# Q.360 Immunization

A retirement benefits scheme has a liability that requires a payment of &dollar;1000 at the end of each year until 5 years ends. The institution wishes to fully immunize this liability by possessing the following assets: ASSET PRICE CASHFLOWS A 1500 500 at the end of each year for 5 years B 500 1000 at the end of each year for 4 years C 1000 500 at the end of the year for 4 years D 4000 1000 at the end of each year for 5 years Calculate the minimum cost to achieve full immunization. A 5000 B 1000 C 3000 D 6000 E 1500 the available choices for full immunization are: $$2A$$ Whose cost is 3000,$$B+2C$$ whose cost is 25000 and $$D$$ whose cost is 4000 Therefore the lowest possible cost is 3000. To make this easy you could divide the prices by the total cash flows to get 0.6, 0.5, 0.5 and 0.8 for $$A,B,C$$ and $$D$$ respectively. Clearly, the cheapest choices are $$B$$ and $$C$$ as much as possible. Note that, $$0.6=\cfrac {1500}{2500}$$ and so to others. *User Question: In this question the cost of b +2c is not coming 25000

Actuarial - FM(Financial Mathematics)

# Q.1496 Market Risk Measurement and Management

When we consider the standard errors of Bootstrap Estimators, we have two questions: how to estimate VaR and how to achieve accuracy in our estimate? Which of the following approaches CANNOT be used to solve these problems? A Applying Brute Force B Using Jackknife-after-bootstrap C Using double bootstrap D Using a large number of re-samples The correct answer is: D Using a large number of re-samples does not assure the accuracy of estimates or bootstrapping. *User Question: Not covered in 2020 syllabus

FRM Part 2

# Q.1489 Market Risk Measurement and Management

All of the following items are generally considered advantages of non-parametric estimation methods except: A little or absolute lack of reliance on covariance matrices B Use of historical data C Ability to accommodate largely skewed data D Availability of data The correct answer is: B Use of historical data is actually a disadvantage of non-parametric estimation methods because the past is not necessarily an indication of the future. In particular, data gathered from a relatively quiet (volatile) past period may lead to the development of models that underestimate (overestimate)the current risk level. *User Question: In the 2020 edition data availability is also explicitly mentioned as a drawback of non-param methods.

FRM Part 2

# Q.2633 Market Risk Measurement and Management

Jimmy Ray, a risk analyst at Alcoa Bank, has just performed a historical simulation for estimating the VAR for the fixed income portfolio of the bank based on the returns for the last 500 trading days. The 10 worst one day returns generated in the simulation are:-9,111, -8,669, -8,127, -7,098, -6,712, -6,698, -5,743, -5,189, -4,811, -4,775Which of the following is the 99% one day expected shortfall for the portfolio? A 8,251 B 6,712 C 9,111 D 7,943 The correct answer is: A From a statistical point of view, the expected shortfall, also known as the conditional VaR (CVaR), is a sort of mean excess function, i.e. the average value of all the values exceeding a special threshold, the VaR. CVAR indicates the potential loss if the portfolio is “hit” beyond VAR. ES = E[L|L is greater than VaR]Given a sample of 500 days, the 1% left tail will have 500 * 1% = 5 worst returns.The fifth worst return (6,712) is the VAR while the 99% expected shortfall will be the average of the 4 worst returns (tail losses) which in this case will be: (-9,111 + -8,669 + -8,127 + -7,098)/4 = -8,251.25 *User Question: Depends on the sample size convention. You actually have 2 possible correct answers here: A and D. A has already been described; D is correct under the typical (in Dowd's literature) calculation of HS VaR to be (1-a)*n + 1 order number of losses. This would result in VaR 6,698 and, correspondingly, (-9,111 + -8,669 + -8,127 + -7,098 + -6,712)/5 = 7,943 Admins, please remove either one of the answers, 'cause frustration is only going to mountain on this question.

FRM Part 2

# Q.2629 Market Risk Measurement and Management

Jason Tyler has invested $100,000 in the shares of Kraken Corp. To calculate the market risk of his portfolio, Tyler gathers the monthly returns for the security over the last 500 months. The 10 worst returns during this period were:-30%, -27%, -24%, -23%, -22%, -21%, -20%, -19%, -18%, -16%What is the monthly VaR for Tyler’s investment using a confidence level of 99%? A$30,000 B $16,000 C$22,000 D $27,000 The correct answer is: C The 99% VaR can be found by finding the value that separates the 1% worst values of the distribution from the rest. Given 500 data points the 1% worst value will be 500 * 1% = 5. The VaR will be the fifth-worst value of the distribution. From the data collected by Tyler it can be observed that the fifth-worst value is -22%. The VaR can be calculated as 100,000 * 22% =$22,000. *User Question: Same here. Dowd acknowledges 3 possible applications of VaR calculation and only one ist covered here as an answer.

FRM Part 2

## Q.3593 Market Organization and Structure

An investment bank offers its customers the option to carry out leveraged trades. The investors are required to maintain a margin of 30% and pay a commission of 0.25% of the trade value. An investor acquires 2,000 shares each at a price of $30. If the shares are currently trading at &dollar;40 and the borrowing cost is 8%, then the return generated by the leveraged trade is closest to: A 89.75% B 9.08% C 90.75% The correct answer is: A) Total fund required to acquire 2,000 shares = 2,000 &ast; &dollar;30 = &dollar;60,000 Margin required for the trade =$60,000 * 30% = $18,000 Commission =$60,000 * 0.25% = $150 Total out-of-pocket investment required for the trade =$18,000 + $150 =$18,150 Total funds required = &dollar;60,000 + &dollar;150 = &dollar;60,150 Funds borrowed = &dollar;60,150 - &dollar;18,150 = &dollar;42,000 Interest cost = &dollar;42,000 &ast; 8% = &dollar;3,360 Profit earned in the leveraged trade = 2,000&ast;(&dollar;40-&dollar;30) - Commissions - Interest paid = 2,000&ast;&dollar;10 - &dollar;60,000&ast;0.25% - &dollar;80,000&ast;0.25% - &dollar;3360 = &dollar;16,290 ROE = &dollar;16,290 / (&dollar;18,150) = 89.75% *User Question: Isnt the profit equation double counting the commissions? ?

## Q.332 Quantitative Analysis

Two random variables X and Y are such that V[X] = 4V[Y] and Cov[X,Y] = V[Y] Let E = X + Y and F = X – YFind Cov[E, F] A V[Y] – V[X] B Cov[X,Y] C V[Y] D 3V[Y] The correct answer is: D Cov[E,F] = Cov[X + Y,X – Y] = Cov[X,X] – Cov[X,Y] + Cov[Y,X] – Cov[Y,Y] = V[X] – V[Y] = 4V[Y] – V[Y] = 3V[Y] Logic applied: I. Given a random variable X, the covariance between X and itself is simply its varianceII. Cov[X,Y] = Cov[Y,X] *User Question: Why is Cov[X + Y,X – Y] = Cov[X,X] – Cov[X,Y] + Cov[Y,X] – Cov[Y,Y] ?