1) = 0.333. Thus, the joint probability is the product of these two probabilities: (0.500) × (0.333) = 0.167.
88
Last year, the average salary increase for poultry research assistants was 2.5%. Of the 10,000 poultry research assistants, 2,000 received raises in excess of this amount. The odds that a randomly selected poultry research assistant received a salary increase in excess of 2.5% are:
A) 20%.
B) 1 to 5.
C) 1 to 4.
C
For event "E," the probability stated as odds is: P(E) / [1 - P(E)]. Here, the probability that a poultry research assistant received a salary increase in excess of 2.5% = 2,000 / 10,000 = 0.20, or 1/5 and the odds are (1/5) / [1 - (1/5)] = 1/4, or 1 to 4.
89
A parking lot has 100 red and blue cars in it.
40% of the cars are red.
70% of the red cars have radios.
80% of the blue cars have radios.
What is the probability of selecting a car at random and having it be red and have a radio?
A) 25%.
B) 48%.
C) 28%.
C
Joint probability is the probability that both events, in this case a car being red and having a radio, happen at the same time. Joint probability is computed by multiplying the individual event probabilities together: P(red and radio) = (P(red)) × (P(radio)) = (0.4) × (0.7) = 0.28 or 28%.
90
An analyst announces that an increase in the discount rate next quarter will double her earnings forecast for a firm. This is an example of a:
A) use of Bayes' formula.
B) joint probability.
C) conditional expectation.
C
| This is a conditional expectation. The analyst indicates how an expected value will change given another event.
91
Bonds rated B have a 25% chance of default in five years. Bonds rated CCC have a 40% chance of default in five years. A portfolio consists of 30% B and 70% CCC-rated bonds. If a randomly selected bond defaults in a five-year period, what is the probability that it was a B-rated bond?
A) 0.625.
B) 0.250.
C) 0.211.
!!! C
According to Bayes' formula: P(B | default) = P(default and B) / P(default).
P(default and B )= P(default | B) × P(B) = 0.250 × 0.300 = 0.075
P(default and CCC) = P(default | CCC) × P(CCC) = 0.400 × 0.700 = 0.280
P(default) = P(default and B) + P(default and CCC) = 0.355
P(B | default) = P(default and B) / P(default) = 0.075 / 0.355 = 0.211
92
Which of the following statements about the defining properties of probability is least accurate?
A)
The probability of an event may be equal to zero or equal to one.
B)
To state a probability, a set of mutually exclusive and exhaustive events must be defined.
C)
The sum of the probabilities of events equals one if the events are mutually exclusive and exhaustive.
B
Stating a probability does not require defining a mutually exclusive and exhaustive set of events. The two defining properties of probability are that the probability of an event is greater than or equal to zero and less than or equal to one, and if a set of events is mutually exclusive and exhaustive, their probabilities sum to one.
93
A bond portfolio consists of four BB-rated bonds. Each has a probability of default of 24% and these probabilities are independent. What are the probabilities of all the bonds defaulting and the probability of all the bonds not defaulting, respectively?
A) 0.00332; 0.33360.
B) 0.96000; 0.04000.
C) 0.04000; 0.96000.
A
For the four independent events where the probability is the same for each, the probability of all defaulting is (0.24)^4. The probability of all not defaulting is (1 − 0.24)^4.
94
If two fair coins are flipped and two fair six-sided dice are rolled, all at the same time, what is the probability of ending up with two heads (on the coins) and two sixes (on the dice)?
A) 0.0069.
B) 0.8333.
C) 0.4167.
A
For the four independent events defined here, the probability of the specified outcome is 0.5000 × 0.5000 × 0.1667 × 0.1667 = 0.0069.
95
The following table summarizes the availability of trucks with air bags and bucket seats at a dealership.
Bucket Seats No Bucket Seats Total
Air Bags 75 50 125
No Air Bags 35 60 95
Total 110 110 220
What is the probability of selecting a truck at random that has either air bags or bucket seats?
A) 107%.
B) 73%.
C) 34%.
