FRM Part - I Test Paper

FRM Part – I Test

Time - 2 hours ; Number of question = 50

1. A multifactor Arbitrage Pricing model is known to have two independent economic factors, F1 and F2. The risk-free

rate of return is 7.5%. Two well-diversified portfolios have the following information available:

Portfolio β on F1 β on F2 Expected Return

A 1.5 2.5 25%

B 2.0 4.0 35%

Assuming no arbitrage opportunities exist, the risk premium on the factor portfolios should be: A. F1 = 1.25% , F2 = 7.25%

B. F1 = 1.25% , F2 = 6.25%

C. F1 = 6.25% , F2 = 7.25%

D. F1 = 6.25% , F2 = 1.25%

2. Suppose that the Treasury bond futures price is 105-14. Which of the following four bonds is cheapest to deliver?

A. Price = 141-18, Conversion Factor = 1.3148 B. Price = 126-28, Conversion Factor = 1.1734 C. Price = 119-07, Conversion Factor = 1.1153 D. Price = 135-11, Conversion Factor = 1.2642

3. Ross is an investment banker at SeaShore Inc. His portfolio consists of various calls and puts option contracts. At the

moment, he is worried about the increase in the interest rate recently announced by the Federal Bank. Which of the following is likely to increase the most with the change in interest rate?

A. In the money put option B. Out of the money put option C. In the money call option D. Out of the money call option

4. A simple regression model was determined to have the following equation: Y = a + bX + e. The correlation between X

and Y is known to be 0.75. The value of a is 3, b is 2, Std (X) = 2.5. The value of Std(e) is A. 4.01

B. 4.41 C. 5.15 D. 4.75

5. In a Treasury bond futures contract, it is known that the cheapest-to-deliver bond will be a 10% coupon bond with a

conversion factor of 1.2458. Also that it is known that delivery will take place in 270 days. Coupons are payable semi-annually on the bond. The last coupon date was 50 days ago, the next coupon date is in 132 days, and the coupon date thereafter is in 315 days. The term structure is flat and the rate of interest (with continuous compounding) is 8% per annum. Assume that the current quoted bond price is $135. Then what would be the quoted futures bond price?

A. $108.97 B. $113.35 C. $122.74 D. $117.18

6. A stock price is currently $35. It is known that at the end of two months it will be either $33 or $39. The risk-free interest

rate is 10% per annum with continuous compounding. Suppose ST is the stock price at the end of two months and X is

the strike price which is $36. What is the value of a derivative that pays off ST2 - √X at this time?

A. $1284.4 B. $1269.4 C. $1204.8 D. $1248.4

7. The variance of the market portfolio is known to be 0.20, i.e. σm2 = 0.20.

Which of the following is/are true?

I. A stock which has a variance of 0.05 gives lower returns than the market

II. A stock which has a variance of 0.3 and gives the same return as the market, has a beta greater than 1 III. A stock which has a variance of 0.27 gives a return more than the market

IV. A stock which gives the same return as the market, has a variance greater than or equal to 0.20 A. I only

B. I, II, III and IV C. I, II and IV D. I and IV

8. A trader hedges the price risk of his commodity with a grain futures contract. The standard deviation of the commodity

futures price is 2.28% while the standard deviation of the spot price on the same commodity is 2.93%. The standard deviation of the difference the spot price and futures price is 1.52%. The hedge effectiveness measure from using this commodity futures contract is closest to:

A. 0.73 B. 0.87 C. 0.83 D. 0.78

9. A non dividend paying stock with volatility of 20% per annum is currently trading at $50. A European call option on the

stock with a strike price of $49 has a time to maturity of 5 months. The risk free rate is 6%. Given that N(0.42) = 0.6627, N(0.41) = 0.6590, N(0.28) = .6102, N(0.29) = .6140, N(0.62) = .7323 and N(0.63) = 0.7356, the price of the option is

A. $3.78 B. $4.28 C. $3.44 D. $3.14

10. Which of the following is/are correct about linear regression?

I. When the variance of residuals is the same across all observations in the sample, homoscedasticity occurs II. Multicollinearity occurs when a high correlation exists between the dependent variable and two or more

independent variables

III. Conditional heteroscedasticity leads to problems with both inference and estimation IV. Error terms are assumed to be heteroscedastic

A. I and II B. I and III C. I, II, III and IV D. III only

11. Which one of the following is true from the following?

A. Treynor Ratio is used to rank the portfolio with the different level of risk of a well-diversified portfolio and it only takes the unsystematic risk of the portfolio into account.

