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CFA Lv2 固收
CFA 2级 固收 思维导图 习题，固定收益市场作为金融体系的基石之一，不仅涵盖了债券、贷款、抵押支持证券等多种金融工具，还深刻影响着投资组合的构建、风险管理以及资产定价等多个方面。
编辑于2024-09-18 22:51:44- CFA
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CFA 2级道德思维导图习题，包含I. Professionalism、II. Integrigy of Capital Markets、III. Duties to Clients、IV. Duties to Employers。
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CFA 2级 衍生品 框架图 习题，包含Key Concepts、M1 Pricing and Valuation of Forward Commitments、M1 Pricing and Valuation of Forward Commitments等。
CFA Lv2 固收
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- CFA Lv2 道德
CFA 2级道德思维导图习题，包含I. Professionalism、II. Integrigy of Capital Markets、III. Duties to Clients、IV. Duties to Employers。
- CFA Lv2 另类
CFA 2级 另类 思维导图 习题，包含M1 Introduction to Commodities and Commodity Derivatives、M2 Overview of Types of Real Estate Investment、M3 Publicly Traded Securities。
- CFA Lv2 衍生品
CFA 2级 衍生品 框架图 习题，包含Key Concepts、M1 Pricing and Valuation of Forward Commitments、M1 Pricing and Valuation of Forward Commitments等。
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CFA Lv2 固收
M1 The Term Structure and Interest Rate Dynamics
Yield curve factor models
Risks
Effective duration: parallel shift
好题
Bill states that effective duration indicates the sensitivity of a bond's price to interest rate changes and is a measure of interest rate risk. He notes: “When interest rates rise and are high relative to the bond's coupon rate, the effective duration of a callable bond falls and is lower than the effective duration of an otherwise similar straight bond. On the other hand, for the same interest rate scenario, the effective duration of a putable bond will be similar to the effective duration of a comparable straight bond.” Bill's comments regarding effective duration are most likely: A. correct with regard to callable bonds and incorrect with regard to putable bonds. B. incorrect with regard to callable and putable bonds. C. incorrect with regard to callable bonds and correct with regard to putable bonds.
B is correct Bill's comments on the effective duration of callable and putable bonds are incorrect. For callable bonds, when interest rates rise and are high compared to the bond's coupon rate, the call option is out of the money and the price of the callable bond and an otherwise identical straight bond are almost the same. Thus, the effect of an interest rate change on the price of a callable bond and the straight bond is similar—that is, the effective duration of the callable and straight bonds is similar. For putable bonds, when interest rates rise and are high compared to the bond's coupon rate, the put option is in the money and the price of the putable bond will not fall as much as the straight bond because the investor can put the bond. Thus, the effective duration of the putable bond is lower than the effective duration of the straight bond.
久期曲线，左边callable bond的ED较小，putable和straight bond一致。右边callable和straight一致，putable较小。中间的拐点就是yeild=coupon rate。
题目提到high relative to the bond's coupon rate，就是在暗示现在在拐点，因为和coupon rate一致
Key rate duration: non-parallel shift
Factors
Level
平行移动
Steepness
长短幅度不同
Curvature
长短期和中期浮动不同
Volatilities
对含权债券很重要
短期利率比长期波动大
Benchmark curve
Forward Curve
forward pricing model
no-arbitrage
F(A,B-A) = DF(B) / DF(A)
主动管理
Yield curve movement
future spot < forward -> current price undervalued
例题
Assuming that the projected spot curve two years from today will be below the current forward curve, is Bond Z fairly valued, undervalued, or overvalued? For Assignment 2, Alexander should conclude that Bond Z is currently: A. undervalued. B. fairly valued. C. overvalued
这题的关键点是projected代表预测，current代表实际。预计的利率低，说明预计的价格高，现在的价格低估，选A。
Riding the yield curve
condition: upward curve
例题
Brown's fund currently has a large position in two option-free and default-risk-free zero-coupon bonds. The first bond has a 1-year maturity and the other bond has a 10-year maturity. Brown's view is that the spot curve one year from today will reflect the current forward curve. If Brown's view of spot rates one year from today is accurate, the 1-year total return of the 10-year bond will be: A. less than the total return of the 1-year bond B. equal to the total return of the 1-year bond C. greater than the total return of the 1-year bond
B is correct A.Incorrect because both bonds will have the same total return for the 1-year period. Candidates may incorrectly assume that the 10-year bond, with its greater duration, will have greater price depreciation than the 1-year bond, as spot rates one year later will have moved higher. Given that spot rates evolved as implied by the current forward curve at the end of the first year, this will not be the case. B.Correct because both bonds will have the same total return. "...returns on bonds of varying tenor over a one-year period always equal the one-year rate (the risk-free rate over the one-year period) if the spot rates evolve as implied by the current forward curve at the end of the first year." C.Incorrect because both bonds will have the same total return for the one-year period.