B
The addition rule for probabilities is used to determine the probability of at least one event among two or more events occurring. The probability of each event is added and the joint probability (if the events are not mutually exclusive) is subtracted to arrive at the solution. P(air bags or bucket seats) = P(air bags) + P(bucket seats) − P(air bags and bucket seats) = (125 / 220) + (110 / 220) − (75 / 220) = 0.57 + 0.50 − 0.34 = 0.73 or 73%.
Alternative: 1 − P(no airbag and no bucket seats) = 1 − (60 / 220) = 72.7%
**mine = (75+35+50)/220
96
A bag of marbles contains 3 white and 4 black marbles. A marble will be drawn from the bag randomly three times and put back into the bag. Relative to the outcomes of the first two draws, the probability that the third marble drawn is white is:
A) dependent.
B) independent.
C) conditional.
A
| balls are put back after each draw, so it is independent.
97
There is a 40% probability that the economy will be good next year and a 60% probability that it will be bad. If the economy is good, there is a 50 percent probability of a bull market, a 30% probability of a normal market, and a 20% probability of a bear market. If the economy is bad, there is a 20% probability of a bull market, a 30% probability of a normal market, and a 50% probability of a bear market. What is the probability of a bull market next year?
A) 20%.
B) 50%.
C) 32%.
C
Because a good economy and a bad economy are mutually exclusive, the probability of a bull market is the sum of the joint probabilities of (good economy and bull market) and (bad economy and bull market): (0.40 × 0.50) + (0.60 × 0.20) = 0.32 or 32%.
*diagram is helpful in this case
98
If the outcome of event A is not affected by event B, then events A and B are said to be:
A) statistically independent.
B) mutually exclusive.
C) conditionally dependent.
A
| If the outcome of one event does not influence the outcome of another, then the events are independent.
99
Jessica Fassler, options trader, recently wrote two put options on two different underlying stocks (AlphaDog Software and OmegaWolf Publishing), both with a strike price of $11.50. The probabilities that the prices of AlphaDog and OmegaWolf stock will decline below the strike price are 65% and 47%, respectively, and these probabilities are independent. The probability that at least one of the put options will fall below the strike price is approximately:
A) 1.00.
B) 0.31.
C) 0.81.
C
We calculate the probability that at least one of the options will fall below the strike price using the addition rule for probabilities (A represents AlphaDog, O represents OmegaWolf):
P(A or O) = P(A) + P(O) − P(A and O), where P(A and O) = P(A) × P(O)
P(A or O) = 0.65 + 0.47 − (0.65 × 0.47) = approximately 0.81
100
What is the standard deviation of a portfolio if you invest 30% in stock one (standard deviation of 4.6%) and 70% in stock two (standard deviation of 7.8%) if the correlation coefficient for the two stocks is 0.45?
A) 6.20%.
B) 0.38%.
C) 6.83%.
A
The standard deviation of the portfolio is found by:
[W1^2 σ1^2 + W2^2 σ2^2 + 2W1W2σ1σ2r1,2]^0.5, or [(0.30)^2(0.046)^2 + (0.70)^2(0.078)^2 + (2)(0.30)(0.70)(0.046)(0.078)(0.45)]^0.5 = 0.0620, or 6.20%.
*remember to do 1/2 at the end!!
101
If the odds against an event occurring are twelve to one, what is the probability that it will occur?
A) 0.0769.
B) 0.9231.
C) 0.0833.
A
If the probability against the event occurring is twelve to one, this means that in thirteen occurrences of the event, it is expected that it will occur once and not occur twelve times. The probability that the event will occur is then: 1/13 = 0.0769.
102
______ measures the extent to which two random variables tend to be above and below their respective means for each joint realization
Covariance
103
Covariance formula?
Sum of Probability x (A-mean of A)(B-mean of B)
104
How is covariance and correlation related?
r = Cov (A,B)/SDa*SDb
105
Personal Advisers, Inc., has determined four possible economic scenarios and has projected the portfolio returns for two portfolios for their client under each scenario. Personal's economist has estimated the probability of each scenario as shown in the table below. Given this information, what is the covariance of the returns on Portfolio A and Portfolio B?
