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- 3. Answer C. • Information Ratio = (Average Return on the Portfolio – Average Return on the benchmark)/Tracking Error Volatility • IR = (13.2 – 12.3)/6.5 = 0.138 • This question tests whether the candidate knows the information ratio. It has a number of destructors that make it difficult to ‘guess’ the formula • A. Incorrect. • B. Incorrect. • D. Incorrect. © EduPristine FRM‐I 2
- 7. Answer B. The current return of the security is = ln (18/20) = ‐10.536%. Using an EWMA model, the updated volatility is given as: V(t) = {lambda* ((V[t‐1]^2) +(1 – lambda)*(current return^2)} ^ 0.5 = {0.9 * ((0.015^2) + (1 ‐ 0.9) * ( ‐0.10536^2 )} ^ 0.5 = 3.62% • INCORRECT: A – Forgets to square the volatility terms • INCORRECT: C – Forgets to square the volatility terms and to take the square root of the resulting variance, then miscalculates conversion to percentage. • INCORRECT: D – Forgets to take the square root of the variance, then miscalculates conversion to percentage. © EduPristine FRM‐I 6
- 8. Question 4 – FRM Exam 2008 A factor analysis of the dividend‐adjusted returns of ABC Ltd.’s stock price was undertaken to determine which economic factors contributed to its performance. The regression was performed on 460 observations. The results are as follows: Table 1: Predictor Coeffecient Table 2 Standard Error of Coefficient Intercept ‐0.0243 0.005772 All_Share_Index 0.0256 0.017655 Industrial_Index 0.0469 0.0012 12,466,47 Sum of squared Errors (SSE) 1,013.22 Sum of Squared Total (SST) 13,479.69 0.006398 Financial_Index Sum of squared regression (SSR) 0.001412 Which one of the following options correctly describes which variables are significant at the 5% level, and the R2 statistic, respectively? Significant Variables at 5% level R2 statistic A. B. C. D. Intercept; Industrial_index 0.924834 Intercept; Industrial_index 0.075166 All_share_index; Industrial_Index 0.924834 All_share_index; Industrial_Index 0.075166 © EduPristine FRM‐I 7
- 9. Answer A. • The following table shows the test statistics for each of the four variables, calculated by dividing the variable coefficient by the standard error . The variable is significant if the absolute value of the t‐stat is greater than the critical value from the student’s t‐distribution for 456 degrees of freedom (which is very close to the z‐ statistic since the number of observations is so high), i.e. 1.96. Predictor t‐stat Significant? • Intercept ‐.0243/0.005772 = ‐4.21 Yes • All_share_index .0256/0.017655 = 1.45 No • Industrial_index .0469/0.006398 = 7.33 Yes • Financial_index .0012/0.001412 = 0.85 No • The R2 statistic is defined as the ratio of SSR/SST = 12,466.47/13,479.69 = 0.924834. © EduPristine FRM‐I 8
- 10. Question 5 – FRM Sample Paper 2011 The following GARCH(1,1) model is used to forecast the daily return variance of an asset: σn2 = 0.000005 + 0.05u2n‐1 + 0.92σ2n‐1 Suppose the estimate of the volatility today is 5.0% and the asset return is ‐2.0%. What is the estimate of the long‐run average volatility per day? A. B. C. D. 1.29% 1.73% 1.85% 1.91% © EduPristine FRM‐I 9
- 11. Answer A. • The model corresponds to α = 0.05, β = 0.92, and ω = 0.000005. Because γ = 1− α− β, it follows that γ = 0.03. • Because the long‐run average variance, VL, can be found by VL = ω / γ , it follows that VL = 0.000167. In other words, the long‐run average volatility per day implied by the model is sqrt(0. 000167) = 1.29%. © EduPristine FRM‐I 10
- 13. Answer D. • To reduce the beta of a portfolio, one needs to lower the position’s exposure to the market. Thus, one needs to short futures contracts. The number of futures contracts, N, is: N ( new old ) ( 0 . 8 1 .5 ) Size of spot Position Size of one Futures contract 100 ,000 ,000 280 250 * 1000 • Thus, one needs to short 280 futures contracts © EduPristine FRM‐I 12
- 15. Answer A. • Since the investor is shorting the futures contract, she/he gains when the futures price goes down. At the end of the first day, the investor has a gain of (294.2 – 286.6) * 100 = $ 760. Therefore, no variation margin is needed © EduPristine FRM‐I 14
- 19. Solution Valuation of currency swap in terms of bonds (millions): Value of swap in million $ = 11.294*0.91 – 9.7225= $0.5448 million © EduPristine FRM‐I 18
- 25. Answer D. • To calculate the VAR of the portfolio, we first must calculate the volatility of the portfolio, σ. The variance of the portfolio equals: • σ2 = (1/3)2 (7%)2 + (2/3)2 (3%)2 + 2*(1/3)*(2/3)*10%*7%*3% = 0.001, Thus, σ = 0.0316 • Assuming a 95% confidence interval, VAR = 1.65 * 0.0316 * 4,500,000 = 234,630 © EduPristine FRM‐I 24
- 26. Question 13 – FRM Exam 2011 Consider a bond with par value of EUR 1,000 maturity in 3 years, and that pays a coupon of 5% annually. The spot rate curve is as follows: Term Annual Spot Interest Rate 1 6% 2 7% 3 8% The value of the bond is closest to: A. B. C. D. EUR 904 EUR 924 EUR 930 EUR 950 © EduPristine FRM‐I 25
- 27. Answer B. • Using spot rates, the value of the bond is: • 50/(1.06) + 50/[(1.07)^2] + 1050/[(1.08)^3] = 924.37 © EduPristine FRM‐I 26
- 28. Financial Risk Manager‐ Fast Track Study Packages Give us a chance to hand hold your FRM prep with our brilliantly coordinated set of topic‐wise quizzes, video tutorials, summarized recordings and mock tests etc. To leverage your FRM Exam prep we have compiled all of this crisp & relevant information in the form of 3 exclusive online crash courses. You can choose the Package most suitable to you and kickstart your FRM preparation. FRM ‐ Mock Tests & Questions to check your Preparation Level 2 Proctored Mock Tests 800+ Topic wise Quiz Questions 24 x 7 Access to Discussion Forums Price: USD 60 Buy Now FRM ‐ Tests & Video Tutorials for Quick Preparation (Basic) 2 Proctored Mock Tests & 800+ Questions worth USD 60. 50+ Hrs of Online Lecture Recordings 15+ Hrs Summarized Recordings Topic wise notes for easy reference 24 x 7 Access to Discussion Forums. Buy Now Price: USD 197 FRM ‐ Complete Package of Webinars, Video Tutorials & Question Bank (Pro) FRM Basic package worth USD 147 Doubt Solving on Forums Live Online Trainings Price: USD 397 Buy Now Contact Us... Feel free to contact us in case of any further queries regarding Level I FRM Exam Preparation. You can Call us at: +1 347 647 9001 Email us at: austin@edupristine.com or Stay Tuned.. www.edupristine.com/ca About Edupristine EduPristine holds a profound history in training Risk Professionals across the globe. It has been an International Authorized Training provider for FRM trainings since past four years. It is also registered with GARP as an Approved Provider of Continuing Professional Education (CPE) credits. EduPristine's program on "Operational Risk Modeling" and “Financial Modeling” qualify for GARP CPE credit hours. © EduPristine FRM‐I 27