GARP.FRM.PQ.P1 Please solve these questions.

1) Which of the following loans has the lowest credit risk? The table data file is attached. It was asked in the quiz.Please explain
Question 8
Choose one answer.
a. Loan A Incorrect
b. Loan B Incorrect
c. Loan C Correct
d. Loan D Incorrect
The correct answer is C
The 1 year probability of default needs to be adjusted to the remaining term using the formula [(1-d_month)12 = (1-d_annual)]. We multiply the monthly PD with the loss given default (LGD) to get the expected percentage loss (EL%):

2) Suppose you are a Risk manager in your firm and after evaluating the results of stress testing, you are recommending that the firm allocate additional economic capital and purchase selective insurance protection to guard against particular events. In order to give management a fully informed assessment, what is important that relates to this strategy?
Choose one answer.
a. While decreasing Liquidity Risk exposure, it will likely increase market risk exposure Incorrect
b. While decreasing correlation risk exposure, it will likely increase credit risk exposure Incorrect
c. While decreasing market risk exposure, it will likely increase credit risk exposure Correct
d. While decreasing credit risk exposure, it will likely increase model risk exposure Incorrect
The correct answer is C
‘C’ is correct, as it is related to the strategy. Why B is incorrect

3)Suppose 3 months and 6 months LIBOR spot rates are 5% and 6%. An investor enters into a FRA in which he will receive 9% on a principle of $8,000,000 between 3 and 6 months. What is the value of a FRA?
Choose one answer.
a. $140,000 Incorrect
b. $560,000 Incorrect
c. $135,862.37 Incorrect
d. $38,817.82 Correct
The correct answer is D

4)Given the following 30 ordered simulated percentage returns of an asset, calculate the VAR and expected shortfall (both expressed in terms of returns) at a 90% confidence level.-16, -14, -10, -7, -7, -5, -4, -4, -4, -3, -1, -1, 0, 0, 0, 1, 2, 2, 4, 6, 7, 8, 9,11, 12, 12, 14, 18, 21, 23
Choose one answer.
a. VAR (90%) = 10, Expected shortfall = 14 Incorrect
b. VaR (90%) = 14, Expected shortfall = 15 Incorrect
c. VaR (90%) = 18, Expected shortfall = 22 Incorrect
d. VAR (90%) = 10, Expected shortfall = 15 Correct

Why the Var is 10 and not 7 as the 27th observation calculated as 90% of 30 observations

5) Why VaR for Fat tail is less than VaR for normal distribution?

6) What do you mean by gross errors or illegitimate errors ?

7)Suppose the 3 and 6 month LIBOR spotes rates are 4% and 5% , respectively ( cc rates) . An investor enters into an FRA in which she will receive 8% ( Assuming quaterly compounding ) on a principle of $5,000,000 between month 3 and 6 . Calculate the value of the FRA.

8)Red Inc. uses glass for manufacturing of LCD screens. Red wants to hedge its exposure to glass price shocks over next 6 months. Futures contracts are not readily available for glass. Red finds out two commodities whose prices are closely correlated with two commodities viz. Commodity X and Commodity Y. Futures on Commodity X have a correlation of 0.79 and that of Commodity Y have a correlation of 0.91 with price of glass. Futures on both Commodity X and Y are available with 4 month and 8 month expiration. Which contract would be the best to minimize basis risk considering information provided

a. Futures on Commodity X with 4 months to expiration Incorrect
b. Futures on Commodity Y with 4 months to expiration Incorrect
c. Futures on Commodity X with 8 months to expiration Incorrect
d. Futures on Commodity Y with 8 months to expiration Correct

9) Lee has portfolio of $ 15 million which is invested in mid cap high beta stocks. His portfolio beta is 1.5 relative to S&P midcap index. The S&P midcap index futures are trading at $1200 with a multiplier of 300. Lee expects market to be volatile for next six months and hence would want to hedge his exposure to market risk using S&P midcap index futures. He executes a short index futures strategy. The next day S&P 500 spot price is $1100 and futures price is $1250. Lee follows tailing the hedge strategy. How many futures contract Lee should trade the next day for following tailing the hedge strategy?
Choose one answer.
a. Lee should go long 7.5 S&P midcap index futures contracts with the same maturity Correct
b. Lee should go short 1.5 S&P midcap index futures contracts with the same maturity Incorrect
c. Lee should go long 1.5 S&P midcap index futures contracts with the same maturity Incorrect
d. Lee should go short 7.5 S&P midcap index futures contracts with the same maturity Incorrect

10)At present the shares of Microsoft Corp. Trade at USD 50. The monthly risk neutral probability of the price increasing by USD 5 is 40% and the risk neutral probability of the price decreasing by USD 5 is 60%. You are required to find out the mean and Standard deviation of the price of Microsoft Corp. after 2 months if the change in price is independent for consecutive months?
Choose one answer.
a. Mean = 48, SD = 6.93
b. Mean = 48, SD = 6.12
c. Mean = 36, SD = 6.93
d. Mean = 36, SD = 6.12