这是一个很重要的结论，如果spot rate curve和forward rate curve一致，则投资多久都可以，total return一致。如果forward rate curve高于spot rate curve，我们应该roll down the yield curve，投资一个期限长的，迟些再卖掉
purchase longer maturities
关键词：倾斜向上+保持不变
Forward rate model
calc forward via spot rate
spot curve upward -> F > S
YTM
YTM是spot的平均
YTM是expected return的前提
hold to maturity
reinvest via YTM
no default
例题
Salah is currently evaluating a corporate bond and makes the following statements: ● Statement 1: "The value of a bond calculated by discounting its future cash flows by their corresponding spot rates will be the same as the value obtained by discounting future cash flows by the yield-to-maturity of a bond, as long as the yield-to-maturity is some weighted average of the spot rates." ● Statement 2: "Yield-to-maturity is a good estimate of the expected return on a bond assuming coupons are reinvested at the prevailing spot rates." ● Statement 3: "If the yield curve remains flat during the holding period, the realized rate of return on a bond will be the same as the expected rate of return." Which of Salah's three statements is least likely correct? A. Statement 1 B. Statement 2 C. Statement 3
B is correct A. Incorrect. Statement 1 is correct. The value of a bond calculated by discounting its future cash flows by their corresponding spot rates will be the same as the value obtained by discounting future cash flows by the yield-to-maturity of a bond, only if the yield-to-maturity is some weighted average of the spot rates used to value the bond. B. Correct. Statement 2 is incorrect. The yield-to-maturity provides a poor estimate of expected return if interest rates are volatile, the yield curve is steeply sloped upward or downward, there is significant risk of default, or the bond has embedded options. Yield-to-maturity is a poor estimate of expected return because it does not capture the effect of reinvesting coupons at new rates due to changes in the shape of the yield curve. Recall that to realize the initial yield-to-maturity requires that coupons be reinvested as implied by the initial yield-to-maturity. C. Incorrect. Statement 3 is correct. If the yield curve remains flat during the holding period, the realized rate of return on a bond will be the same as the expected rate of return.
用YTM来预估，有3个苛刻条件：1. 持有至到期，2. 不违约， 3. coupon用YTM再投资
B如果想改对，需要把good estimate改成poor estimate，或者把reinvested... spot rate改成YTM
Par curve
bootstrapping
例题
Tyo asks her assistant how these spot rates were obtained. The assistant replies, "Spot rates are determined through the process of bootstrapping. It entails backward substitution using par yields to solve for zero-coupon rates one by one, in order from latest to earliest maturities.' Did Tyo, s assistant accurately describe the process of bootstrapping? A. Yes B. No, with respect to par yields C. No, with respect to backward substitution
C is correct. The assistant states that bootstrapping entails backward substitution using paryields to solve for zero-coupon rates one by one, in order from latest to earliest maturities.Bootstrapping entails forward substitution, however, using par yields to solve for zero-couponrates one by one, in order from earliest to latest maturities.
