# (Q. 3328) and Q.3397 FRM part 1

Someone please make me understand the solution of these questions.

#### 纳 # Q.374 Quantitative Analysis

72年之后纳第1部分学生模拟考试,mean score was 75. Assuming that the population standard deviation is 10, construct a 99% confidence interval for the mean score on the mock exam. A (75, 85) B (65, 75) C (71.96, 78.04) D (75, 78.04) The correct answer is: C A 99% CI for the mean, μ = x̄ ± Zα/2 *σ/√n where α =0.01From the normal dist. table, Z0.005 = 2.58μ = 75 ± 2.58 * 10/√72= 75 ± 3.04Giving us a CI = 71.96 ≤ μ ≤ 78.04 *User Question: Please when do we have to use 1,96 for the normal distribution instead of using the normal dist tabke?

#### frm-2,frm-1,frm,question # Q.136 Annuities/cash flows with non-contingent payments

A company pays a dividend of $100,000 quarterly forever starting from now. Assume an annual nominal rate of interest of 4%. Calculate the present value of the dividends. A$9,000,000 B $9,100,000 C$10,100,000 D $11,100,000 E$11,200,000 This is perpetuity-due: $$\cfrac {100000}{d}= \cfrac {100000(1+i)}{i}=10,100,000$$ *User Question: could help to put in the solution why the interest rate is 1% and not 4% (its because it's quarterly and so you would divide the i by 4 and then you multiply by (1+i) because its a perpetuity due)

Actuarial - FM(Financial Mathematics)

#### Financial Mathematics,acturial,exam,question # Q.3500 Financial Markets and Products

## Q.378 Quantitative Analysis

A random sample of 50 FRM exam candidates was found to have an average IQ of 125. The standard deviation among candidates is known (approximately 20). Assuming that IQs follow a normal distribution, carry out a statistical test (5% significance level) to determine whether the average IQ of FRM candidates is greater than 120. Compute the test statistic and give a conclusion. A Test statistic: 1.768; Reject H0 B Test statistic: 2.828; Reject H0 C Test statistic: 1.768; Fail to reject H0 D Test statistic: 1.0606; Fail to reject H0 The correct answer is: A The first step: Formulate H0 and H1H0: μ = 120H1:μ > 120Note that this is a one-sided test because H1 explores a change in one direction onlyUnder H0, (x̄ - 120)/(σ/√n) ∿N(0,1) Next, compute the test statistic: = (125 – 120)/(20/√50) = 1.768Next, we can confirm that P(Z > 1.6449) = 0.05, which means our critical value is the upper 5% point of the normal distribution i.e. 1.6449. Since 1.768 is greater than 1.6449, it lies in the rejection region. As such, we have sufficient evidence to reject H0 and conclude that the average IQ of FRM candidates is indeed greater than 120. Alternatively, we could go the “p-value way” P(Z > 1.768) = 1 – P(Z < 1.768) = 1 – 0.96147 = 0.03853 or 3.853%This probability is less than 5% meaning that we have sufficient evidence against H0. This approach leads to a similar conclusion. *User Question: Can you please explain how did we get P(Z > 1.6449) = 0.05 ?

## Q.1179 Valuation and Risk Models

A fund manager has the option to buy the following bonds: I. A bond with 10% coupon and a tenure of 15 years II. A bond with 10% coupon and a tenure of 10 years The fund manager expects the interest rate volatility to increase and wants to compose a portfolio which will help him generate maximum return due to the volatility. The fund manager must buy: A The bond with a tenure of 15 years B The bond with a tenure of 10 years C Both bonds, since they react in a similar manner to interest rate volatility D Both bonds, since the diversification effect will help him generate maximum return The correct answer is: A The larger the duration, the more the impact of interest rate volatility is on the portfolio. It has been observed that bonds with large tenures have higher durations. Therefore, the bond with a tenure of 15 years will have a higher duration as compared to the bond with a tenure of 10 years. Therefore, in order to generate maximum return due to the interest rate volatility, the fund manager must invest in the bond with a tenure of 15 years. *User Question: A bit confused between the earlier Q1178 and this Q1179. Q1178 stated longer duration (locked-in tenure and fixed coupon) will minimize the impact of interest rate change. i.e. lower risk. Q1179 asking about portfolio that can maximize return from interest rate volatility, a longer tenure or duration will mean the return of 10% coupon rate is locked in and the investors shouldn't expose to any interest rate fluctuation until the bond mature in 15 years. So how to maximize return from interest rate volatility?

## Q.3190 Risk Management and Investment Management  