11)You are asked to find the price of the US Treasury note. The following table gives the prices of two out of three US Treasury notes for settlement on August 30, 2012. All three notes will mature exactly one year later on August 30, 2013. Assume annual coupon payments and that all three bonds have the same coupon payment date.
5% 97.5
7% ?
8% 103.2
Approximately what would be the price of the 4 1/2 US Treasury note?
Choose one answer.
a. 99.64 Incorrect
b. 98.20 Incorrect
c. 98.64 Correct
d. 100.20 Incorrect

12)A financial institution has agreed to pay 6-month LIBOR and receive 8% per annum (with semi-annual) compounding on a principal of $100 million. The swap has a remaining life of 1.25 years. The LIBOR rates with continuous compounding for 3-month, 9-month, and 15-month maturities are 9%, 9.5%, and10% respectively. The 6-month LIBOR rate at the last payment date was 9.2% (with semiannual compounding). What is the value o f the swap to the financial institution?
Choose one answer.
a. -1.854 million dollars Incorrect
b. -4.566 million dollars Incorrect
c. -2.854 million dollars Correct
d. +1.854 million dollars Incorrect
The correct answer is C
Sol. We can value an interest rate swap either in terms of bond prices or in terms of FRA’s. Let’s use the FRA approach here.
Here the institution receives a fixed cash flow of 4 million (100x0.08x0.5) semi-annually but the cash outflow is floating dependent on the LIBOR. The floating rate of the first outflow i.e. at T=0.25 years from now was the 6-month LIBOR rate at the last payment date i.e 9.2%.
The next outflow which occurs at time 0.75 years from now is dependent on the current LIBOR which can be calculated using the 3-month and 9-month LIBOR rates. i.e
(0.75x9.5-0.25x9)/0.5=9.75% with continuous compounding or 9.99% with semi-annual compounding.
Similarly the next cash outflow occurs at time = 1.25 from now and the floating rate is determined similarly. i.e.
( 1.25x10-0.75x9.5)/0.5 = 10.75% with continuous compounding = 11.044% with semi-annual compounding

I did not get how to find the cash outflow.

Thanks a lot.
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Nicole Seaman

Director of FRM Operations
Staff member

Are all of these questions from a previous GARP practice exam? I searched the 2015 and 2016 practice exams, and I did not find these questions anywhere. Please make sure to list the source of your questions when posting. Also, make sure to search the forum to make sure the questions have not already been answered first. Below I've listed any questions that I found that were already discussed in the forum. Please discuss those specific questions in these forum threads:
Just one last is difficult to keep our forum organized when 12 different questions are asked in one thread. When other members begin to answer your questions, it can become very unorganized and confusing when there are so many different concepts and questions being asked. The best way to get an answer to a specific practice question (after searching to make sure it wasn't already answered) is to post one thread for each question. This way, only one concept and question is being discussed and it doesn't turn into a confusing and congested thread.

Thank you


cc: @David Harper CFA FRM


Well-Known Member
1) For Loan A we need to find 3 month PD ,1-(1-3 month PD)^4=1 year PD =>3 month PD=1-(1-1 year PD)^(1/4)=1-(1-.025)^(1/4)=.00631 =>EL(3mnths)=.00631*50%=.3155%
Loan B: 9 month PD=1-(1-1 year PD)^(.75)=1-(1-.011)^(.75)=.00826=>EL(9mnths)=.00826*65%=.5369%
Loan C: 6 month PD=1-(1-1 year PD)^(.5)=1-(1-.01)^(.5)=.0050=>EL(6 mnths)=.0050*60%=.30%
Loan D: 12 month PD=1-(1-1 year PD)^(1)=1-(1-.0075)^(1)=.0075=>EL(12mnths)=.0075*50%=0.375%
Thus the Loan C has the lowest credit risk with the lowest EL of .30%.

David Harper CFA FRM

David Harper CFA FRM
Staff member
Q (4) is wrong. 90% ES is the average of the 10% tail and has nothing to do with VaR (ES is defined by a probability threshold; TCE is another matter....). So here 90% ES = average(16, 14, 10) without regard for which of the three 90% VaRs is retreived. Re 90% VaR, you are correct: best answer is 7. But as discussed extensively on the forum, VaR has three valid answers here so question needs to be more precise (GARP is fully aware of this and has been for years and would not put this question on the exam). Some of the others questions are just wrong but it's not productive to spend time on them in my opinion. I agree with @Nicole Seaman We are happy to answer and debug questions from any source (most of the time, it's good learning), but batching them commingles some questions that are actually counterproductive to FRM candidates because they are ill-formed or wrong, sorry. Not all of them, some are good don't get me wrong.
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Nicole : I apologise for not being aware of the questions posted in the forum previously. I shall henceforth take care of the same and also not mingle so many questions in one thread.

David : Thanks for the answer. Will make sure that specific questions are posted on specific threads.
Shakti Rathore : Thanks.