Quiz - C1 - Quantitative

Q 2.3 - Given a €1,000,000 investment for four years with a stated annual rate of 3% compounded continuously, the difference in its interest earnings compared with the same investment compounded daily is closest to: A. 1 B. 6 C. 455

Continuously = 1,000.000e^(.03 x 4) -1,000,000 = 127,496..85 Compounding N = 365 I/Y = .008 = 3/365 PV = -1,000,000 PMT = 0 FV = Solving for

QR 40 - The probability stock A ends the day with a price below $20 is 40%. The probability stock B ends the day with a price below $20 is 25%. The probability stock A ends the day with a price below $20 given stock B ends the day with price below $20 is 60%. Calculate the probability stock A or stock B ends the day with price below $20

QR 40 - = .40 + .25 (.40 from stock A and .25 from stock B) *Answer 1= .65* =.60(0.25) =.60 from both together and .25 from stock B Answer 2= .15 Final answer = .65 - .15 =.50

QR 41 - IF you flip a coin with a heads and tails 3 times, what is the probability of getting heads?

QR 41 - =.5 x (2 /(2 x 3)) =.5 from the two sides x (2 from two sides per flip / ( 2 from two side per flip 3 times)) =1/6

QR 5 -How do you find the FV for the following: N = 8 (bi-weekly) I/Y = 9.5% PV = 2,500 PMT = 0 A. $5,338.28 B. $5,338.29 C. $5,338.27

QR 5 - FV x (1+(rate/bi-weekly) ^n x bi-weekly 2500 x (1 + .095/26) ^ (8 x 26) = $5,338.29

QR 51 - Covariance matrix on expected returns on a portfolio with 3 securities is as follow: Asset A B C A 0.2 0.3 0.4 B 0.3 0.4 0.8 C 0.4 0.8 0.6 The weights for each asset on the portfolio are: Asset Weight A 0.5 B 0.4 C 0.1 The variance of expected return on the portfolio is closest to: A. 0.300 B. 0.321 C. 0.344

QR 51 - C. 0.344 = 0.5^2(0.2) + 0.4^2(0.4) + 0.1^2(0.6) + 2(0.5)(0.4)(0.3) + 2(0.4)(0.1)(0.8) + 2(0.5)(0.1)(0.4) =0.344

QR 52 - You are given the following potential stock price in a range of future scenarios: Environment P Stock A V B V Up 30% $40 $15 Middle 50% $32 $13 Down 20% $30 $5 Covariance between these two stock is closet to: A. 8 B. 10 C. 12

QR 52 - B. 10 E(A) = 0.3 x $40 + 0.5 x $32 + 0.2 x $30 =$34 E(B) = 0.3 x $15 + 0.5 x $13 + .2 x $5 =$12 Cov(A,B) = 0.3($40 - $34)($15 - $12) + 0.5($32 - $34)($13 - $12) + 0.2($30 - $34)($5 - $12) =10

QR 53 - Mitch is doing research on 2 assets. He found that the covariance of returns between asset A and asset B is 0.1 . In addition, he calculated the STD of returns to be 0.3 and 0.4 for return on asset A and asset B, respectively. The correlation of return between the two assets is closets to: A. 0.289 B. 0.833 C. 0.913

QR 53 - = 0.1 / 0.3 x 0.4 =0.833

QR 54 - You have settled on the following proper probabilities regarding drilling activity: P (Drilling activity is above normal) = 0.45 P(Drill activity is normal) = 0.30 P (Drill activity is below normal) = 0.25 You have also deduced the following conditional probabilities: P (Natural gas prices increase | Drilling activity is above normal) = 0.80 P (Natural gas prices increase | Drilling activity is normal) = 0.35 P (Natural gas prices increase | Drilling activity is below normal) = 0.10 Natural gas prices have increased substantially. Calculator the posterior probabilities relating to the drilling activity

QR 54 - First, P (Natural gas price increase) = 0.8(0.45) + 0.35(0.3) + 0.1(0.25) = 0.49 P (Drilling activity is above | Natural gas prices increase) = (0.8/ 0.49) x 0.45 =0.735 P (Drilling activity is normal | Natural gas price increase) = (0.35/0.49) x 0.3 = 0.214 P (Drilling activity is below normal | Natural gas price increase) = (0.10/0.49) x 0.25 = 0.051 Add the numbers up and it should alway equal 1 = 0.214 + 0.051 +0.735 =1

QR 55 - Calculate the following for a board with directors: 1. How many different ways is it possible to select a 4-member investment committee? 2. How many ways is it possible to choose a board chair, vice-chair and secretary? 3. How many ways is it possible to assign director to an 8-member compensation committee, a 7-member compile committee, and a 5-member audit committee?

