# Q.311 Probability Concepts

You want to assign 4 analysts to cover 4 different industries. In how many ways can the assignment be made? A 24 B 6 C 12 The correct answer is: A) The number of ways we can assign 4 analysts to 4 tasks is 4! = 4 &times; 3 &times; 2 &times; 1 = 24. *User Question: Remember 4Prime

CFA Level 1

# Q.3352 Quantitative Analysis

In a hypothetical world, GDP is regressed against interest rate and inflation and regression results are shown below. $$GDP = a + b\quad (Interest\quad rate) + c\quad (Inflation) + Error \quad term$$ Coefficient p-value a 9 0.042 b 2 0.035 c 1.5 0.012 ANOVA df SS Regression 2 240 Residual 37 1070 Total 39 1300 Multiple R 0.428 R2 0.183 Observation 40 Assume that on a certain significance level, the critical value of the F-statistic is 4. Which of the following is correct? A The value of F-statistic is less than its critical value B We fail to reject the null hypothesis: H0: All slope coefficients = 0 C The model as a whole is statistically significant D The model as whole is not statistically significant The correct answer is: C $$F=\cfrac {RSS/k}{SSE/((n-k-1)}=\cfrac {240/2}{1070/(40-2-1)}=\cfrac {120}{1070/37}=4.1495$$ The F-statistic is 4.1495 and its critical value is 4. If F-statistic &gt; F critical, we reject the null hypothesis. H0: All slope coefficients = 0 Ha: At least one slope coefficient $$\neq$$ 0 Model as a whole is significant. *User Question: RSS wouldnt be 1070 since is the residual sum of squares, and SSE 240 under the same logic? also i dont quite understan where that formula came from, i know there is a pretty similar formula for F with multivariate regression, but not the same.

FRM Part 1

# Quantitative problem

Your staff has determined that your 95% daily VaR model is perfectly accurate: on any given day, the probability that the loss exceeds VaR is 5%. What is the probability that next month, which has 20 trading days, VaR will be exceeded on two days or less?&nbsp; For this question I tried using Poisson distribution to solve it and I got 91.97% for the answer, but apparently my workbook shows that the answer should be C which is 92.45% ( p[X=0]＋p[X=1]＋ p[X=2] = 35.85% ＋ 37.74% ＋ 18.87% ) For P(X=0), I did 0.95^20=0.3585, and P(X=1)= 0.95^19=0.3774, whereas the 0.05 is missing, but I don't think these calculations make any sense. Can anyone here in the forum help with this question?? Should I use Poisson for this question or not?

FRM Part 1

# Q.154 Foundations of Risk Management

Ravi Kumar is a junior fixed-income analyst who is comparing a 7-year AA+ rated asset-backed security collateralized debt obligation (ABS CDO) with a comparable 7-year corporate bond which is also AA+ rated. Kumar made some analogies in his report. Which of these is incorrect? A The equity tranche of an ABS CDO has a lower risk than the equity tranche of an original ABS B The probability of loss of the ABS CDO is lower than the probability of loss of the bond C Turning an ABS into an ABS CDO helps high-risk subprime mortgages turn into high-rated investments D The nature of the risk of the AA+ ABS CDO is different from the AA+ bond regardless of its similar rating The correct answer is: B The probability of loss of the ABS CDO is higher than the probability of loss of the bond because ABS CDOs are made up of the mezzanine tranche of ABS and carry higher prepayment risk and subordination risk to the senior tranche of the original ABS. Option A is accurate as the ABS CDO is created from the mezzanine tranche of the ABS. The equity tranche of the ABS CDO is less risky than the equity tranche of the original ABS. Option C is accurate as turning an ABS into an ABS CDO helps high-risk subprime mortgages turn into high-rated investments when the ABS CDO is created from the mezzanine tranche of the ABS senior tranche. Option D is accurate because the nature of the risk of a AA+ ABS CDO is different from a AA+ bond regardless of its similar ratings. *User Question: If the senior tranche of ABS CDO is created from the mezzanine tranche of the original ABS which has higher risk than the Senior tranche of original ABS; correspondingly, the equity tranche of ABS CDO should also be more riskier than the equity tranche of original ABS. If so, is option A still correct?