例题
Katrina Black, a portfolio manager at Coral Bond Management, Ltd., is conducting a training session with Alex Sun, a junior analyst in the fixed-income department. Black wants to explain to Sun the arbitrage-free valuation framework used by the firm. Black presents Sun with Exhibit 1, showing a fictitious bond being traded on three exchanges, and asks Sun to identify the arbitrage opportunity of the bond. Sun agrees to ignore transaction costs in his analysis. Exhibit 1:Three-Year, €100 par, 3.00% coupon, Annual PayOption-Free Bond Price: Eurex: €103.7956 NYSE Euronext: €103.7815 Frankfurt: €103.7565 Black shows Sun some exhibits that were part of a recent presentation. Exhibit 3 presents most of the data of a binomial lognormal interest rate tree fit to the yield curve shown in Exhibit 2. Exhibit 2: Yield-to-Maturity Par Rates for One-,Two-, andThree-Year Annual Pay Option-Free Bonds One-year: 1.25% Two-year: 1.50% Three-year: 1.70% Based on Exhibits 1 and 2, the exchange that reflects the arbitrage-free price of the bond is: A. Eurex. B. Frankfurt. C. NYSE Euronext.
答案：C 解析：C is correct. The bond from Exhibit 1 is selling for its calculated value on the NYSE Euronext exchange. The arbitrage-free value of a bond is the present value of its cash flows discounted by the spot rate for zerocoupon bonds maturing on the same date as each cash flow. The value of this bond, 103.7815, is calculated as follows
这题要注意，给的是par curve，不是spot curve。要先把spot rate算出来，才能继续算price。不要中招。
Swap rate curve
pros compared with government bond
reflect credit risk of banks
can be compared cross countries
many maturities, highly liquid market
Spread
Swap spread
Swap rate - treasury yield
例题
Tyo continues, "We also look at risk in terms of the swap spread. We considered historical three-year swap spreads for Country B, which reflect that market" s credit and liquidity risks, at three different points in time." Tyo provides the information in Exhibit 2. Based on Exhibit 2, the implied credit and liquidity risks as indicated by the historical three-year swap spreads for Country B were the lowest: A. 1 month ago. B. 6 months ago. C. 12 months ago.
B is correct. The historical three-year swap spread for Country B was the lowest six monthsago. Swap spread is defined as the spread paid by the fixed-rate payer of an interest rate swap overthe rate ofthe " on the run" (most recently issued) govemment bond security with the samematurity as the swap. The lower (higher) the swap spread, the lower (higher) the return thatinvestors require for credit and/or liguidity risks.The fixed rate ofthe three-year fixed-for-floatingLibor swap was 0.01%% six months ago, and the three-year govemment bond yield was-0.08%six months ago. Thus the swap spread six months ago was 0.01%(-0.08%)=0.09%.0nemonth ago, the fixed rate of the three-year fixed-for-floating Libor swap was 0.16%, and thethree-year government bond yield was -0.10%. Thus the swap spread one month ago was 0.16%-(-0.10%)=0.26%Twelve months ago, the fixed rate of the three-year fixed-for-floatingLibor swap was 0.71%6, and the three-year goverment bond yield was -0.07%. Thus, the swapspread 12 months ago was0.71%-(-0.07%)=0.78%
这里考spread本身的定义。这题还好，只给了2个参数，但是如果给了一堆数字，需要知道每个spread，到底是哪个减哪个，很重要！
例题
Investment 2: Buy a four-year, zero-coupon corporate bond and then sell it after two years. Smith illustrates the returns from this strategy using the swap rate as a proxy for corporate yields In presenting Investment 2, Smith should show an annual return closest to: A. 4.31%. B. 5.42%. C. 6.53%.