QR 55 - 1. Use calculator 20 then 2nd + 4 =4,845 2. Use calculator 20 then 2nd - 3 = 6,840 3. Use calculator (x!) 20! / (8!)(7!)(5!) =99,768,240

QR 56 - FRS Corp. is considering issuing a $1,000 bond next month, depending on what happens to the interest rate. The probability that FRS Corp. will issue the bond, based on the change in the interest rate, is: Interest rate rises: 20% Interest rate remains the same: 40% Interest rate falls: 65% There is an equally likely chance that the interstate will rise, fall, or remain the same over the next month. Given that FRS Corp. issues a bond next month, the probability that the interest rate stays the same is closet to: A. 32% B. 40% C. 42%

QR 56 - First, define the possible events A = Interest rate rises B = Interest rate remains the same C = Interest rate falls X = FRS Corp. issues a bond The probabilities given in the problem are as follows: P(X | A) = 20% P(X | B) = 40% P(X | C) = 65% P(A) = 33.33% P(B) = 33.33% P(C) = 33.33% Formula = 33.33% x 40%/ P(X) P(X) = 0.2(.3333) + 0.3 (0.3333) + 0.65(0.3333) = .417 =.3333 x (0.4/.417) = 0.32

QR 57 - What is discrete uniform distribution?

QR 57 - It a simple why of giving equal probability to all the outcomes Dice roll 1 = 16.7% 2= 16.7% 3= 16.7% 4=16.7% 5= 16.7% 6=16.7% or 1/6

QR 58 - How do you calculate the cumulative sum of p(x) for a dice roll? What's the probability the outcome is 3 or less?

QR 58 - Roll 1= 16.7% Roll 2= 33.3% Roll 3= 50% Roll 4= 67% Roll 5= 83% Roll 6= 100% = 50%

QR 59 - A random variable with an infinite number of possible value can be classified as: A. A lognormal random variable only B. a continuous random variable only C. Either a continuous or a discrete random variable

QR 59 - C. Either a continuous or a discrete random variable

QR 6 - How to find Effective Annual Rate for a CD of 8% annual rate, inflation rate is 2% plus; 1. Quarterly 2. Monthly 3. Continuously

QR 6 - How to solve 1. 2nd > 2 (ICONV) 2. NOM = nominal interest rate 3. C/Y = n (year x times) 4. EFF the CPT 5. Clear the screen once to leave the menu 6. divided the number on the screen by 100 7. add 1 to the number 8. ^ of the number of years 9. x 1,000 1. $1,195.62 2. $1,196.68 3. $1,197.22

QR 60 - You are given the following distribution function for a discrete random variable: X = x p(x) F(x) 1 0.05 0.05 2 0.15 0.20 3 0.15 0.35 4 0.25 0.60 5 0.20 0.80 6 0.10 0.90 7 0.05 0.95 8 0.05 1.00 The probability that a random variable from the distribution is either greater than 7 or less than 3 is closet to: A. 35% B. 40% C. 25%

QR 60 - C. 25% 5% + 5% + 15% =25%

QR 61 - You are given the following cumulative distribution function fo a discrete random variable. X=x F(x) 1 0.20 2 0.50 3 0.70 4 0.80 5 1.00 The probability that a random variable from this distribution is greater than 1 and then 4 closet to: A. 30% B. 50% C. 60%

QR 61 - B. 50% 70% - 20% = 50% Don't count 20% Include 3 but not 4

QR 62 - A random variable Y has a continuous uniform distribution over the interval [0.1]. The probability of Y having a value between 0.1 and 0.5 is closet to: A. 30% B. 40% C. 50%

QR 62 - B. 40% 0.5 - 0.1 = 0.4 x 100 = 40%

QR 63 - At the end of the month, a stock will be worth between $0 and $128. There is an equally likely chance that the stock will take on any value in that range. The probability that the stocks month-end will fall outside a range of $40 to $65 is closet to: A. 20% B. 50% C. 80%

QR 63 - C. 80% please solve !

