# Q.4829 Current Issues in Financial Markets

Which of the following is NOT true about SOFR? A It is a benchmark rate whose maturity ranges from overnight to twelve months. B It is a new benchmark rate introduced to replace LIBOR. C SOFR is based on actual transaction data rather than on estimated borrowing rates. D It is a benchmark interest rate for dollar-denominated derivatives and loans. The correct answer is: A SOFR is based on overnight borrowing in the U.S. Treasury repo market. B is incorrect: SOFR was introduced in 2018 as a new benchmark rate to replace LIBOR. C is incorrect: SOFR is focused on Treasury repurchase market transactions and is seen to be superior to LIBOR since it is based on actual transaction data rather than on estimated borrowing rates. D is incorrect: Regulators are working to ensure that SOFR becomes the benchmark rate for dollar-denominated derivatives and loans. However, other nations have found their own alternative rates. *User Question: SOFR - is an overnight rate,it was introduced to replace LIBOR ,seen as superior SOFR is to replace Libor and pushed by regulators

FRM Part 2

# Q.4827 Current Issues in Financial Markets

Isaac, an FRM candidate, gives the following statements concerning LIBOR. LIBOR is a risk-free rate. LIBOR comes in five different currencies. LIBOR is the world's most important benchmark rate. Which of the above statements is NOT true about LIBOR? A I only. B I &amp; II. C III only. D All of the above. The correct answer is: A Statement I is incorrect: Theoretically, LIBOR is not risk-free since it is subject to manipulation by banks. Banks may manipulate the rate to fit the prevailing financial situations, e.g., during a financial crisis. Statement II is correct: LIBOR comes in five different currencies, and these include the U.S. dollar, the euro, the British pound, the Japanese Yen, and the Swiss franc. Statement III is correct: LIBOR is the world's most important benchmark rate for contracts worth about USD 400 trillion, ranging from complex financial derivatives to residential mortgages. *User Question: Libor can be manipulated by banks and thus is not RF Libor comes in 5 different currencies

FRM Part 2

# Q.2759 Sampling and Estimation

The mean return on the stocks of automotive companies is $26.5, while the sample standard deviation of 36 automotive companies is$3.1. What is the standard error of the sample mean? A $0.51 B$0.73 C $4.42 The correct answer is: A) Standard Error = Standard deviation of the sample mean/&radic;Sample size =$3.1/&radic;36 = 3.1/6 = \$0.51 *User Question: I think the result should be 0,52 and not 0,51.

CFA Level 1

# Q.3727 Common Probability Distributions

The marketing department of a large mutual fund estimates that 82% of all new employees put on probation for the first year eventually get fully employed. During a recent recruitment drive, a total of 30 new employees were recruited. What is the probability that at least 27 of these will eventually earn themselves permanent roles in the company after one year? A 0.0034 B 0.0018 C 0.0082 We need the probability: $$P(X\geq 27)=P(X=27)+P(X=28)+P(X=29)+P(X=30)$$ Using the the binomial distribution: $$P(X=x)= \binom {n}{x} p^x\left(1-p\right)^{n-x}$$ We have: \begin{align}P(X\geq 27)&=\binom {30}{27} 0.82^{27}\left(1-0.82\right)^{30-27}\\ &+\binom {30}{28} 0.82^{28}\left(1-0.82\right)^{30-28}\\ &+\binom {30}{29} 0.82^{29}\left(1-0.82\right)^{30-29}\\ &+\binom {30}{30} 0.82^{30}\left(1-0.82\right)^{30-30}=0.00335 \approx 0.0034\end{align} *User Question: I think the good answer should be B) I arrive at result equal to : 0,001856

CFA Level 1

# Q.3545 Financial Markets and Products

A corporate bond has the following characteristics: Price: USD 106.50 Coupon rate: 5% Duration: 7.5 years Convexity: 101 If the credit spreads narrow by 175 basis points, then what will be the price of the bond? A USD 114.68 B USD 122.13 C USD 123.78 D USD 117.68 The correct answer is: B Return impact = (Duration * &Delta;Spread) + (1/2 *Convexity * (&Delta;Spread)2) = -(7.5 * (-0.0175)) + (1/2 *101 * (-0.0175)2) =0.1313 + 0.0155 = 0.1468 = 14.68% Price = 106.5 * (1 + 0.1468) = 122.13 *User Question: Why -(7.5 * (-0.0175)) rather than (7.5 * (-0.0175))? where does the first negative sign come from?