答案：C 解析：C is correct. The swap spread is a common way to indicate credit spreads in a market. The four-year swap rate (fixed leg of an interest rate swap) can be used as an indication of the four-year corporate yield. Riding the yield curve by purchasing a four-year zero-coupon bond with a yield of 4.75% {i.e., 4.05% + 0.70%, [P4= 100/(1 + 0.0475)4 = 83.058]} and then selling it when it becomes a two-year zero-coupon bond with a yield of 3.00% {i.e., 2.70% + 0.30%, [P2 = 100/(1 + 0.0300)2 = 94.260]} produces an annual return of 6.53%: (94.260/83.058)0.5 – 1.0 = 0.0653.
这里要注意，是gov rate + swap spread，而不是减去
default risk
I-spread
bond yield - swap rate
credit, liquidity risk
Z-spread
试错法
P = C/(1+S1+Z) + C/(1+S2+Z)^2+...
credit, liquidity and option risk
不能比较含权和不含权债券
TED spread
MMR - T-bill rate
credit, liquidity risk
banking system
例题
Brown next focuses his attention on the short end of the yield curve. He observes the US Treasury bill rate, the overnight indexed swap rate (OIS), and the secured overnight transactions market reference rate (MRR). He collects the current rate and spread information in Exhibit 2 and uses it to calculate the 3-month TED spread. Exhibit 2 3-mth US Treasury Bill Rate: 4 bps 3-mth OIS Rate: 6 bps 3-mth MRR - 3-mth OIS Spread: 9 bps The 3-month TED spread that Brown calculates should equal: A. 5 bps B. 11 bps C. 13 bps
B is correct Because the candidate was able to extract the value of the three-month MRR from Exhibit 2 and calculate the three-month TED spread: (Three-month MRR – three-month OIS spread) = Three-month MRR – Three-month overnight indexed swap (OIS) rate Solving for Three-month MRR: Three-month MRR = (Three-month MRR – three-month OIS spread) + Three-month overnight indexed swap (OIS) rate = 9 basis points + 6 basis points = 15 basis points Three-month TED spread = Three-month MRR – Three-month US Treasury Bill Rate = 15 basis points – 4 basis points = 11 basis points
TED是MMR - T-bill。 这里外面有MMR和OIS，可以拼出MMR。
MRR-OID spread
MMR - OIS rate
money market securities
例题
Mathews is somewhat confused by the various spread measures. She is curious to know whether there is one spread measure that could be used as a good indicator of the risk and liquidity of money market securities during the recent past. The most appropriate response to Mathews' question regarding a spread measure is the: A. Z-spread. B. TED spread. C. MRR–OIS spread, formerly the Libor–OIS spread.
答案： C 解析： The MRR–OIS spread is considered an indicator of the risk and liquidity of money market securities. This spread measures the difference between MRR and the OIS rate.
送分题
SOFR
Secured funding markets
Traditional term strtucture theories
local expectations theory
短期风险中性
长期风险溢价
pure expectation theory
FW是future spot rate的无偏估计
不存在风险溢价
market segment theory
不同期限的利率市场是独立的
关键词：independent
例题
Many fixed-income portfolio managers are limited in or prohibited from high-yield bond investments. When a bond is downgraded from an investment-grade to a high-yield (junk) rating, it is referred to as a fallen angel. Because of restrictions, many pension funds sell fallen angels when they are downgraded from investment grade to high yield (junk). This coordinated selling action often results in depressed prices and attractive yields for the fallen angels. Which of the following reasons best explains why fallen angel yields often exceed otherwise identical bonds? A. The preferred habitat theory B. The segmented markets theory C. The local expectations theory
B is correct. Market segmentation in this example results from the requirement that some fixed-income fund managers are prohibited or limited in their capacity to hold high-yield bonds. The segmentation results in selling pressure on fallen angels that depresses their prices.
