2013年11月FRM考试二级考前错题集锦！

　　1. HB第300页12.8怎么做，答案为什么要乘以3?
　　EXAMPLE 12.8: MARKET RISK CHARGE
　　The 95%, one-day Risk Metrics VAR for a bank trading portfolio is $1,000,000. What is the approximate general market risk charge, as defined in 1996?
　　A. $3,000,000
　　B. $9,500,000
　　C. $4,200,000
　　D. $13,400,000
　　Answer: D
　　答疑：本题考查的是巴塞尔协议1996年修订案中内部模型法的内容，具体的计算公式参见HB P299。3是巴塞尔协议规定的一个乘数，是对银行自己估计的风险的调整。这个乘数最小的设定值是3。此题将给出的VaR视作平均VaR来进行计算。
　
　　2. EXAMPLE 23.9: FRM EXAM 2008-QUESTION 3-31
　　Helman Bank has made a loan of USD 300 million at 6.5% per annum. Helman enters into a total return swap under which it will pay the interest on the loan plus the change in the marked-to-market value of the loan, and in exchange Helman will receive LIBOR+50 bps. Settlement payments are made semiannually. What is the cash flow for Helman on the first settlement date if the mark-to-market value of the loan falls by 2% and LIBOR is 4%?
　　A. Net inflow of USD 9.0 million
　　B. Net inflow of USD 12.0 million
　　C. Net outflow of USD 9.0 million
　　D. Net outflow of USD 12.0 million
　　答案选择Net cash outflow 9M, 我认为答案错误，此题无答案。因为TRS中，marked to market price of loan drop 2%，所以流出现金流应该是贷款利率(6.5%/2-2%)，而不是解答中的+2%。书中例题对价格减少也是“-”处理，不是“+”，所以我认为解答是错误的。
　　答疑：此题答案确实有问题
　　由于是半年结算，在*9笔结算时的现金流包括：
　　支付：
　　利息：300*6.5%/2=9.75
　　溢价：-300*2%=-6
　　收入：
　　300*（4%+0.5%）/2=6.75
　　净现金流：3;（参阅HB P567）
　　3. Handbook，p596，24.5这个题目不是很理解，感觉不是严密，求解
　　EXAMPLE 24.5：CREDIT VAR FOR ONE BOND
　　A risk analyst is trying to estimate the credit VAR for a risky bond. The credit VAR is defined as the maximum unexpected loss at a confidence level of 99.9% over a one-month horizon. Assume that the bond is valued at $1,000,000 one month forward, and the one-year cumulative default probability is 2% for this bond. What is the best estimate of the credit VAR for the bond, assuming no recovery?
　　A. $20,000
　　B. $1,682
　　C. $998,318
　　D.  $0
　　Answer: C
　　答疑：这道题首先告诉我们计算的是信用风险的VAR，信用风险的VAR的计算一般需要我们计算的是worst credit loss或者unexpected credit loss。而这边告诉我们这个VAR是*5的unexpected loss，所以需要用worst credit loss – expected loss。那么我们需要求解的就是WCL和ECL。这边给出的PD是年的，但是需要计算的VAR是月的，所以要通过PD的折算方法折算到一个月的。并且，这边说了no recovery，所以LGD=1，Exposure = $1,000,000，有了这些信息首先可以求出ECL=1,682。然后我们来看WCL（handbook P589），由于LGD = 1，所以只有两种情况，一种是不违约没有损失，一种就是违约全部损失。根据我们之前换算出的一个月的PD = 0.1682%，因此99.9%的分位点是违约的情况，所以WCL = $1,000,000，因此最终求得的credit VAR = 1,000,000-1,682 = 998,318.
　　4. 请问下p607页24.12这个题目
　　EXAMEPLE 24.12: FRM EXAM 2007-QUESTION 59
　　You are given the following information about a firm. The market value of assets at time 0 is 1,000; at time 1 is 1,200. Short-term debt is 500; long-term debt is 300. The annualized asset volatility is 10%. According to the KMV model, what are the default point and the distance to default at time 1?
　　A. 800 and 3.33
　　B.650 and 7.50
　　C.650 and 4.58
　　D.500 and 5.83
　　Answer: C
　　答疑：
　　(handbook P602),这道题要注意两个问题，首先题目中问的是“at time 1”所以采用1200，另外给出的波动率是百分比形式，所以要乘以1200。
　　5.问下老师，TED价差是怎么回事？
　　答疑：The credit spread between Eurodollar Libor and Treasuries is known as the TED spread. 可以理解为银行间同业拆借利率和国债利率的差额。由于国债利率可以看成无风险利率，而银行间同业拆借利率反映了银行间借贷的成本及信用风险，所以这个价差既反映信用风险，又反映了市场上的流动性问题。
　　6.EXAMPLE 30.5: RISKS IN FIXED-INCOME ARBITRAGE
　　Identify the risks in a fixed-income arbitrage strategy that takes long positions in interest rate swaps hedged with short positions in Treasuries.