B. Sharpe Ratio is used to rank the portfolio with the different level of risk of a well-diversified portfolio and it only takes the systematic risk of the portfolio into account.

C. Information Ratio is used to measure the residual return of the portfolio compared with its residual risk. D. Jensen Alpha is used to rank the portfolio with the different level of Beta and thus used to measure the

12. In the 1995, Mexican government developed different type of bonds in which the amount received by the holder at

maturity varies with a foreign exchange rate. There was a trade with the Long Term Credit Bank of Australia. The bond specified that if the aus-US dollar exchange rate, X, is greater than 78 aus per dollar at maturity (in 2010), the holder of the bond receives $500. If it is less than 78 aus per dollar, the amount received by the holder of the bond is 500 – max[0, 500(78/X – 1)]. When the exchange rate is below 35.4, nothing is received by the holder at maturity. Then the bond is combination of

A. Regular bond and one option B. Regular bond and two options C. Regular bond and one future D. Regular bond and two futures

13. The transition matrix of a PiSquare Ratings Agency is given below. What is the probability that a C rated firm today will

default only in the 3rd year from now.

Rating From Rating To

A B C Default A 90 5 5 0% B 5 80 7 8 C 0 7 80 13 A. 9.27% B. 8.35% C. 8.97% D. 9.62%

14. Ed has recently carried out a survey of consumer habits in Singapore and Malaysia. He wants to check whether the

variances of the survey results in a particular country are significantly different or not. To check this, he plans to uses F-statistic which is the ratio of the variances of the collected sample. Which of the following is/are correct:

I. F- distribution is left skewed

II. Null hypothesis is that the variance of the two country’s results is different III. F(α, s12, s22)=1/F(1 - α, s22,s12)

A. I only B. I, II and III C. II and III D. III only

15. Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.80, the standard deviation of

quarterly changes in a futures price on the commodity is $0.95, and the co-efficient of correlation between the two changes is 0.75. What is the optimal hedge ratio for a 3-month contract?

A. 0.853 B. 0.632 C. 0.358 D. 0.562

16. Two countries A and B have recently announced suspensions on their outstanding loans. Country A has suspended only

interest payments while Country B has suspended both interest as well as principal payments. A Country Risk Analysis (CRA) model uses current data and the results from electoral polls, and is constantly updated. Which of the following problem is it most likely to suffer from?

A. Timing or forecasting problems B. Stability

C. Population grouping D. Political risks

17. An Investor has obtained the following information on his portfolio which is well-diversified.

 Beta: 1.12

 Standard deviation of Market: 10.2%

 Treynor Ratio = 1.5

Calculate the Sharpe Ratio for the given Portfolio? A. 0.542

B. 0.147 C. 1.345 D. 1.192

18. The following table gives the data on monthly changes in the spot price and the future price for a certain commodity. Use

the data to calculate a minimum variance hedge ratio. Correlation of the spot price change and future price change is 0.94.

Spot Price Change 0.45 -0.32 -0.64 0.37 0.52

Future Price Change 0.35 -0.04 -0.23 0.12 0.21 A. 3.18

B. 1.46 C. 2.22 D. 0.654

19. Suppose the rate on 1-year zero-coupon corporate bonds is 16.3% and the implied probability of default is 5.87%.

Assume Loss Given default is 100%. Then, 1-year T-bill rate is closest to: A. 8.63%

B. 9.47% C. 10.17% D. 7.51%

20. Which of the following statements regarding hypothesis testing is/are true?

I. If the significance level is more than the p-value, the null hypothesis is rejected II. A decrease in the level of type I error causes a decrease in Type II error as well III. Type I error is the error when a false null hypothesis is not rejected

IV. Systematic error is caused by non-random variations due to unknown sources A. I only

B. I and IV C. I and III D. I, II and IV

21. The firm with risk management is appropriate in the following case EXCEPT

A. Present value of bankruptcy cost is less than Present value of the incremental cash flow through risk management program

B. Present value of the reduction in the cost of the financial distress is greater than Present value of the risk management program

C. Present value of the incremental tax-shield from debt through the risk management program is less than cost of the financial distress

D. None of the above

22. A company has a $11 million portfolio with a beta of 1.5. It would like to use futures contracts on the NASDAQ to

hedge its risk. The index futures price is currently standing at 1100, and each contract is for delivery of $500 times the index. What should company do if it wants to increase the beta of the portfolio to 2.0?