这题的破题点是，评级下降的时候，就不能再投资了，因为投资有限定，这就是市场分割利率，自己只能投资指定的市场，所以才导致抛售。
liquidity theory
FW has upward bias of expected future spot rate
liquity premium
higher uncertainty, higher liquity premium
题目出现流动性一般可以猜一发liquidity theory
例题
Tyo' s assistant asks, "Assuming investors require liquidity premiums, how can a yield curve slope downward? What does this imply about forward rates?,F Tyo answers, J,Even if investors require compensation for holding longer-term bonds, the yield curve can slope downward—for example, if there is an expectation of severe deflation. Regarding forward rates, it can be helpful to understand yield curve dynamics by calculating implied forward rates. To see what I mean, we can use Exhibit 1 to calculate the forward rate for a two-year Country C loan beginning in three years." With respect to their discussion of yield curves, Tyo and her assistant are most likely discussing which term structure theory? A. Pure expectations theory B. Local expectations theory C. Liquidity preference theory
C is correct. Liquidity preference theory suggests that liquidity premiums exist to compensateinvestors for the added interest rate risk that they face when lending long term and that thesepremiums increase with maturity, Tyo and her assistant are assuming that liquidity premiums exist.
看到liquidity premium，无脑猜流动性偏好理论。不要被后面的一堆文字给干扰了
preferred habitat theory
投资者对期限有强烈偏好
溢价未来让投资者转移至preferred habitats
例题
The term structure theory in which investors can be induced by relatively attractive yields to hold debt securities whose maturities do not match their investment horizon is best described as the: A. preferred habitat theory. B. segmented markets theory. C. unbiased expectations theory.
A is correct. Preferred habitat theory asserts that investors are willing to deviate from theirpreferred maturities if yield differentials encourage the switch, Segmented markets theory is morerigid than preferred habitat in that assetliability management constraints force investors to buysecurities whose horizons match those of their liabilities. The unbiased expectations theory makesno assumptions about maturity preferences. Rather, it contends that forward rates are unbiasedpredictors of future spot rates.
这里的关键是，明显和自己的预期不一致，还是愿意去投资，说明被什么吸引了，只有偏好理论可以解释
Prefer是可以偏离，不是一定偏离
关键词：deviate from
Marcoeconomic variables
factors
货币政策
经济扩展
bearish flattening
例题
During economic expansions, monetary authorities raise benchmark rates to help control inflation. This action is most often consistent with: A. bearish flattening. B. bullish steepening. C. bearish steepening.
答案： A 解析： This action is most often consistent with bearish flattening, or short-term bond yields rising more than long-term bond yields resulting in a flatter yield curve.
这里的关键是，经济扩张，货币局目的是抑制，所以肯定是熊市。
经济衰退
bullish steepening
财政政策
budget deficits rise
yield上升
budget deficits fall
yield下降
例题
When government budget deficits fall, fiscal supply-side effects are most likely to result in: A. higher bond yields. B. a steeper yield curve. C. lower bond yields.
C is correct. When goverment budget deficits fall, fiscal supply-side effects are most likelyto result in lower bond yields.
当政府预算赤字减少时，政府需要借的钱变少了，这意味着政府会发行更少的债券，这会导致市场上的债券供给减少。供给变少，价格会变高，所以yield会变低。
flight to quality
bullish flattening
例题
A flight to quality is most often associated with: A. a general rise in the level of interest rates. B. bullish flattening. C. bearish flattening.