Scenario Probability Return (A) Return (B)
A 15% 18% 19%
B 20% 17% 18%
C 25% 11% 10%
D 40% 7% 9%
A) 0.002019.
B) 0.890223.
C) 0.001898.
C
E(RA) =11.65%, E(RB) =12.55%
```
[RA - E(RA)]x [RB - E(RB)] x P(S):
0.000614
0.000583
0.000041
0.000660
Thus, Cov(RA,RB) =0.001898
```
106
Given Cov(X,Y) = 1,000,000. What does this indicate about the relationship between X and Y?
A) Only that it is positive.
B) It is strong and positive.
C) It is weak and positive.
A
A positive covariance indicates a positive linear relationship but nothing else. The magnitude of the covariance by itself is not informative with respect to the strength of the relationship.
107
Range of covariance is?
negative infinity to positive infinity
| thus a big positive cov doesn't mean it's strong, since it could go all the way to infinity
108
In any given year, the chance of a good year is 40%, an average year is 35%, and the chance of a bad year is 25%. What is the probability of having two good years in a row?
A) 10.00%.
B) 16.00%.
C) 8.75%.
B
The joint probability of independent events is obtained by multiplying the probabilities of the individual events together: (0.40) × (0.40) = 0.16 or 16%.
109
Given the following probability distribution, find the standard deviation of expected returns.
```
Event P(RA) RA
Recession 0.10 -5%
Below Average 0.30 -2%
Normal 0.50 10%
Boom 0.10 31%
```
A) 10.04%.
B) 7.00%.
C) 12.45%.
A
Find the weighted average return (0.10)(−5) + (0.30)(−2) + (0.50)(10) + (0.10)(31) = 7%.
Next, take differences, square them, multiply by the probability of the event and add them up. That is the variance. Take the square root of the variance for Std. Dev. (0.1)(−5 − 7)^2 + (0.3)(−2 − 7)^2 + (0.5)(10 − 7)^2 + (0.1)(31 − 7)^2 = 100.8 = variance.
100.8^0.5 = 10.04%.
110
How to calculate variance and SD
sum of
(each value - expected value)^2 x probability
SD is ^.5 of variance
111
what does this calculate?
sum of
(each value - expected value)^2 x probability
variance
112
what does this calculate?
sum of
each value * probability
Expected value
113
The probabilities of earning a specified return from a portfolio are shown below:
Probability Return
0. 20 10%
0. 20 20%
0. 20 22%
0. 20 15%
0. 20 25%
What are the odds of earning at least 20%?
A) Three to two.
B) Three to five.
C) Two to three.
A
Odds are the number of successful possibilities to the number of unsuccessful possibilities:
P(E)/[1 − P(E)] or 0.6 / 0.4 or 3/2.
114
If given the standard deviations of the returns of two assets and the correlation between the two assets, which of the following would an analyst least likely be able to derive from these?
A) Expected returns.
B) Covariance between the returns.
C) Strength of the linear relationship between the two.
A
| The correlations and standard deviations cannot give a measure of central tendency, such as the expected value.
115
An investor is considering purchasing ACQ. There is a 30% probability that ACQ will be acquired in the next two months. If ACQ is acquired, there is a 40% probability of earning a 30% return on the investment and a 60% probability of earning 25%. If ACQ is not acquired, the expected return is 12%. What is the expected return on this investment?
A) 18.3%.
B) 16.5%.
C) 12.3%.
B
(tree diagram helps!)
E(r) = (0.70 × 0.12) + (0.30 × 0.40 × 0.30) + (0.30 × 0.60 × 0.25) = 0.165.
116
Use the following data to calculate the standard deviation of the return:
50% chance of a 12% return
30% chance of a 10% return
20% chance of a 15% return
A) 2.5%.
B) 3.0%.
C) 1.7%.
C
The standard deviation is the positive square root of the variance. The variance is the expected value of the squared deviations around the expected value, weighted by the probability of each observation. The expected value is: (0.5) × (0.12) + (0.3) × (0.1) + (0.2) × (0.15) = 0.12. The variance is: (0.5) × (0.12 − 0.12)2 + (0.3) × (0.1 − 0.12)2 + (0.2) × (0.15 − 0.12)2 = 0.0003. The standard deviation is the square root of 0.0003 = 0.017 or 1.7%.