　　A. The strategy could lose form decreases in the swap – Treasury spread.
　　B. The strategy could lose from increases in the Treasury rate, all else fixed.
　　C. The payoff in the strategy has negative skewness.
　　D. The payoff in the strategy has positive skewness.
　　Answer: C
　　答疑：fixed-income arbitrage采用的是duration match的方式，建议看一下handbook P760长期资本管理公司的案例帮助理解。总的来说，这个策略在swap-treasury spread （swap rate - treasury rate）增大的时候是亏钱的。而通常情况下这个spread增大的可能性是无限的，而缩小的可能性是有限的，因此这种策略的收益是有限的，但损失是无限的，所有payoff是左偏的，也就是负偏的。
　　7. EXAMPLE 30.6: RISKS IN CONVERTIBLE ARBITRAGE
　　Identify the risk in a convertible arbitrage strategy that takes long positions in convertible bonds hedged with short positions in Treasuries and the underlying stock.
　　A. Short implied volatility
　　B. Long duration
　　C. Long stock delta
　　D.  Positive gamma
　　Answer: D
　　答疑：convertible arbitrage strategy的基本策略是购买可转债，然后卖出国债和股票来进行duration对冲和delta对冲，对冲可转债的线性风险。因此这种策略中duration和delta都是中性的。而可转债的非线性风险还是存在的，可转债相当于买入一个一般债券+买入一个股票的看涨期权，所以存在的风险应该是正的vega以及正的gamma。
　　8.  How would you describe the typical price behavior of a low premium mortgage pass-through security？
　　A. It is similar to a U.S. Treasury bond.
　　B. It is similar to a plain vanilla corporate bond.
　　C. When interest rates fall, its price increase would exceed that of a comparable duartion U.S. Treasury.
　　D. When interest rates fall, its price increase would lag that of a comparable duration U.S. Treasury.
　　答疑：这道题主要考察的是提前偿付问题，mortgage pass-through security通常存在提前偿付的问题，一旦利率下降，借款人可以以更低的利率进行融资，因此会提前偿还之前的借款，然后重新借入一笔利息更低的借款。所以这样的债券当利率下降的时候价格虽然会上升，但是相对于普通的的债券来说上升得比较少。
　　9. Trader A purchases a down-and-out call with a strike price of USD 100 and a barrier at USD 96 from Trader B. Both traders need to unwind their delta hedge at the barrier. Which trader is more at risk if there is a price gap (discontinuity) that prevents them from exiting the trade at the barrier?
　　A. Trader A has the bigger risk.
　　B. Trader B has the bigger risk.
　　C. They both have the same risk.
　　D. Neither trader has any risk because both are hedged.
　　答疑：这道题说的是动态对冲的问题，对于一个call来说买方的对冲是卖出标的资产，对于卖方来说是买入标的资产，那么对于一个障碍期权来说，如果达到障碍水平，那么就需要清算对冲头寸，对于买方来说就要在低价的时候买入标的资产，而对于卖方来说就要在低价的时候卖出标的资产，所以卖方的损失更大。
　　10.  EXAMPLE 17.5: PROFITS FROM DYNAMIC HEDGING
　　A trader buys an at-the-money call option with the intention of delta-hedging it to maturity. Which one of the following is likely to be the most profitable over the life of the option?
　　A. An increase in implied volatility.
　　B. The underlying price steadily rising over the life of the option
　　C. The underlying price steadily decreasing over the life of the option.
　　D. The underlying price drifting back and forth around the strike over the life of the option.
　　答疑：这道题说的是持有这个看涨期权至到期，然后对它进行delta-hedge，因为是直到到期日都要进行delta hedge，所以是动态对冲，而动态对冲最担心的问题是变动太大造成对冲成本增加，因此标的资产价格变动越小成本越小。
　　11. 问下handbook上23.13那道题 答案是什么意思啊？
　　A three-year credit-linked note (CLN) with underlying company Z has a LIBOR + 60bp semiannual coupon. The face value of the CLN is USD 100. LIBOR is 5% for all maturities. The current three-year CDS spread for company Z is 90bp. The fair value of the CLN is closest to
　　A. USD 100.00
　　B. USD 111.05
　　C.USD 101.65
　　D. USD 99.19
　　答疑：这道题的解析其实写的不太好，这道题其实不涉及到CLN的结构，就把CLN就看成一个普通的公司债，coupon是LIBOR + 60bps，也就是0.056，半年付息一次。面值100，贴现率不是LIBOR，因为是公司债，所以还要考虑信用风险，所以贴现率是LIBOR + CDS spread = 0.059，然后求现值就可以了。