解析： fly to qualify的特点是长短端一起跌，导致牛市，但是短端跌的少，导致平滑。所以bullish flattening。选B。
【PS1】常见的3+1避险方式：黄金，美元，美国国债，虚拟货币（有些人不认可）
【PS2】4种利率走势分析：默认利率上涨曲线。如果利率下跌，会导致价格上涨，是bullish。1. flight to quality等避险手段是买长期国债，所以长期价格涨的高，也就是长期利率跌的多，所以曲线更佳平滑，牛平。2. 如果宽松的货币政策，主要影响短期，短期跌的多，更陡峭，牛陡。反之如果利率上涨，会导致价格下跌，是bearish。3. 如果紧缩货币政策，短期涨的多，更平滑，熊平。4. 如果预计未来通胀/经济增长高，长期涨的更多，更陡峭，熊陡。
【PS3】经济下行一般直接影响股市，股市下跌。避险去买国债，债券上涨。不同市场。
fixed-income trade
steeper curve
卖长期，买短期
flatter curve
买长期，卖短期
M2 The Arbitrage-Free Valuation Framework
Arbitrage-free valuation
套利机会
value additivity
Dominance
例题
Alvarez is a junior fixed-income analyst with Canzim Asset Management. Her supervisor, Stephanie Hartson, asks Alvarez to review the asset price and payoff data shown in Exhibit 1 to determine whether an arbitrage opportunity exists. Exhibit 1:Price and Payoffs for Two Risk-Free Assets Asset | Price Today | Payoff in One Year Asset A | $500 | $525 Asset B | $1,000 | $1,100 Based on Exhibit 1, Alvarez finds that an arbitrage opportunity is: A. not available. B. available based on the dominance principle. C. available based on the value additivity principle
dominance principle指的是不同东西低买高卖讨论。比如借2A卖了后买1B，期初金额是0，期末汇报是1100-525*2=50，套利。选B。
【PS】value additivity principle指的是单个东西的价格和总价不同。比如一个组合有几个债券等组成部分。这几个组成部分单独买的价格的合计，不等于直接买这个组合的价格，产生套利空间。
【PS2】2种套利方法，基于价格套利Value additivity，基于收益率套利Dominance。前者是未来的收益抹平，套今天的价格差。后者今天现金流抹平，套未来的收益差。
【PS3】这套题是可以强行卖(1100/525)份A，买1份B。套期初的价格，但是，要领会出题人的意图。
Implications of arbitrage-free valuation
P = C/(1+S1) + C/(1+S2)^2 + ...
Modern term structure models
Arbitrage-free model
回归模型
假设市场利率是正确
使用risk-neutral probabilities
参数会随着时间发生改变
例题
Which term structure model can be calibrated to closely fit an observed yield curve? A. The Ho-Lee model B. The Vasicek model C. The Cox-lngersoIl-Ross model
A is correct. The HoLee model is arbitrage free and can be calibrated to closelymatch the observed term structure.
代表
Ho-Lee model
没均值回归
利率可能为负
KWF model
没均值回归
不产生负利率
例题
Which of the following statements comparing the Ho-Lee and Kalotay-WilliamsFabozzi (KWF) equilibrium term structure models is correct? A. The Ho-Lee model assumes constant volatility, while the KWF model does not. B. The KWF model incorporates the possibility of negative rates, while the HoLee model does not. C. The KWF model describes the log of the dynamics of the short rate, while the Ho-Lee model does not.
答案： C 解析： The KWF equilibrium term structure model is similar to the Ho-Lee model in that it assumes constant drift, no mean reversion, and constant volatility, but the KWF model describes the log of the dynamics of the short rate, while the Ho-Lee does not
HK无套利，都假设波动稳定，所以A是错的。CK无负数，所以B是错的。并且log才可以无负数，所以C是对的。
Equilibrium model
不反应市场信息
使用real probabilities
经济变量影响利率
代表
Vasicek model
有均值回归
利率可能为负
Cox-Ingersoll-Ross model
有均值回归
不产生负利率
对比
无套利模型参数更多
HK无套利，CK不为负
modern model (multi-factor)
例题
Porter also analyzes Government-guaranteed mortgage backed securities (MBS). He considers the appropriate method to value those MBS, and the interest rate term structure model he should use to generate interest rates. Porter decides to use a model that avoids the generation of negative rates. Which of the following interest rate term structure models most likely meets Porter's preference? A. Ho-Lee model B. Vasicek model C. Cox-Ingersoll-Ross model
正确答案：C
A.Incorrect because the Ho-Lee model, similar to the Vasicek model, has constant volatility, and interest rates may become negative because of the symmetry of the normal distribution and the model’s use of constant volatility. B.Incorrect because a key characteristic of the Vasicek model worth noting is that it is theoretically possible for the interest rate to become negative. C.Correct because in the Cox-Ingersoll-Ross (CIR) model the short-rate volatility is a function of the short rate. Importantly, at low rates, [the random term] becomes small, which prevents rates from turning negative.