QR 64 - What is uniform distribution? (discrete & continuous) When you are rolling a dice 6-times

QR 64 - Discrete: 1. 16.7% 2. 16.7% 3. 16.7% 4. 16.7% 5. 16.7% 6. 16.7% Notes: No matter what you rolled last, the probability will stay the same Continuous: 1. 16.7% 2. 33.3% 3. 50% 4. 66.7% 5. 83.3% 6. 100% Notes: Every time you roll the dice your chances go up

QR 65 - Solving a simple continuous uniform probability problem when: Assuming a continuous uniform distribution between 3 and 8. Probability of being 5 or less P(x) = 5 a = 3 b = 8

QR 65 - = 5 - 3 /8 - 3 = .40 =40%

Q 32 - Probabilities are based on personal judgement then it's... A. Empirical B. Priori C. Subjective

Q 32 - C. Subjective

Q 33 - Probabilities are deduced using logic rather than observation. Both empirical and a priori probabilities are considered objective because they are typically the same for all people then... A. Priori B. Subjective C. Empirical

Q 33 - A. Priori

Q 34 - Probabilities are derived from relative frequencies from historical data. This only works if relationships are stable through time. It will not be useful for very rare events then... A. Subjective B. Empirical C. Priori

Q 34 - B. Empirical

Q 35 - Based on the universe of all possibilities. They can be thought of as stand-alone probabilities. Example: An investor could calculate the probability that the return is less than 8% A. Joint probability B. Unconditional probabilities C. Conditional probabilities

Q 35 - B. Unconditional

Q 36 - A probability that restriction on the set of possibilities. Example: An investor could calculator the probability that the return is less than 8% given it is positive. This is how incorporate new information A. Conditional probabilities B. Joint probability C. Unconditional probabilities

Q 36 - A. Conditional

Q 42 - Probability Return 0.15 -7% 0.45 6% 0.30 9% 0.10 14% Calculate the expected value and the variance of the return

Q 42 - i.e = P x return + P2 x return2 + etc =0.15(-0.07) + 0.45(0.06) + 0.3 (0.09) + 0.1 (0.14) = 5.75% repeat steps above but include the 5.75% in each line as a - at the end and square each one example part = 0.15 [-0.07 - 0.0575]^2 = 0.15[-0.1275]^2 + 0.45[0.0025]^2 + 0.3[0.0325]^2 + 0.1[0.0825]^2 = 0.24%

QR 25 - Solve the following dataset with a target downside of 3 using the sample target semi-deviation? 0 1 3 4 5 5

QR 25 - Look at any number equal to or less than the target for this example 0 1 3 Square root the following (first number in set under target - target) squared + (second number in set under target - target) squared + etc / n - 1 = Square root of (13/5) = 1.61

QR 26 - What are key points about normal distribution?

QR 26 - - Mean and median are equal -Percentage of the observation is fixed *1 STD 68% **2 STD 95% ***3 STD 99%

QR 27 - What is the difference between kurtosis and excess kurtosis? TEST

QR 27 - Kurtosis is with a K using 3 as the standard measure Excess Kurtosis is with Ke, uses 0 as its standard

QR 28 - How to find mean?

QR 28 - STD/mean or Square Root of Variance/mean IF this number is less than the median, its skewed left

QR 29 - Formalu for sample covariance

QR 29 - Sample covariance / STD of x * STD of y

QR 3 - Corporate bond is selling at $1,000 with an interest rate of 6%. The bond will mature in 3 years and will compound monthly. Their will be no payments made before maturity. What is the FV of this bond? A. $1,196.68 B. $1,196.67 C. $1,196.66

QR 3 - FV x (1+(rate/monthly) ^n x monthly 1,000 x (1 + .06/12) ^ (3 x 12) = $1,169.68

QR 37 - A probability that reflects the probability of two or more outcomes occurring A. Conditional probabilities B. Joint probability C. Unconditional probabilities

QR 37 - B. Joint probabilities

QR 38 - The probability mutual fund A earns a positive return in a given year is 65%. The probability that manual funds A and B both earn positive return in the same year is 20%. Calculate the probability mutual fund B earns a positive return, given mutual fund A earns a positive return?