FRM Part 1

## Q.4620 Valuation and Risk Models

The futures price of an asset is USD 40, and the annual volatility of the futures price is 20%. If the risk-free rate is 5%, what is the value of a put option to sell futures in 6 months for USD 45? A USD 0.028 B USD 4.498 C USD 0.026 D USD 5.520 The correct answer is: D In this case, $${\text{F}}_{0}$$=40, K=45, r=0.05, s=0.20, T=0.5 The following formula gives the value of the put option: $${ \text{P} }_{ 0 }=\text{K}{ \text{e} }^{ -{ \text{r} }\text{T} }\times \text{N}\left( -{ { \text{d} } }_{ 2 } \right) -{ \text{S} }_{ 0 }{ \text{e} }^{ -{ \text{r} }\text{T} }\times \text{N}\left( -{ { \text{d} } }_{ 1 } \right)$$ Where: $${\text{P}}_{0}$$= value of the put option $${\text{F}}_{0}$$= current futures price K= strike price s= volatility of the futures price r= risk-free rate T= time $${ \text{d} }_{ 1 }=\cfrac { \text{ln}\left( \cfrac { { \text{F} }_{ 0 } }{ \text{K} } \right) +\cfrac { { \sigma }^{ 2 }\text{T} }{ 2 } }{ \sigma \sqrt { \text{T} } } =\cfrac {\text{ln}\cfrac { 40 }{ 45 } + \cfrac{{ 0.20 }^{ 2 }}{2}\times 0.5 }{ 0.20\sqrt { 0.5 } } =-0.76214 \\ { \text{d} }_{ 2 }={ \text{d} }_{ 1 }-{ \sigma \sqrt { \text{T} } }=-0.9036 \\ \text{N}\left( -{ \text{d} }_{ 1 } \right) =\text{N}\left( 0.762 \right) =0.7764 \\ \text{N}\left( -{ \text{d} }_{ 2 } \right) =\text{N}\left( 0.9036 \right) =0.8159$$ The value of the put option is given by: $${ \text{P} }_{ 0 }=\text{K}{ \text{e} }^{ -{ \text{r} }\text{T} }\times \text{N}\left( -{ { \text{d} } }_{ 2 } \right) -{ \text{S} }_{ 0 }{ \text{e} }^{ -{ \text{r} }\text{T} }\times \text{N}\left( -{ { \text{d} } }_{ 1 } \right) \\ { P }_{ 0 }=45{ \text{e} }^{ -0.05\times 0.5 }\times 0.8159 -40{ \text{e} }^{ -0.05\times 0.5 }\times 0.7764=\text{ USD } 5.520$$ *User Question: I do not understand why the calculation of d1 does not take into account the risk free rate. Any thoughts as to why that is the case? My d1 = -0.5856 .

## 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: &mu; = 120H1:&mu; &gt; 120Note that this is a one-sided test because H1 explores a change in one direction onlyUnder H0, (x&#772; - 120)/(&sigma;/&radic;n)&nbsp;&#8767;N(0,1) Next, compute the test statistic: = (125 &ndash; 120)/(20/&radic;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 &lt; 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.3190 Risk Management and Investment Management

Jack Marconi is an equity strategist at Gandhara Investment and is evaluating the performance of four large-cap equity portfolios: Azgard, Lambda, Tricky, and Jackpot. As part of his analysis, Jack computes the Sharpe ratio and the Treynor measure for all four funds. Based on his finding, the ranks assigned to the four funds are as follows: $$\begin{array}{|c|c|c|} \hline Fund & Treynor\quad Measure\quad Rank & Sharpe\quad Ratio\quad Rank \\ \hline Azgard & 1 & 4 \\ \hline Lambda & 2 & 3 \\ \hline Tricky & 3 & 2 \\ \hline Jackpot & 4 & 1 \\ \hline \end{array}$$ The difference in rankings for Funds Azgard and Jackpot is most likely due to: A Different benchmarks used to evaluate each fund's performance B A difference in risk premiums C A lack of diversification in Azgard Fund as compared to Jackpot Fund D None of the above The correct answer is: C The most likely reason for a difference in ranking is due to the absence of diversification in Azgard Fund. The Sharpe ratio measures excess return per unit of total risk, while the Treynor ratio measures excess return per unit of systematic risk. Since Azgard Fund performed well on the Treynor measure and so poorly on the Sharpe measure, it seems that the fund carries a greater amount of unsystematic risk, meaning it is not well diversified and unsystematic risk is not the relevant risk measure. *User Question: Hello, I believe the explanation is not correct (the answer is correct though). Azgard is the fund that performed poorly on the TREYNOR ratio and performed well on the Sharpe (not vice versa as you state it) Therefore, Azgard carries a greater amount of systematic risk (Beta is greater ,therefore Traenor is low) or it was not well diversified. Please comment because the current explanation is confusing - e.g. if a porftolio performes well on the Treynor it means it is WELL diversified.

## 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.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?