117
Given the following table about employees of a company based on whether they are smokers or nonsmokers and whether or not they suffer from any allergies, what is the probability of being either a nonsmoker or not suffering from allergies?
Suffer Allergies No Allergies Total
Smoker 35 25 60
Nonsmoker 55 185 240
Total 90 210 300
A) 0.38.
B) 0.88.
C) 0.50.
B
The probability of being a nonsmoker is 240 / 300 = 0.80. The probability of not suffering from allergies is 210 / 300 = 0.70. The probability of being a nonsmoker and not suffering from allergies is 185 / 300 = 0.62. Since the question asks for the probability of being either a nonsmoker or not suffering from allergies we have to take the probability of being a nonsmoker plus the probability of not suffering from allergies and subtract the probability of being both: 0.80 + 0.70 − 0.62 = 0.88.
Alternatively: 1 − P(Smoker & Allergies) = 1 − (35 / 300) = 88.3%.
118
After repeated experiments, the average of the outcomes should converge to:
A) the variance.
B) one.
C) the expected value.
C
| This is the definition of the expected value. It is the long-run average of all outcomes.
119
Given P(X = 20, Y = 0) = 0.4, and P(X = 30, Y = 50) = 0.6, then COV(XY) is:
A) 25.00.
B) 125.00.
C) 120.00.
C
The expected values are: E(X) = (0.4 × 20) + (0.6 × 30) = 26, and E(Y) = (0.4 × 0) + (0.6 × 50) = 30.
The covariance is COV(XY) = (0.4 × ((20 − 26) × (0 − 30))) + ((0.6 × (30 − 26) × (50 − 30))) = 120.
120
If X and Y are independent events, which of the following is most accurate?
A) P(X | Y) = P(X).
B) P(X or Y) = (P(X)) × (P(Y)).
C) P(X or Y) = P(X) + P(Y).
A
Note that events being independent means that they have no influence on each other. It does not necessarily mean that they are mutually exclusive. Accordingly, P(X or Y) = P(X) + P(Y) − P(X and Y). By the definition of independent events, P(X|Y) = P(X).
121
Thomas Baynes has applied to both Harvard and Yale. Baynes has determined that the probability of getting into Harvard is 25% and the probability of getting into Yale (his father's alma mater) is 42%. Baynes has also determined that the probability of being accepted at both schools is 2.8%. What is the probability of Baynes being accepted at either Harvard or Yale?
A) 10.5%.
B) 64.2%.
C) 7.7%.
B
Using the addition rule, the probability of being accepted at Harvard or Yale is equal to: P(Harvard) + P(Yale) − P(Harvard and Yale) = 0.25 + 0.42 − 0.028 = 0.642 or 64.2%.
122
P (X or Y) = ?
P(X) + P(Y) - P (X and Y)
123
Which of the following sets of numbers does NOT meet the requirements for a set of probabilities?
A) (0.10, 0.20, 0.30, 0.40).
B) (0.50, 0.50).
C) (0.10, 0.20, 0.30, 0.40, 0.50).
C
| A set of probabilities must sum to one.
124
An analyst expects that 20% of all publicly traded companies will experience a decline in earnings next year. The analyst has developed a ratio to help forecast this decline. If the company is headed for a decline, there is a 90% chance that this ratio will be negative. If the company is not headed for a decline, there is only a 10% chance that the ratio will be negative. The analyst randomly selects a company with a negative ratio. Based on Bayes' theorem, the updated probability that the company will experience a decline is:
A) 69%.
B) 18%.
C) 26%.