QR 38 - 20% of both funds earning a positive return / 65% from group A being the baseline Answer = 31%

QR 39 - Addition rule for probabilities formula

QR 39 - = P(A) + P(B) - P(AB)

QR 4 - Solve for the future value of this bond, with the a maturity of three years and compounding quarterly. Interest rate on the bond will be 6% and the there will be no payments made before maturity. The current value of this bond will be $1,000. A. $1,195.60 B. $1,195.61 C. $1,195.62

QR 4 - FV x (1+(rate/quarterly) ^n x quarterly 1000 x (1 + .06/4) ^ (3 x 4) = $1,195.62

Q 43 - The current annual risk-free rate is 3.00%. A risky bond has a 5% chance of defaulting. If a default occurs, the bondholder will receive nothing. Calculate the required annual default risk premium that will make the expected return on the risky bond equal to the risk-free rate.

Q 43 - Assume $1 is invested in broth the risk-free and risky bonds. - risk-free bond will have a value of $1.03 at maturity - risk bond will have a value of $0 (with a 5% chance of going belly up) or $(1 + R) (with a 95% chance) R = represent the return of the risky bond 0.05 (0) + 0.95(1 + R) = 1.03 0 + .95 ( 1 + R) = 1.03 (1 + R) = 1.03 / .95 R = 8.42% D = 8.42% - 3% = 5.42%

Q 44 - You draw 2 marbles sequentially from an urn containing 5 red marbles and 5 black marble. The probability of drawing a red marble and a black marble is closest to: A. 56% B. 50% C. 28%

Q 44 - A. 56% = 5/9 x 5/10 =25/90 =27.8% per marble =56 for both

Q 45 - The odds of rolling a 4 on six-sided die are most likely: A. 1 to 6 B. 1 to 5 C. 5 to 1

Q 45 - A. 1 to 5 = 1/6 / 1 - 1/6 = 1/6 / 5/6 = 1 / 5 Key cross out the similar numbers at the bottom that match

Q 46 - You are given the following: P(B) = 40% P (A | B) = 20% P (A | B^C) = 70% A. 40% B. 45% C. 50%

Q 46 - =1 - 40% = 60% = 20% x 40% + 70% x 60% =50%

QR 20 - So if you collect the sample values and want to use the compounding returns, what will you do?

QR 20 - Geometric mean RAD # ((1 + rate of return)(1 + rate of return 2)(1 + rate of return 3)) - 1

QR 21 - How do you find the interquartile range? (IQR)

QR 21 - IQR = Q3 - Q1

QR 22 - How do you find what percentile you fell into?

QR 22 - (n + 1) * y/100 n = count of the total number of numbers y = percentile

QR 23 - Find the third quartile and 67th percentile? 0 0 0 1 3 4 6 9 12 12 13 14 17 20 25 27 30 32 37 38

QR 23 - Third quartile: (20 + 1) * 75/100 67th : (20 + 1) * 67/100

QR 24 - How do you find the mean absolute deviation (MAD), sample mean and sample variance? 0 1 3 4 5 5

QR 24 - First find the sample mean for the dataset x = 0+1+3+4+5+5/6 = 3 MAD = (first number in set - sample mean) + (second number in set - sample mean) + etc.. ALL divided by/ Sample mean MAD = (0-3)+(1-3)+(3-3)+4-3)+5-3)+(5-3)/6 = 1.67 Sample variance = repeat MAD but square the top groups and - 1 from sample mean = 4.4 =Square Root 4.4 Sample variance = 2.10

Q 30 - The return on a risky asset is ______ because the outcomes are uncertain A. Consist variable B. Semi-random variable C. Random variable D. Uncertain variable

Q 30 - C. Random as the outcomes are uncertain

Q 31 - IF an event is impossoble then its probability of is ____ ? A. 0 B. -1 C. 1

Q 31 - A. 0

Q 11 - A company is able to borrow over 5 years at a 5.7% interest rate. If the nominal risk-free rate is 4% and lenders require premiums of 1% for inflation, 0.8% for liquify and 0.4% for maturity, the compensation for possibility that the company does no repay the loan is closet to? A. 0.5% B. 3.5% C. 4.5%t

Q 11 - A. 0.5% 5.7% - 4% - 0.8% - 0.4% = 0.5% Interest rate - nominal risk-free rate - liquidity - maturity = answer

Q 12 - You own a property that will pay you $200 starting 6 years from now, calculator the PV with a discount rate of 4%?