A. A short position in 10 contracts B. A long position in 10 contracts C. A short position in 20 contracts D. A long position in 20 contracts

23. Consider the following portfolio of the bonds. Then, what is the value of the portfolio’s DVBP (Dollar Value per Basis

Point)?

Bond Price Par Amount Modified Duration

X 114.24 $5000 4.27 Y 89.71 $6000 5.39 Z 127.37 $9000 8.54 A. 15.13 B. 13.75 C. 17.32

D. None of the above

24. A box contains four types of marbles with different colours. There are 5 Red, 7 Yellow, 12 Blue and 8 Green marbles.

Person P picks one marble at a time and places it outside. What is the minimum number of attempts required to get at least 1 red marble and 1 green marble definitely out of the box?

A. 21 B. 28 C. 27 D. 24

25. Kumar holds an American call contract on a stock Y, which is a dividend paying stock. The option has an expiry time

period of 6 months. Today, 5th March, the stock is trading at $105 and the strike price is $100. A dividend of $2.5 is expected 3 months later with the ex-dividend date being 5th June. Assume that the risk free rate of return compounded continuously is 5% per annum. Kumar can

A. Exercise the option on 4th June B. Exercise the option at expiry date C. Exercise the option today D. Exercise the option on 5th June

26. Suppose ABC bank finalised the loan with the following characteristics: Total commitments of $4,000,000, of which

$2,300,000 is currently out standings. The bank has assessed an internal credit rating equivalent to a 1.5% default probability over the next year. Draw down upon default is assumed to be 68%. The bank has additionally estimated a 30% loss given default. Then what will be the expected loss?

A. $14538 B. $15552 C. $17346

D. None of the above

27. The correlations of returns among the various indices for last 5 yrs were presented in table below. Use the table to select

the correct statement(s)

Nifty Hang-seng Straits Times Nikkei 225 Shanghai Comp. Nifty 1.00

Hang-seng (HS) 0.22 1.00

Straits Times (ST) 0.03 0.25 1.00

Nikkei 225 0.04 0.13 0.26 1.00

Shanghai Comp. (SC) 0.02 0.02 -0.01 0.12 1.00 A. The variation in Nifty is explained 22.00 % by variation in Hang-seng (HS) index. B. The variation in Nifty is explained 78.00 % by variation in Hang-seng (HS) index. C. The variation in Nifty is explained 48.40 % by variation in Hang-seng (HS) index. D. The variation in Nifty is explained 04.84 % by variation in Hang-seng (HS) index

28. Harold is an avid investor and regularly invests in options and futures. He is planning to create a Calendar spread using

A: Call option at strike price 5000, maturity = 6 months B: Call option at strike price 5200, maturity = 3 months C: Call option at strike price 5000, maturity = 3 months D: Call option at strike price 5250, maturity = 3 months E: Put option at strike price 5000, maturity = 6 months Which of the following will allow Harold to create a Calendar spread?

A. Buy A, Sell C B. Buy C, Sell A C. Buy C, Sell B D. Buy E, Sell C

29. Which one of the following statements is false?

A. Rating agencies require issuing short-term ratings rather than long term ratings.

B. With the help of credit ratings, it is possible to determine risk weightings for capital requirements. C. In solicited ratings, a ratings agency will assign ratings without a request from the issuer.

D. Securities rated as investment grade sometimes receive ratings downgrades into the speculative ratings category.

30. An investor is holding a portfolio of 10 BBB-rated bonds. The probability that a bond will be defaulted is 0.25. The

default between the bonds is independent. What is the probability that at least 4 bonds will not be defaulted? A. 0.2241

B. 0.3478 C. 0.7759 D. 0.6522

31. Your Board of Directors wants a comprehensive review of each business units’ operational risk activities. As the head of

the corporate operational risk unit, you know that little has been done to implement an operational risk process at the business unit level and that you need to immediately come up with a framework. Which of the following statements offers the best strategy?

I. The audit committee of the Board should first define its objectives to ensure that all the firm’s business units’ operational risk programs are providing required information

II. The auditing department is to be charged with developing an operational risk program for each business unit, with the business unit being made clearly aware that they will be held accountable for its

implementation

III. That your department immediately assess the operational risk for each business unit using independent data feeds to ensure the information fed into the assessment cannot be manipulated

IV. A senior manager from each profit center is to be charged with developing their own operational risk self assessment program based on guidelines you provide.