A
Given a set of prior probabilities for an event of interest, Bayes' formula is used to update the probability of the event, in this case that the company we have already selected will experience a decline in earnings next year. Bayes' formula says to divide the Probability of New Information given Event by the Unconditional Probability of New Information and multiply that result by the Prior Probability of the Event. In this case, P(company having a decline in earnings next year) = 0.20 is divided by 0.26 (which is the Unconditional Probability that a company having an earnings decline will have a negative ratio (90% have negative ratios of the 20% which have earnings declines) plus (10% have negative ratios of the 80% which do not have earnings declines) or ((0.90) × (0.20)) + ((0.10) × (0.80)) = 0.26.) This result is then multiplied by the Prior Probability of the ratio being negative, 0.90. The result is (0.20 / 0.26) × (0.90) = 0.69 or 69%.
125
A very large company has equal amounts of male and female employees. If a random sample of four employees is selected, what is the probability that all four employees selected are female?
A) 0.0625.
B) 0.1600
C) 0.0256
A
126
The covariance of the returns on investments X and Y is 18.17. The standard deviation of returns on X is 7%, and the standard deviation of returns on Y is 4%. What is the value of the correlation coefficient for returns on investments X and Y?
A) +0.85.
B) +0.32.
C) +0.65.
C
| The correlation coefficient = Cov (X,Y) / [(Std Dev. X)(Std. Dev. Y)] = 18.17 / 28 = 0.65
127
Pat Binder, CFA, is examining the effect of an inverted yield curve on the stock market. She determines that in the past century, 75% of the times the yield curve has inverted, a bear market in stocks began within the next 12 months. Binder believes the probability of an inverted yield curve in the next year is 20%. Binder's estimate of the probability that there will be an inverted yield curve in the next year followed by a bear market is closest to:
A) 38%.
B) 15%.
C) 50%.
B
This is a joint probability. From the information: P(Bear Market given inverted yield curve) = 0.75 and P(inverted yield curve) = 0.20. The joint probability is the product of these two probabilities: (0.75)(0.20) = 0.15.
128
The following table summarizes the results of a poll taken of CEO's and analysts concerning the economic impact of a pending piece of legislation:
Group positive impact negative impact Total
CEO's 40 30 70
Analysts 70 60 130
110 90 200
What is the probability that a randomly selected individual from this group will be an analyst that thinks that the legislation will have a positive impact on the economy?
A) 0.35.
B) 0.30.
C) 0.45.
A
| 70 analysts / 200 individuals = 0.35.
129
The multiplication rule of probability is used to calculate the:
A) joint probability of two events.
B) probability of at least one of two events.
C) unconditional probability of an event, given conditional probabilities.
A
The multiplication rule of probability is stated as: P(AB) = P(A|B) × P(B), where P(AB) is the joint probability of events A and B.
130
Helen Pedersen has all her money invested in either of two mutual funds (A and B). She knows that there is a 40% probability that fund A will rise in price and a 60% chance that fund B will rise in price if fund A rises in price. What is the probability that both fund A and fund B will rise in price?
A) 0.40.
B) 1.00.
C) 0.24.
C
| P(A) = 0.40, P(B|A) = 0.60. Therefore, P(AB) = P(A)P(B|A) = 0.40(0.60) = 0.24.
131
Use the following probability distribution to calculate the standard deviation for the portfolio.
State of the Economy Probability Return on Portfolio
Boom 0.30 15%
Bust 0.70 3%
A) 6.5%.
B) 5.5%.
C) 6.0%.
B
Expected return = .3*15%+.7*3% = 0.066
SD = [0.30 × (0.15 − 0.066)^2 + 0.70 × (0.03 − 0.066)^2]^1/2 = 5.5%.
132
The multiplication rule of probability is used to determine _____
the joint probability of two events
| P(AB) = P(A | B) × P(B)
133
The joint probability of two events formula?
P(AB) = P(A | B) × P(B)
134
The addition rule of probability is used to determine _____.
the probability that at least one of two events will occur
| P(A or B) = P(A) + P(B) − P(AB)
135
P(A or B) = P(A) + P(B) − P(AB) is a formula for?
at least one of two events will occur
136
The total probability rule is used to determine ______
the unconditional probability of an event, given conditional probabilities:
P(A) = P(A | B1)P(B1) + P(A | B2)P(B2) +...+ P(A | BN)P(BN)
where B1, B2,...BN is a mutually exclusive and exhaustive set of outcomes.