Q 12 - You own a property that will pay you $200 starting 6 years from now, calculator the PV with a discount rate of 4%?

Q 19 - Calculate all the marital frequencies 2. Construct a contingency table with relative frequencies based on total count 3. Construct a contingency table with relative frequencies based on risk level Domestic Fund Low Risk 65 Domestic Fund High Risk 51 International Fund Low Risk 38 International Fund High Risk 46

Q 19 - Domestic: 65+51 = 116 International: 38+46=84 Last row Domestic: 116 International: 84 Total count: 200 2. Covert all of those numbers into % by dividing each number by 200 3. Compare the low risk with the low risk and the high risk with the high risk Domestic Fund low risk: 63.1% International Fund low risk: 100%-63.1% = 36.9% etc...

Q 47 - A stock is currently trading for $30. An analyst estimate that, if the economy expands, a stock's price has a 30$ chance of reaching $40 and a 70% chance of trading at its current level. Alternatively. if the economy contracts, there is a 60% chance that the stock price will be unchanged and a 40% likelihood that it will fall to $20. If the likelihood that the economy expand is 40% and the probability of a economic contraction is 60%, the stock is most likely: A. trading below its expected value B. trading above its expected value of $28.80 C. trading above its expected value of $29.50

Q 47 - B. trading above its expected value of $28.80 Expansion solve = 0.3 x $40 + .7 x $30 = $33 Contraction = 0.6 x $30 + 0.4 x $20 = $26 = $33 + $26 / 2 =$59/2 =$28.80

Q 48 - A stock is currently trading for $30. An analyst estimates that, if the economy expands, a stock's price has a 30% chance of reaching $40 and a 70% chance trading at its current level. Alternatively, if the economy contracts, there is a 60% chance that the stock's price will be unchanged and a 40% and the probability of an economic contraction is 60%, the conditional variance given an economic expansion is closest to: A. 8 B. 21 C. 23

Q 48 - B. 21 Expansion = 0.3 x $40 + 0.7 x $30 = $33 Price | Expansion = 0.3 x ($4 - $33)^2 + 0.7 x ($30 - $33)^2 = 21

Q 49 - The odds that the value of Corporations A's stock will increase by tomorrow are 3 to 1, while the odds that Corporation B will announce a stick spilt tomorrow are 2 to 5. If the two events are dependent on what is the probability that Corporation A's stock will increase by tomorrow and that Corporation B will announce a stock split? A. 0.13 B. 0.21 C. 0.82

Q 49 - P(X) = 3 / (3 + 1) = 3/4 P (Y) = 2 / (2 + 5)= 2/7 P(X)P(Y) = (3/4)(2/7) = 3/14 = 0.2143

Q 50 - The expected return is 20% for security A and 12% for security B. The STD is 34% for security A and 17% for security B. The correlation coefficient for security A and B is 0.57. You have decided to invest 70% in security A and 30% in security B. Calculate the portfolio expected return and STD?

Q 50 - = 0.7(0.2) + .3(0.12) = 17.6% = 0.7^2(0.34)^2 + 0.3^2(0.17)^2 + 2(0.7)(0.3)(0.57)(.34)(0.17) =0.0731 =Square root 0.0731 =27%

Q1 - Which of the following is least likely to be included in the portion of a corporate bond's yield that reflects investors' time preferences for current versus future nominal consumption? A. Inflation premiums B. Liquidity premiums C. Real risk-free rate

Q1 B. Why? Investors' time preferences for current versus future real consumption are captured by the real risk-free rate. Adding an inflation premium produces a rate that reflects the tradeoff between current and future consumption in nominal terms. The liquidity premium component of a corporate bond's yield reflects compensation for the discount to market value that investors expect to incur in order to quickly convert their position into cash. By contrast, newly-issued government securities typically do not carry a liquidity premium due to the large number of investors who are active in the government bond market and are willing to pay the current market value.