A. I only B. I and IV only C. I and III only D. IV only

32. Brown, an avid investor has created a peculiar spread as shown below using call options. Assume that the horizontal

lines have a slope of 0 and the slanted lines have a slope of +1 or -1. The call prices are as given below:

The values of P1, P2 and P3 respectively are:

A. $0, $5,$10 B. $0,$10,$15 C. $5,$10,$15 D. $5,$7,$10

33. Suppose a bank has finalised the loan with the following characteristics: Total commitments of $8,700,000, of which

$4,200,000 is currently out standings. The bank has assessed an internal credit rating equivalent to a 1.8% default probability over the next year. Draw down upon default is assumed to be 71%. The bank has additionally estimated a 67% recovery rate. Then what will be the expected loss?

A. $51562 B. $45927 C. $36248 D. $43926

34. Which of the following statement is true for the continuous uniform distribution?

A. The probability that a uniformly distributed random variable falls within any interval of fixed length is dependent of the location of the interval.

B. The skewness of the uniform distribution is 1.

C. The variance of the uniform distribution is equal to (b – a)/12 D. None of these

35. A certain contract (future/forward) closed at $5500 on Friday evening, and trades at both exchange and OTC. Two

parties enter into the agreement (@ $5500, just before the close) to buy and sell on exchange (Initial Margin: 5% of the price traded) and two other parties enter into the agreement (@ $5500, just before the close) on OTC (No

collateral/margin). Consider the following two scenarios:

I. Market opened @ $5250 in the morning

II. Market opened @ $5050 in the morning

Which of the following is correct regarding these two scenarios?

A. In the case of the trade on exchange, there is no credit risk in both scenarios, as on exchange there is no counterparty risk. But in case of OTC, there is counterparty risk in both scenarios

B. There is no credit risk on OTC or Exchange in both scenarios

C. There is credit risk on both OTC and Exchange in scenario II and no credit risk in scenario I on both OTC and Exchange

D. On Exchange, there is credit risk in scenario II and no credit risk in scenario I, but on OTC there is credit risk in both scenarios

Strike Price Call Price

$50 $10 $60 $9 $65 $8 $70 $7.5 $75 $7.26 $80 $7 $85 $6 $90 $5.5 $95 $5

36. Suppose a bank finalised the loan with the following characteristics: Total commitments of $6,600,000, of which

$3,900,000 is currently out standings. The bank has assessed an internal credit rating equivalent to a 1.4% default probability over the next year. Draw down upon default is assumed to be 74%. The bank has additionally estimated a 32% loss given default. The standard deviation of EDF and LGD is 6% and 22%, respectively. Then what will be the unexpected loss to the bank?

A. $190,774 B. $235,563 C. $273,462 D. $285,926

37. Long-Term Capital Management (LTCM), incorporated in early 1994, grew enormously in the first few years of its

existence. Which of the following is true about LTCM?

I. LTCM’s possibility of insolvency before convergence of credit spread was similar to the funding liquidity risk in the Metallgesellschaft case

II. Revaluation of its currency by Brazil led to even more losses in LTCM’s equity volatility strategies III. Russia’s unexpected debt default triggered investor concern about ailing economies in the Pacific rim IV. LTCM’s diversification strategy protected them from the market risk to a great extent.

A. I only B. II and IV C. III and IV D. I and III

38. Which of the following is correct:

A. Daily Mark to Market is done for all securities on both OTC and Exchanges B. Daily Mark to Market is done for all securities on Exchanges

C. Daily Mark to Market is done for only large and liquid enough securities on both OTC and Exchanges D. Daily Mark to Market is done for only large and liquid enough securities on Exchanges

39. Tina’s portfolio has a large (negative) theta. She is planning to add a call option on a non dividend paying stock to her

portfolio. She doesn’t want the new option to change the overall theta of her portfolio by a large extent. The 6-month call options which she is considering have a time to maturity of 1 month. The current stock price is $105. Which of the following options should she buy?

A. Call option with Strike price = $105 B. Call option with Strike price = $100 C. Call option with Strike price = $115 D. Call option with Strike price = $110

40. Which one of the following properties holds true for kurtosis?

A. Kurtosis refers to the extent to which a distribution is not symmetrical.

B. Leptokurtic describes a distribution that is less peaked than a normal distribution. C. For a normal distribution, excess kurtosis is equal to 1.

