Consolidated Answer Thread for Full FRM Exam Questions.

Alright all I was thinking about the questions from the exam and couldn’t really remember that many. I was hoping that by starting this thread we could all bring up the questions we remember and this would jog my and maybe your memory (we have already done this in some of the other threads but this has been a very disparate approach). Here are a few I remember: 1. LVAR question: Answer on my exam was D, this was also the largest of the 4 amounts given. Trick was to use the quote midpoint ($72) and average of the bid-ask spread (i.e. [Ask-Bid]/2=.16) to solve for the %Spread as=(Ask-Bid)/.5(Ask+Bid) which you can work out as being %Spread=.32/.5(72.16+71.84)=.004444. The plug into Var+.5*72000*Spread and solve, ends up being something like 1649 contract I think. 2. Ethics question answer was all 4, i.e. GARP can suspend and take away your letters (this was confirmed in another thread) 3. Bayesian question answer was like 38.7%, but there is no use even talking about this one since it will be thrown out once the exam gets graded since they didn’t take the time to proofread (sucks cus I got this one right) 4. MLE estimation in EWMA framework: no idea on this one 5. Geometric Brownia Motion question for stock price two periods from now I remember I put something like $99.79, cus it first went up and then back down. Throw out some others and we can see if we as group remember anything about them. I know that if someone jogs my memory on some of these I will be able to provide good feedback as this will kick start my memory.

Just remembered another one: 6. Growth in the Surplus of assets over liabilities using simulation approach with 1000 simulated end of year outcomes at the 99% CL. The 10th worst simulated surplus was -291, which was one of the answer choices, but the wrong one. The correct choice was 591 as the question had asked for the change in the surplus from the start of the year to the simulated end. At the start we had A=1,200 and L=900 so a positive surplus of 300, hence if the ending surplus was -291 then the change in the surplus had to of been 591.

  1. How do make an arbitrage profits (aka the box spread question). I remember the put was 25, the call was 5. I chose sell a put, buy a call and get 6 box spreads. This was a complete guess on my part between the two choices that had sell put as a part of the answer (the other was sell put, buy call, do 4 box spreads). I thought the right answer would include selling a put just because it was so expensive compared to the call based on the strike and underlying price. 8. The Beta questions where you are given the fact that Betai=Corri*(stdev(i)/stdev§) or whatever and then they ask you what beta 1 and beta 2 actually equal in numerical terms. I have never answered not enough info on any of the practice exams but I did on this question since I had no clue how to get the actual numerical values of the beta coefficients when we are given no numbers at all and only formulas. Thoughts? What did you guys put? Why?

For number 1) referencing the LVaR question. I could have sworn that the spread of USD 0.16, was referred to as the average spread. Which I took as the average spread over time (Ask - Bid) average over x number of days was 16 cents, rather than the average of the spread, which infers that the spread was 32 cents.

For #5 I put the same thing.

The damn herfindahl index came up on this exam as well in one of the credit risk questions. Test creators love this thing, it would randomly show up on the CFA as well.

@Rydex: pretty sure it said average spread, but it would be awesome if you’re right cus if you are then the correct answer would be C (i.e. second highest amount which was like 1569, which is what I put cus I was being an idiot and only did the calculation “properly” in my car after having gotten out of the AM portion). 9. Which of the following cannot be used to asses the credit concentration within a portfolio? Two were obvious eliminations which left the HHI (thanks Rydex) and another option. I chose the other option (can’t recall what it was) because I figured you can adapt the HHI to calculate the exposure you have to a single issuer (relative to the size of said issuers industry in much the same way as you would calculate the percentage of the industry that this single issuer controls as computed using the HHI for regulatory purposes). Edit: Just remembered what the answer I chose was. I chose the one that discussed the Asymptotic Risk Factor feature of the IRB’s being able to assess concentration risk. I chose this answer because the ARF assumes a single systematic risk factor and assumes that exposures are granular (i.e. and hence no concentration risk even exists in the portfolio).

