Q.3290 Quantitative Analysis

Which of the following statement(s) is/are correct? I. Decreasing the significance level will decrease the probability of failing to reject a false null II. Decreasing the significance level will increase the power of the test. A Both statements are correct. B Only Statement I is correct. C Only Statement II is correct. D Both statements are incorrect. The correct answer is: D Decreasing the significance level will INCREASE the probability of failing to reject a false null and DECREASE the power of the test. *User Question: please check the first statement in question, it doesn't match with answer explanation, but still its correct

FRM Part 1

Q.2 Case Study 59 - Music Inc.

<div contentEditable='false' class='margin_bottom_40 view_questionhtml bg_blue ' > Using the equivalent annual annuity (EAA) approach and assuming no other expenses, Music Inc. should most likely undertake the contract proposed by: A Event Managers Ltd. as it has an EAA of &dollar;1,649,604.46. B H.S. Creations as it has an EAA of &dollar;1,465,588.24. <div class='col-sm-12 margin_bottom_30 no-cursor' id='choice_c' > C Event Managers Ltd. as it has an EAA of &dollar;2,277,104.46. The correct answer is: C In order to determine the EAA for both projects, it is necessary first to determine the NPV of the project. Using your financial calculator and the 2nd CF function, the following values are input&colon; Event Managers Ltd.&colon; CF0=–&dollar;700,000 (–&dollar;500,000 + –200,000) CF1=+&dollar;1,882,500 &#91;&dollar;3,500,000 – 990,000 – (&dollar;3,500,000 – 990,000) (0.25)&#93; CF2=+&dollar;1,882,500 CF3=+&dollar;1,882,500 CF4=+&dollar;1,882,500 The relevant discount rate is 12.50&percnt;. Using the discount rate and cash flows, the NPV of the Event Managers Ltd. contract is &dollar;4,958,116.14. For a four-year life and a 12.5&percnt; discount rate, the payment with an equivalent annuity is &dollar;1,649,604.46 (PV = -&dollar;4,958,116.14&#59; I/Y = 12.50&percnt;&#59; N = 4&#59; FV = 0; CPT PMT) H.S. Creations&colon; CF0=–&dollar;700,000 CF1=+&dollar;1,882,500 CF2=+&dollar;1,882,500 The relevant discount rate is 12.50. Using the discount rate and cash flows, the NPV of the H.S. Creations contract is &dollar;2,460,740.74. For a four-year life and a 12.5&percnt; discount rate, the payment with an equivalent annuity is &dollar;1,465,588.24 (PV = -&dollar;2,460,740.74&#59; I/Y = 12.50%&#59; N = 2&#59; FV = 0&#59; CPT &#61;&gt; PMT) Thus, the project with the highest EAA is the Event Management project. Study Session 7, Reading 19: Capital Budgeting, LOS 19(c): evaluate capital projects and determine the optimal capital project in situations of 1) mutually exclusive projects with unequal lives, using either the least com-mon multiple of lives approach or the equivalent annual annuity approach, and 2) capital rationing *User Question: why don't we take into account the opportunity cost here?

CFA Level 2

Q.2 Case Study 42 - Aseylis Lync

<div contentEditable='false' class='margin_bottom_40 view_questionhtml bg_blue ' > Using the equivalent annual annuity approach, the annuity payment for the Pincro project is closest to: A &dollar;4,733,500 B &dollar;4,920,900 <div class='col-sm-12 margin_bottom_30 no-cursor' id='choice_c' > C &dollar;5,013,900 The correct answer is: C (1+m) = (1+ r) (1+ i) (1+m) = (1.12) (1.04) m = 16.48&percnt; PV=&dollar;8,000,000; FV=0; I&sol;Y=16.48; n=2; CPT &equals;&gt; PMT = 5,013,900Study Session 7, Reading 19: Capital Budgeting, LOS 19(c): evaluate capital projects and determine the optimal capital project in situations of 1) mutually exclusive projects with unequal lives, using either the least common multiple of lives approach or the equivalent annual annuity approach, and 2) capital rationing *User Question: Why not use real rate+inflation here?

CFA Level 2

Q.2 Case Study 42 - Aseylis Lync

<div contentEditable='false' class='margin_bottom_40 view_questionhtml bg_blue ' > Using the equivalent annual annuity approach, the annuity payment for the Pincro project is closest to: A &dollar;4,733,500 B &dollar;4,920,900 <div class='col-sm-12 margin_bottom_30 no-cursor' id='choice_c' > C &dollar;5,013,900 The correct answer is: C (1+m) = (1+ r) (1+ i) (1+m) = (1.12) (1.04) m = 16.48&percnt; PV=&dollar;8,000,000; FV=0; I&sol;Y=16.48; n=2; CPT &equals;&gt; PMT = 5,013,900Study Session 7, Reading 19: Capital Budgeting, LOS 19(c): evaluate capital projects and determine the optimal capital project in situations of 1) mutually exclusive projects with unequal lives, using either the least common multiple of lives approach or the equivalent annual annuity approach, and 2) capital rationing *User Question: Why not use real rate+inflation here?

CFA Level 2

Q.820 Financial Markets and Products

An analyst is identifying the effects of storage cost, lease rate, and convenience yield on the forward prices of storable commodities. After testing these effects, the analyst has concluded the following three points: I. The presence of a lease rate reduces the forward price of a commodityII. The presence of a convenience yield increases the forward price of a commodityIII. The presence of storage costs reduces the forward price of a commodityWhich of the above statements are correct? A I & II B II & III C I & III D I only The correct answer is: D Statements II and III are incorrect. II is incorrect because the presence of a convenience yield reduces the forward price of a commodity. III is incorrect because storage costs increase the forward price of a commodity. *User Question: CHEN CHI YU, Совершенно согласен

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.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.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.4666 Valuation and Risk Models

The standard deviation of the daily portfolio value changes is given as 0.0231, and its mean as 0.0012. Given that there are 250 trading days in a year, what is the annual 99% VaR for the portfolio according to the delta-normal model? A 0.78 B 0.83 C 0.58 D 0.63 The correct answer is: B According to delta-normal mode, VaR is given by: $$\text{VaR}={ \mu }_{ \text{P} }+{ \sigma }_{ \text{P} } { \text{U} }$$ Since we are dealing with 99% VaR, it implies that $$\text{U}=-2.326$$ So that daily VaR is given by: \begin{align*} \text{VaR}=& 0.0012+0.0231\times-2.326=-0.05253 \\ \text{Annual VaR}=& \sqrt{250}\times-0.05253=-0.8306 \end{align*} *User Question: While scaling up and finding an annual VAR, shouldn't the return be multiplied by 250 and the standard deviation be multiplied by square root of 250. Since we will use the property that the sum of 'n' IID with mean R and Std Dev D is n*R and (square root of n)*(Std Dev D). This will give us a normal distribution with mean of n*R and std dev of (square root of n*Std Dev D), which will be 250*0.0012= 0.3 (mean) and standard deviation of (square root of 250)*0.0231= 0.3652. Now applying U = -2.33 we get VAR as 0.5509. How can we scale up a value of a normal distribution at a particular percentile directly by the square root of time as it is done in the solution?

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?