FRM Part 1

# Q.2683 Statistical Concepts and Market Returns

Temple Investments publishes a stock pick report on a weekly basis for its subscribers. The list contains the categories of stocks based on their risks. 'Category 1' is the least risky and 'Category 4' represents the riskiest stocks. Which measurement scale does Temple Investment most likely use? A Nominal scale B Cardinal scale C Ordinal scale The correct answer is: C) The ordinal scale categorizes data based on some differentiating characteristics. Temple Investment uses different categories to sort data based on the risk characteristics of the stocks. *User Question: The data gathered by the ordinal scale cannot + or -, they can only show the bigness or the smallness

CFA Level 1

## Q.3768 Quantitative Analysis

The following data represents a sample of daily profit of a sales company for six weeks in a particular year. $$\begin{array}{c|c} \textbf{Week} & \bf{\text{Amount of the Profit} ()} \\ \hline {1} & {3,800} \\ \hline {2} & {2,800} \\ \hline {3} & {2,700} \\ \hline {4} & {9,900} \\ \hline {5} & {2,600} \\ \hline {6} & {4,300} \\ \end{array}$$ What is the 75% quantile profit? A 4,000 B 4,234 C 4,175 D 4,654 The correct answer is: C The 75% level is found between the 4th and the 5th observations so that: $$\text q_{75}=0.75×3800+0.25×4300=4175$$ *User Question: shouldn't the observations be stated in ascending order prior to calculating the quantile value?

## Q.8 The Time Value of Money

How much money will you have if you invest $100,000 today in a project paying 8% interest rate compounded continuously for 3 years? A$127,124.90 B $108,328.70 C$125,971.20 The correct answer is: A) PV=100,000; r=8%=0.08; N=3;FV = PV*erN = 127,124.90Note: The question asks about continuous compounding. You don't have to use your financial calculator to solve this problem. You also have to use the the constant ''e'' which is 2.7182. *User Question: How do we calculate this on the Calculator because I put in all of those values and keep coming to \$125,971.20. please explain? ?

## Q.528 Quantitative Analysis

An autoregressive process is considered stationary if: A The roots of the characteristic equation lie on the unit circle B The roots of the characteristic equation lie outside the unit circle C The roots of the characteristic equation lie inside the unit circle D The characteristic equation are of order 1 The correct answer is: B In any autoregressive process, the roots of the characteristic equation must lie outside the unit circle, which means the absolute value of the roots must be larger than one. *User Question: which roots and unit circle are these? what do they imply. ?

## Q.183 Foundations of Risk Management

Given the following information, compute the expected return of the portfolio.Risk-free rate = 5%Expected market return = 25%Standard deviation of market portfolio = 10%Standard deviation of portfolio = 5% A 0.25 B 0.0015 C 0.1 D 0.15 The correct answer is: D The equation of the CML is $${ R }_{ p }={ R }_{ f }+\left\{ \frac { { R }_{ m }-{ R }_{ f } }{ { \sigma }_{ m } } \right\} { \sigma }_{ p }$$Where: Rp is the expected portfolio returnRf is the risk-free rateRm is the expected market returnAnd &sigma;m, &sigma;p are the standard deviations of the market and the portfolio, respectivelyTherefore, E(Rp) = 5 + (25 - 5)/10) * 5= 5 + 2 * 5= 15% *User Question: This question is missing correlation information. We cannot make the assumption that correlation is 1 based on the given information

## Q.228 Foundations of Risk Management

A manager uses a two-factor model to examine the returns of two assets, X and Y. The two factors are unexpected percentage changes in inflation (IF) and consumer sentiment (CS). The following data has also been given:E(RX) = 10%E(RY) = 12%&beta;X, IF = &beta;Y, IF = 2&beta;X, CS = &beta; Y, CS = 2All other factors constant, Which of the following statements is true? A Asset Y is more sensitive to inflation than asset X B Inflation and consumer sentiment have different effects on the returns of X and Y C An arbitrage opportunity exists D None of the above are true The correct answer is: C Based on the information given, an arbitrage opportunity exists because despite the two assets having equal systematic risks, they are priced based on different expected returns. To avoid the making of risk-free profit, expected returns should be equal as long as systematic risks are identical. In this case, an investor can make risk-free profit by shorting asset Y and using the proceeds to take a long position in asset X. *User Question: Does it mean that assets should not have different firm specific return if their systematic risk is similar?