Some more courtesy of one of the other members: 10. Gold forward arbitrage with continuous yield (2%) and Rf (4%). The future price was lower that the computed one. What should be done to “gain” the arbitrage? 11. One BII market risk capital charge computation, be careful daily var was 95%. So we had to convert to 99%. 12. Currency forward arbitrage (Rf and time provided) 13. Volatility smile descriptive question (currencies and equities) 14. Easy Binomial: What is the prob that a student has less than 8 answers right if he answers randomly a two possibility answer test with 20 question. You did not have to compute but just to say how to compute. 15. Several questions that required put/call parity (including S*exp(-y*t)). Help with the details if you remember. 16. Several questions on option combinations (butterfly spread) 17. One greek question 18. Several CDS questions (impact of correlations) 19. Lots of var questions 20. Not too many questions on BII compared to var questions. 21. One Tier1 and Tier2 BII computation 22. Model risk question 23. One UBS (easy) question 24. Why stress testing var 25. Indirect question on backtesting var 26. One easy swap computation (2 years remaining, Libor against 8%) 27. One easy question on interest rate: Which one is higher? They gave yearly, monthly, quarterly and continuous numerical values. The answer was continuous. tongue laugh 28. Several questions on linear regression: Compute R^2. Beta has bad t-stat and the strategy is to be market neutral -> what can be concluded? 29. A few questions on IR, Sharpe and Treynor ratio. I was confused by one because they were calling the tracking error, the systemic volatility or something like that. 30. One portfolio credit risk model question 31. One very easy question on matrix transition: Which statement is incorrect? There was a line with BBB down grade proba > 80%… 32. Question about similarities of CreditMetrics, CreditRisk+ and KMV 33. Difference between CDO and MBS (I answered the tranching) 34 CDS question on price of first to default versus second to default. 35. One SPE usage question. 36. A few modified duration question. (DeltaV = -D* * V * deltaY) 37. Which obligation has negative convexity: obvi the callable 38. An easy probability computation: z-proba of not been between 1 and 1.5 or something like that. The z table was provided for each test on the first page. 39. One easy question kurtosis: The normal has lowest proba of extreme value than 4, 8 kurtosis distributions. 40. Several EVT questions: one was to compute it with extreme returns provided. 41. One var question: 20 worst returns provided but unsorted. Find the var, It was 1% of 80 Million as far as I remember. 42. You decrease significance what happens to Type I and Type II probs. 43. One binomial tree call computation question that I failed. 44. One Ted behaviour (after Lehman episode) question. I answered that the after Lehman collapsed the TED kept increasing for some time as other answers focused only on TED declining (even though LIBOR continued to climb) or incorrectly stated that the spread continued to increase through the first half of 2009. 45. One or two linear hedging question (rho * sigma(S) / sigma(F)) 46. Concerning study cases, a single question on MetallGesellshaft 47. Two questions on basis risk. 48. One Garch (compute the long term vol for Garch) 49. An interesting question on style drift versus leverage increase for HF. They were providing the fund returns and the benchmark returns. 50. Tracking error: 3 graphs were given with benchmark and fund returns. Tell which one has lowest tracking error. 51. Correlation: 3 graphs were provided. Which group of variables has the highest correlation? 52. An easy question on credit risk: Which operation adds CR: sell/buy options 53. One Merton question close to the one provided in Garp2009: Compute prob of default 54. Two EL and UL computations (PD, LGD, COM, sigma(PD), sigma(LGD) were provided) 55. Two questions on credit “modifiers” (Triggers, Netting, collateral, MTM) 56. One Raroc computations (no taxes were involved and RC was provided) 57. One BS call/put computation N(d1) and N(d2) were provided 58. One interest risk reduction question (buy a cap, sell a floor, …) 59. One or two questions on MVAR, CVAR questions: Compute the global VAR if a fund is removed Compute an MVAR 60. a) normal b) binomial c) negative binomial distribution d) possion 61. RAROC question with the following choices: a) 2.6 b) 2.9 c) 3.x d) something higher than 3.x (4.x?) 62. Tracking error question where the investing company required an active manager whose IR (?) and alpha were above preset levels. Two funds (A and B) got eliminated right away because they didn’t meet these satisfactions, and between the two left I choose the one that had the IR given, it was like 1.4 (this was Fund C), because for fund D I believe IR was lower. Please help fill out the details of these questions along with what you answered and why. Thanks for your help. I will be editing my post to add my thoughts on the listed questions that I can remember. Thanks again to everyone and particularly v.raghavan as most of these are the result of his excellent memory.

  1. Compute risk neutral probability of an up move for one period. The answer should be .5258. Here is what I wrote in the other thread regarding this question: a) 20% is in fact the volatility, however this is already the one period volatility (the period in this example was clearly 3 months not one year), hence we don’t need to do anything to this number to get our U, which is just equal to the following: U=exp(.20*sqrt(1)), again T=1 hence we are multiplying by sqrt(1) since one period is 3 months (it does say that every period the stock can go up or down 20% percent correct? and it does say that there are two such periods prior to expiration correct? right then one period has to equal 3 months and there is no need to mess with the volatility). b) U=exp(.2*sqrt(1))=1.2214, which implies D=.81873, hence c) Prob(U)=[exp(rT)-D]/[U-D]=[exp(.12*.25)-.81873]/[1.2214-.81873]=.21172453/.40267=.5258, hence Prob(D)=.4742. These are the risk neutral probabilities of an up and down move for this problem. Note that here we do have to convert the risk free rate to our corresponding 3 month period by multiplying it by .25 since the risk free rate was given on an annual basis and for us 1 period=3months, as was explained above. 64. Compute the value of the option with #63 based risk neutral probabilities assuming it expires in two periods time. I got something like $2 here. 65. There was another question with storage costs for bushels of wheat and you had to calculate the forward price I believe.

Freaking site won’t let me edit so here it goes: 10. Fro this question I believe you had to borrow the money, buy the gold, sell the future forward and lend out the gold you purchased at the lease rate. Then at maturity collect your lease rate deliver the gold at the forward price and pay back the loan. I got an answer of something like $1.55 for this question, as the forward in the market was selling for 755 and it should have been selling for something like $753.45, I think.

  1. Don’t remember the answer or the details but you had to divide by 1.65 and multiply by 2.33 to convert the VaR from 95% to 99%. 12. Don’t remember the details, help. 13. I remember on asked for a true statement about the largest change in the value of an option due to a change in the underlying, I chose the answer that said the absolute change in the value of deep-in-the-money option is larger than the absolute change in the value of either an ATM or deep out of the money option. Chose this answer based on the fact that delta is greatest for deep in the money options. There was another question in this vein comparing a volatility smile for currency options and a volatility smirk for equity options. I don’t remember the details of this question or what I answered, so if you do help. 14. This was an easy one, the answer was the cumulative probability of each of these 8 occurrences computed using the binomial distribution. 15. Don’t remember the details of these so please help.