# Q.4658 Valuation and Risk Models

The bank of Aides has a portfolio consisting of 100,000 loans, each amounting to $1 million, and has a 1% probability of default in a year. The recovery rate is 40%, and the correlation coefficient is 0.3. Calculate $$\alpha$$, the standard deviation of the loss from the loan portfolio as a percentage of its size? A 0.033 B 0.045 C 0.056 D 0.045 The correct answer is: A The $${\alpha}$$ parameter is given by: $$\alpha =\cfrac { \sigma \sqrt { 1-\left(\text{n}-1\right)\rho } }{ \text{L}\sqrt { \text{n} } }$$ For this case, L =$ 1 million $$\rho$$ = 0.1 n = 100,000 R = 0.4 \begin{align*} \sigma & =\sqrt { { p }-{ p }^{ 2 } } \left[ { L }\left( 1-{ R } \right) \right] \\ & =\sqrt { 0.01-0.01^{ 2 } } \left[ 1\left( 1-0.4 \right) \right] =0.05970 \end{align*} Therefore, $$\alpha =\cfrac {0.05970\sqrt { 1+(100,000-1)0.3 } }{ 1\times \sqrt { 100,000 } } =0.03270$$ *User Question: In the formula of alpha you wrote 1 - (n-1), it should be 1+(n-1) right? Thanks

FRM Part 1

# Q.987 Valuation and Risk Models

Donald Morisette, a risk analyst at TNZ Associates, collects 20 days data on the stock price of ANH. The analysis of the collected data gives an estimate of the yearly volatility of the stock as 15.45%. What is the standard error of the estimate (approx.)? A 0.0244 B 0.0039 C 0.0345 D 0.0691 The correct answer is: C Standard error of the estimate = Volatility/&radic;(n) Standard error of the estimate = 0.1545/&radic;(20) = 0.03454 *User Question: Shouldn't it be sqrt(2n) as per the GARP books?

FRM Part 1

# Q.877 Financial Markets and Products

Which of the following is the most accurate explanation of the sovereign risk faced by the central counterparty (CCP)? A The sovereign risk faced by the CCP is referred to as the intervention of sovereign governments in the operation and activities of the CCP B The sovereign risk faced by the CCP is due to the failure of members who have held sovereign bonds as margin, which may have declined in value due to sovereign failure C The sovereign risk faced by the CCP is referred to as the pressure and the undue influence that can arise when one of the members of the CCP is the agency of a sovereign fund/government D None of the above The correct answer is: B The sovereign risk faced by the CCP is due to the failure of members who have held sovereign bonds as margin, which may have declined in value due to sovereign failure. Members and CCPs frequently use repo rates. During the Eurozone crises, we noted that sovereign risk is strongly correlated with repo rates. *User Question: the decline in value of the collateral (gov. bond) should be a market risk rather than sovereign risk?

FRM Part 1

# Q.1067 Valuation and Risk Models

Nicolson Finance has taken credit exposure to two corporate clients. The credit risk characteristics of these two loans have been provided below:Loan to customer 1: Sanctioned amount: USD 600 millionExposure amount: USD 540 millionProbability of default over the next year: 2%Loss rate if the customer defaults: 20%Standard deviation of the probability of default: 3%Standard deviation of the loss rate: 35%Loan to customer 2: Sanctioned amount: USD 300 millionExposure amount: USD 200 millionProbability of default over the next year: 1%Loss rate if the customer defaults: 40%Standard deviation of the probability of default: 2%Standard deviation of the loss rate: 20%The correlation between the two loan accounts is 0.5. What is the unexpected loss of the loan portfolio held by Nicolson Finance? A USD 31.23 million B USD 34.22 million C USD 29.316 million D USD 35.22 million The correct answer is: C Unexpected loss = Exposure amount * &radic;{Probability of default * (Standard deviation of loss rate)2 + Loss rate2 * Standard deviation of probability of default2}Unexpected loss (customer 1) = USD 540 million * &radic;{0.02 * (0.35)2 + 0.202 * 0.032} = USD 26.924 millionUnexpected loss (customer 2) = USD 200 million * &radic;{0.01 * (0.20) 2 + 0.402 * 0.022} = USD 4.308132 millionUnexpected loss on the portfolio = &radic;{Unexpected loss on customer 12 + Unexpected loss on customer 22 + (2 * Unexpected loss on customer 1 * Unexpected loss on customer 2 * correlation)} Unexpected loss on the portfolio = &radic;{26.9242 + 4.30812 + (2 * 26.924 * 4.3081 * 0.5)} = USD 29.316 million *User Question: If weighted is applicable in standard deviation of portfolio = σP = √ (wA2σA2 + wB2 σB2 + 2wAwBσAσBρAB), shall we also adopt same approach of applying weighing to compute the Unexpected Loss on portfolio?