Q2 - A company is able to borrow over 5 years at a 5.7% interest rate. If the nominal risk-free rate is 4% and lenders require premiums of 1% for inflation, 0.8% for liquidity, and 0.4% for maturity, the compensation for the possibility that the company does not repay the loan is closest to? A. 0.5% B. 3.5% C. 4.5%

Q2 A. Interest rate for longer - nominal risk-free -

Q2.1 - Investor A deposits $10,000 into an account earning 7% simple interest, while Investor B deposits $10,000 into an account earning 5.5% interest compounded annually. Assuming that all interest earned is kept in the accounts and no additional funds are deposited, the difference in the value of these accounts after 12 years is closest to: A. $610 B. $1,800 C. $3,510

Q2.1 Simple interest amount 10,000 x (1 + (7% X 12)) = 18,400 Compounding 10,000 x (1 + 5.5)^12) = 19,012 = 612

Q2.2 - An investment of $1,000 into a savings account earns a 6% stated annual rate compounded monthly for 2 years. The effective annual rate is closest to: A. 6.00% B. 6.17% C. 6.20%

Q2.2 (1 + 6%/12)^12 - 1 = 6.17

QR 1.1 - An investor gather the following information to determine how much they should get back on their money 1-year govmnt 3.0% 1-year crop 4.2% 10-govmnt 3.8% If the investor needs a return with the liquid of 0.5%, how much do they need? A. 4.2% B. 5.0% C. 4.3%

QR 1.1 B. Step 1 - Find the maturity rate of the bonds 3.8% - 3.0% = 0.8% Maturity Step 2 - Find the default risk 4.2% - 3.0% = 1.2% 1.2% - 0.5% = 0.7% default risk Step 3 - rf 3.0% rf + M + L + D = return rate 3.0% + 0.8% + 0.5% + 0.7% = 5.0%

QR 10 - How to find out how long it will take to double your investment? Interest rate: 5%

QR 10 - N: Solving I/Y: 5 PV: -1 PMT: 0 FV: 2 <-- this is because we requested to find out how long it would take to double the investment Answer: 14.21

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QR 13 - How do you find FV of a continuous compounding bond?

QR 13 - Interest rate x number of years (x monthly.. etc) = answer then 2nd & LN = answer 2 Answer 2 x principle

QR 14 - How to change your calculator from Begin to End of year payments?

QR 14 - 1. 2nd then PMT 2. 2nd Enter

QR 15 - What is the dataset shown below? Year P/E for Company X P/E for Company Y 1 18.31% 12.59% 2 X X 3 X X 4 X X

QR 15 - Cross-sectional dataset because it only uses the first row of data and does not show the data set over multiple years

QR 16 - What is the dataset shown below? Year P/E for Company X P/E for Company Y 1 X 12.59% 2 X 9.83% 3 X 6.91% 4 X 10.11%

QR 16 - Time-series dataset because it shows the data for one company over a period of time. Instead of over one year

QR 17 - What is the dataset shown below? Year P/E for Company X P/E for Company Y 1 13.56% 12.59% 2 7.84% 9.83% 3 7.01% 6.91% 4 9.43% 10.11%

QR 17 - Panel data is combination of time-series and cross-sectional data sets. This dataset shows data for multiple companies over many years.

QR 18 - Create a frequency distribution of the returns given below; Interval will be 5 (this is chosen by me and will be how many sub-ranges I will have in my table) -36% -24% 0% 15% 20% 28% 34% 37% 39% 44%

QR 18 - Step 1: Max - min 44% - (-36%) = 80% Step 2: 80%/5 = 16% 16% this will be the interval-width for the data set, which means the first set would "-36% to -20%", "-20% to -4%", "-4% to 12%", "12% to 28%, "28% to 44%"

QR 66 - A binomial distribution is used to model price changes for a particle stock. The following parameter are used: - Initial stock price: $10 - Probability of an up move for the stock per period: 60% - During an up move, the stock price increase by 1% - During a down move, the stock price decrease by 1% - Number of periods: 10 Calculate the probability the stock price after 10 period will exceed $10.80