D. Platykurtic distribution will have excess kurtosis less than 0.

41. Jill Bunter, FRM is a relationship manager at a multinational bank. As part of his duties, he manages portfolios for

several clients of the bank. One of the clients is Steve, who is the CEO of the company DiGamma Inc. which is listed on the NYSE. Steve informs Jill of a new product that they are planning to launch in the next quarter. Later, Jill mails his other clients advising them to go long on the DiGamma Inc’s stock, based on Steve’s inputs. Which of the following is most likely correct?

A. Jill violated the Code by failing to failing to maintain the confidentiality of his clients information B. Jill did not violate the Code as he recommended an investment which would be profitable to his clients C. Jill violated the Code by recommending an investment which would not be suitable for all of his clients D. Jill violated the Code by not properly identifying the features of the product which could make its launch a

42. Consider the following statements:

I. Stop-loss orders are used only to limit losses

II. There can be a chance that ‘limit orders’, ‘stop-loss’ orders & ‘market if touched’ orders may never be executed

III. A discretionary order is to buy or sell at the best price available

IV. Basis trade is to buy the contract when future price is equal to spot price Which of the following is correct?

A. II only B. I, II and IV C. I and IV D. I and III

43. Company A is using Top-Down approach and Company B is using Bottom-Up approach for the measurement of their

operational risk. Then which of the following statements hold true?

I. The company B is using Intensive data for their operational risk measurement. II. The company B doesn’t distinguish between HFLS and LFHS events.

III. It is possible for Company A to model the effects of new operational risk controls. IV. Company A is using Specific operational procedures for the operational risk measurement. V. Approach of company B is complex whereas that of the company A is simple.

A. I, II and IV only B. II and V only C. III and IV only D. I and V only

44. As you know generalized autoregressive heteroskedastic (GARCH) estimation model weights new information more

heavily than the old information. Which of the following GARCH models will show the fastest reversion to mean? A. Ht=0.1+0.09 r2t-1+0.89 ht-1

B. Ht=0.07+0.08 r2t-1+0.80 ht-1

C. Ht=0.08+0.07 r2t-1+0.92 ht-1

D. Ht=0.1+0.05 r2t-1+0.80 ht-1

45. Consider the following two statements:

I. A foreign exchange trader who is hedging a long spot position with a short forward position doesn’t have

basis risk

II. After hedging corporate bond with Treasuries, there is only one risk left i.e. spread risk between treasury yield and corporate yield

Which of the following options are correct: A. I is correct

B. II is correct C. Both are correct D. None is correct

46. The following factors of economic strength are established by the S&P in order to determine a Sovereign entity’s ability

to pay EXCEPT

A. Fiscal flexibility B. External debt burden C. Inflation flexibility D. Contingent liabilities

47. Using strategies that reduce fixed costs to decrease firm systematic risk

A. Will always decrease firm value B. Will always increase firm value

C. Will reduce only diversifiable risk

D. Can increase firm value if the costs are low enough

48. Use the following data to answer the questions.

HFGC bank issues $30 million in US Certificate of Depositories to fund its loan portfolio. The following characteristics pertain to asset-liability position of the bank.

 A promised 1-year rate on the CD’s of 8.5%.

 It invests 50% of its $30 million in 1-year Japan loans at 14% (loans made in yen).

 The bank invests the other 50% in US loans at 10% for the year.

 At the beginning of the year, the bank sells $15 million for yen in the spot currency markets at an exchange rate of $0.4/yen.

 The 1 year forward exchange rate is $0.38/yen.

If the exchange rate falls to $0.36/yen, then what is the weighted return on the bank’s asset portfolio? A. 5.6%

B. 7.9% C. 5.8% D. 6.3%

49. For a $ 10 million portfolio of XY Inc with some positive expected return has the following 3 assets:

I. Liquid Bonds worth $500,000

II. Equity worth $300,000

III. Convertible bonds worth $200,000

Monthly volatility of the portfolio P is 13%. Calculate the daily VAR of the portfolio P at 5% significance. Assume 30 business days in a month.

A. $ 39,162 B. $ 214,500 C. $ 46,994

D. Can’t be determined with the information provided

50. Security A offers a return of 12% and has a standard deviation of 11%. Security B has a standard deviation of 13% with

a return of 17%. What is the return and standard deviation of an equally weighted portfolio if the correlation between A and B is 0.3?

A. 14.50%, 13.88% B. 14.50%, 9.69% C. 29.00%, 13.88% D. 29.00%, 11.78%