FRM Part 1

# Q.4649 Valuation and Risk Models

In a particular developed country, a known rating agency published a report on the rating transition probabilities. The ratings are given as A, B, and C. According to the report, a B-rated bank has a probability of 0.20% of defaulting in one year, and A-rated bank has a probability of 0.05% of defaulting. A bank with a large loan portfolio is currently B-rated, and the management is determined for the bank to be upgraded to A-rating. How should the bank determine its economic capital? A The bank should calculate its unexpected loss at a confidence of 99.95% B The bank should calculate its unexpected loss at a confidence of 99.98% C The bank should calculate its unexpected loss at a confidence of 99.75% D All of the above The correct answer is: A The bank should use 99.95% confidence when calculating the unexpected loss to satisfy the rating transition rule. Option B is incorrect: This is suitable for an A-rated bank that wishes to be downgraded to B ratings. Option C is incorrect: The intuition is similar to that of option B. *User Question: If the explanation for Option B is correct, then isn't the confidence level should be at 99.80% for a B-rated bank?

FRM Part 1

## Q.644 Financial Markets and Products

A French carmaker expects to purchase 50,000 tons of copper at the end of April. The copper futures contracts on the Eurex Exchange are available for the delivery months of March, June, September, and December, and the size of one contract is for one ton of copper. The company took a long position in June contracts on March 1st at a futures price of 2.450 Euros per ton. If the futures price and spot price on the closing date are 2.42 and 2.30, respectively, then calculate the effective price paid in Euros and the gain or loss on the futures contract. A The effective price is €128,500 and the loss on the contract is €6,000 B The effective price is €121,000 and the loss on the contract is €6,000 C The effective price is €128,500 and the loss on the contract is €7,500 D The effective price is €121,000 and the loss on the contract is €7,500 The correct answer is: C Since the company has a long position in futures contracts and the price of the futures contract has decreased over the period of the hedge, the company has incurred a loss on its exposure in the futures contracts. The loss on the contract is €2.3 - €2.45 = €0.15 per ton of copper or €7,500The basis when the contract is closed is €2.42 - €2.30 = €0.12The effective price obtained in Euros per ton is the final spot price minus the loss on the futures. €2.42 - (€2.30 - €2.45) = €2.57The total amount received by the French automaker for the 50,000 tons of copper is 50,000 * €2.57 = €128,500 *User Question: basis calculated seems to be wrong as it should be Spot price - Future price= 2.3-2.42=-0.12?Please clarify

## Q.3316 Valuation and Risk Models

A firm originally maintains a 1% VaR for a 250-day horizon. Recently, the firm shifted to the worst-case scenario (WCS) measure. What will be the capital requirement change if the firm targets a 1% WCS instead of the previous 1% VaR capital requirement? Refer to the following table for further information. $$E[Z_i &lt; -2.33]$$ $$E[Z_i &lt; -1.65]$$ Expected WCS 1% WCS 5% WCS H=250 2.5 12.5 -2.82 -3.92 -3.54 A 168% decrease B 68% decrease C 168% increase D 68% increase The correct answer is: D The 5% VaR is -2.33 and the 1% WCS is -3.92. Capital requirement = $$\frac{3.92}{2.33} = 1.68$$ Thus, it is a 68% increase from the original value of 1 $$(1.68 – 1 = 68\%).$$ *User Question: The question said the original target was 1% VAR and not 5% VAR. Why was the answer talking about 5% VAR originally?

## Q.325 Quantitative Analysis

Compute the sample standard deviation given the following sample data:&sum;x = 31,353n = 100&sum;x2 = 10,687,041 A 8654.64 B 93 C 313.53 D 315 The correct answer is: B The formula for calculation of sample variance is s2 = 1/(n – 1)[&sum;x2 – n x&#772;2]From the data, x&#772; = 31353/100 = 313.53s2 = 1/99[10,687,041 – 100 * 313.532] = 8654.64The sample standard deviation = &radic;s2 = &radic;8654.64 = 93 *User Question: Shouldn't it be  s2 = 1/(n – 1)[∑x**2 – x̄**2] only?

## 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.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?