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2010FRM一级模拟考试(一)答案1
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2020 年 10 月 FRM 一级模拟考试(一)参考答案VaR measures the expected amount of capital one can
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金 程 教 育 WWW.GFEDU.NET 专业·创新·增值
2020
年
10
月
FRM
一级模拟考试(一)参考答案
1. Answer
:
A
VaR measures the expected amount of capital one can expect to lose within a given confidence
level over a given period of time. One of the problems with VaR is that it does not provide
information about the expected size of the loss beyond the VaR. VaR is often complemented by the
expected shortfall, which measures the expected loss conditional on the loss exceeding the VaR.
Note that since expected shortfall is based on VaR, changing the confidence level may change
both measures. A key difference between the two measures is that VaR is not sub-additive,
meaning that the risk of two funds separately may be lower than the risk of a portfolio where the
two funds are combined. Violation of the sub-additivity assumption is a problem with VaR that
does not exist with expected shortfall.
2. Answer: A
To obtain the d(1.0) discount factor, first solve for d(0.5), In the equation below, the price for
Bond A is equated to its terminal cash flow in six months, which is the principal plus the
semiannual coupon of $3.00.
101.182 = 103.00 × d(0.5)
d(0.5) = 0.9823
Next use the price and cash flows of Bond B to calculate the d(l .0) discount factor. The cash flow
in six months is the semiannual coupon of $6.00 and is discounted by d(0.5). The cash flow in one
year is the principal plus the semiannual coupon of $6.00.
102.341 = 6.00 × d(0.5) + 106.00 × d(1.0)
102.341 = 6.00 × 0.9823 + 106.00 × d(1.0)
d(1.0) = 0.9099
3. Answer: A
The level of significance is the probability of rejecting the null hypothesis when it is true. The null
hypothesis will be rejected if the z-statistic is greater than 1.645.
4. Answer: D
A strap is betting on volatility in a bullish market since it pays off more on the upside.
5. Answer: D
Standard deviation 160,000 400; 400 / 100 40= = =
The researcher is correct that a possible consequence of increasing the sample size is sampling
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more than one population. In addition, increasing sample size will increase its costs. The need for
additional precision must be balanced with cost and the risk of sampling more than one
population.
6. Answer: B
The formula for computing the forward price on a financial asset is:
( )
r δ T
0,T 0
F Se
−
=
where S
0
is the spot price of the asset, r is the continuously compounded interest rate, and δ is the
continuous dividend yield on the asset.
The no-arbitrage futures price is computed as follows:
( )
0.035 0.02 0.5
750e 755.65
−×
=
Since the market price of the futures contract is higher than this price, there is an arbitrage
opportunity. The futures contract could be sold and the index purchased.
7. Answer: C
The delta of a call option with a continuous dividend yield is given by the following formula:
( )
qt 1% 2
1
Delta N d e 0.64 e 0.63
− −×
= ×= × =
8. Answer: D
Government bond futures offer a mechanism to transfer interest rate risk, not credit risk.
9. Answer: D
The probability of default during the first two years is 1-exp(-0.015*2)=0.02955.The average
hazard rate during the first five years is(1.5*3+2.5*2)/5=1.9% The probability of default during
the first five years is 1-exp(-0.019*5)=0.09063. The probability of default between years two and
five is 0.09063 -0.02955 =0.06107.
10. Answer: B
Buy-and-hold is an asset acquisition strategy and would in fact contribute to the accumulation of
credit exposures.
11. Answer: B
Even prior to the 2007-2009 financial crisis, regulators were concerned about the relatively small
number of liquidity providers in the credit derivatives markets. They feared this nascent market
could face systemic disruption if any of the major participants were to experience distress (in
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isolation or in concert).
12. Answer: D
Let:
A = event that a policyholder has an auto policy
H = event that a policyholder has a homeowners policy
Then, based on the information given:
( )
( )
( ) ( )
( )
( ) ( )
c
c
P A H 0.15
PA H PA PA H 0.5
P A H P H P A H 0.35
=
=−=
=−=
1
11
11
Therefore, the proportion of policyholders that will renew at least one policy is shown below:
( ) ( )
( )
cc
0.4 P A H 0.6 P A H 0.8 P A H 0.53×+×+×=1 11
13. Answer: D
The minimum value for a European-style call option, cT, is given by:
(
) ( )
T 3/12
TF
max 0,S X / 1 R max 0, 86 80 / 1.03 $6.59
−+ = − =
An American-style call option must be worth as least as much as an otherwise identical
European-style call option and has the same minimum value. Note that this fact alone limits the
possible correct responses to Choices A and D. Since the American-style call is in-the-money and
therefore must be worth more than the $6 difference between the strike price and the exercise
price, you can eliminate Choice A and select Choice D without calculating the exact minimum
value.
14. Answer: C
Standards 2.1 and 2.2: Conflicts of Interest. Members and candidates must act fairly in all
situations and must fully disclose any actual or potential conflict to all affected parties. Sell-side
members and candidates should disclose to their clients any ownership in a security that they are
recommending.
15. Answer: B
Delta is 0.5 when call option is at the money. So,
VaR = 10 × 0.5 × 1.65 × 2% = 0.165
16. Answer: D
The classical linear regression model assumes homoskedasticity, which means that the variance
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does not vary across the sample and would not depend on the value of the independent variable.
17. Answer: A
N = 2 × 22; PMT = 40/2; FV = 1,000; I/Y = 5/2; CPT→PV = 867.481 = V
0
N = 2 × 22; PMT = 40/2; FV = 1,000; I/Y = 5.05/2; CPT→PV = 861.484 = V
+
N = 2 × 22; PMT = 40/2; FV = 1,000; I/Y = 4.95/2; CPT→PV = 873.534 = V
-
0
22
0
V V 2V
873.534 861.484 2(867.481)
Convexity 258.22
V(Δy) (867.481)(0.0005)
−+
+−
+−
= = =
18. Answer: C
All of the statements are correct except for the one relating to SIMEX. Nick Leeson was eligible
to trade on the SIMEX.
19. Answer: B
The z-statistic equals: (x – μ)/σ
where x is the value for a randomly selected observation from the population, μ is the mean value
for the population, and σ is the standard deviation of the population. Therefore, as indicated by the
formula, the z-statistic is the number of standard deviations x is from the mean. (Ecko is correct).
According to the normal distribution, 95% of the observations lie within 1.96 standard deviations
of the mean, which implies that 95% of the z-statistics lie within plus and minus 1.96. Therefore, 5%
of the z-statistics lie above plus 1.96 and below minus 1.96 and since the normal distribution is
symmetrical, then 2.5% of the z-statistics lie below minus 1.96. As a result, 97.5% (not 95%) of
the z-statistics lie above minus 1.96. (Charles is not correct).
20. Answer: A
Metallgesellschaft implemented a stack-and-roll hedge strategy, which uses short-term futures
contracts to hedge long-term risk exposure. The stack-and-roll hedge strategy proved ineffective
due to interim funding cash outflows created by margin calls, a shift in the market from
backwardation to contango, and other factors. No offsetting interim cash inflows were available on
their long-term customer contracts, creating a liquidity crisis that was exacerbated by their size of
their futures positions in relation to the liquidity of the market. Central themes were not
diversification, fraud, or operational controls.
21. Answer: B
The expected loss in USD is 0.005 × 1 × (1 0.4) = 0.003
This is USD 3,000.
The variance of the loss is
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