QR 66 - S = $10.80 u = 1.01 d = 0.99 = 10((1.01)^8) x ((0.99)^2) = 10.61 < 10.80 = This means with 8 upwards moves we still did not hit the stock price goal set =10((1.01)^9) x ((0.99)^1) =10.83 > 10.80 = This means if we move upwards on 9 out the 10 we will hit the stock prices goal P(X = 9) = (10 9)(0.60)^9(1-.60)^(10-9) =(10! / (10 - 9)!9!) x ((0.60)^10) x (0.40)^1 = 0.0403 =(10 10) (0.60)^10 ((1-.60)^ 10-10) = (10!/ (10 - 10) !10!) x ((0.60)^10) x ((0.40)^0) = .006 Probability = (P x = 9) + (P x = 10) Probability = .0403 + .006

QR 67 - An analyst is pricing a stock using a five-step binomial model with annual nodes. The probability of the stock price moving upwards in any given year is 60%. The probability that the stock price will move downward at most 1 time over the next 5 years is closet to: A. 0.207 B. 0.259 C. 0.337

QR 67 - =(5 1) x (0.4^1) x (0.6^4) + ( 5 0) x (0.4^0) x (0.6^5) = 0.2592 + 0.07776 =0.33696

QR 68 - A non-dividend paying stock registered the following year-end prices: 31 December 20X1 $1,065 31 December 20X2 $1,.001 31 December 20X3 $1,213 31 December 20X4 $1,684 The mean continuous compounded annual return for the stock is closet to: A. 15.3% B. 17.3% C. 19.4%

QR 68 - r 0,1 = ln (1,001 / 1,065) = -0.0620 r 1,2 = ln (1,213/1,001) = 0.1921 r 2,3 = ln (1,684 / 1,213) = 0.3281 = (-0.620 + 0.1921 + 0.3281) /3 = 15.27%

QR 69 - Which of the following statement is least likely accurate concerning both the chi-square and F-distributions? A. Both distribution are asymmetric B. Neither distribution allows for negative value C. F-distribution is expressed as the sum of two chi-squared distributions

QR 69 - C. F-distribution is expressed as the sum of two chi-squared distributions

QR 7 - How to calculate the PV of a perpetuity if the first payment is made at year 6? Interest Rate: 4% N: 6 PMT: $200

QR 7 - Step 1: Present value the CF = PMT/Rate Step 2: Use this number as the FV for problem two Step 3: Plug in the correct numbers and discount back at n - 1 N: 5 Y/I: 4 PV: Solving PMT: 0 FV: 5,000 (200/.04) Answer: - $4,109.64

QR 70 - Compared to Monte Carlo simulation, which of the following is most likely to be cited as an advantage of the Black-Scholes-Merton (BSM) option pricing model? A. BSM model can be used to value any European-style option B. BSM model is more efficient for pricing European-style options C. Monte Carlo simulation cannot be used to value newer, more complex options

QR 70 - B. BSM model is more efficient for pricing European-style option

QR 71 - You have invested in a portfolio with a mean return of 8% and standard deviation of 17% per year. Assume that returns are normally distributed. Calculate: 1. Probability the return will be positive for a given year. 2. Probability the return will be between 10% and 20% EXAM

QR 71 - 1. Z = (0 - 8)/ 17 = - 0.47 P(Z >= -0.47) = P(Z <= 0.47) ^had to change the sign so we had to change the greater than to less than = 68.08% (There will be a table on the exam and you will look at the .4 and then .07 to find this) 2. 10% & 20% Z1 = (10 - 8)/ 17 = 0.12 Z2 = (20 -8)/ 17 = 0.71 =P(Z<= 0.71) + P(Z<= 0.12) = 0.7611 - 0.5478 =21.33%

QR 72 - You portfolio is currently worth $400,000. At the end of one year, you want to have at least $420,000. The expected return is 10%, and the standard deviation is 14% annually/ Calculate the probability the portfolio will not grow to at least $420,000?

QR 72 - Rl = 20,000 / 400,000 = 5% SFRation = (10% - 5%)/ 14% =.36 = 1 - (N x .36) = 1 - 64.1% = 35.94% (from chart on exam)

QR 73 - If you want to find the continuously compounded return from t to t Example: Stock price today: $100 Stock price tomorrow: $105

QR 73 - = ln(100 / 105) =0.0488 or if given rate than use todays price x e^0.0488 =100 x 1.05 = 105

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QR 8 - Find the interest rate on this investment; Year 0 bought a stock for $300 Year 4 sold the stock for $500

QR 8 - N: 4 Y/I: Solving PV: -300 PMT: 0 FV: 500 Answer: 13.62%

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