只有CIR和KWF不产生负利率
Binomial trees model
利率二叉树
Equal probability
上下都是50%
middle forward rate用FW rate model计算
2个节点差了e^(2o)
计算
o的来源
历史
Implied
例题
Ann tells Hake that he needs to calibrate the binomial interest rate tree to match a term structure of interest rates. Hake wants to better understand this process and asks Ann to describe it. Ann says, "Calibrating an interest rate tree requires an iterative process that ensures that the upper and lower rates are consistent with the volatility assumption, the interest rate model, and the observed market value of the benchmark bond. The cash flows of the bond are discounted using the interest rate tree, and if this doesn't produce the correct price, another pair of forward rates is selected and the process is repeated." Is Ann most likely correct in regard to his comments on calibrating a binomial interest rate tree? A. No, he incorrectly describes the iterative process. B. Yes. C. No, he is incorrect regarding the interest rate used.
B is correct Ann is correct with regards to his comments on calibrating a binomial interest rate tree.
利率二叉树的构建，先有隐藏利率和波动性，然后去构建得到基于spot rate的二叉树；然后去市场找个benchmark债券，把自己算出来的利率二叉树套一下，看看最后价格是不是一致的，如果不是的话，调整利率二叉树，然后重新算。
例题
Which of the following statements regarding binomial interest rate trees is correct? A. The only requirements needed to create a binomial interest rate tree are current benchmark interest rates and an assumption about interest rate volatility. B. Potential interest rate volatility in a binomial interest rate tree can be estimated using historical interest rate volatility or observed market prices from interest rate derivatives. C. A bond value derived from a binomial interest rate tree with a relatively high volatility assumption will be different from the value calculated by discounting the bond’s cash flows using current spot rates.
答案： B 解析： 在构建利率二叉树时需要假设利率波动性， 可以使用历史波动性， 也可 以根据利率衍生品来估计隐含波动性。 因此选项B正确。 对于选项A， 构建利率二叉树需要三个条件， 利率曲线、 利率波动性以及利率模 型。 因此该选项错误。 对于选项C， 同一个债券， 使用即期利率定价与使用利率二叉树定价的结果一致。 因此该选项错误。
注意利率二叉树3个条件，以及2个来源
例题
Holly states: "I believe the iterative process must involve a trial-and-error search to determine the higher and lower rates subsequent to each node in the tree, which branches out from an average yield centered on the forward rate curve. The rates must also be consistent with an assumption of log-normality, the volatility assumption, and the observed market value of the bond being evaluated. When describing calibrating the interest rate tree, Holly is least likely correct with respect to the: A. volatility assumption. B. assumption of log-normality. C. value of the bond being evaluated.
答案：C 解析：C is correct. Calibration of the interest rate tree is dependent on a volatility assumption, an interest rate model, and the observed market value of the benchmark bond—not the bond being evaluated. The assumption of log-normality results in the binomial tree spreading out around the implied forward rate curve, but slightly higher. A and B are incorrect, as they are part of the interest rate tree calibration process.
要注意，利率是log分布是其中一个假设，虽然理论上，利率可以是负数，但是我们正常情况不考虑，所以假设利率Log分布。
而我们一般找benchmark，不直接假设要估值的股票的价格是正确的。目的是因为我们拿其他假设正确的benchmark，来给我们要估值的股票来估值，才能判断要估值的股票是高估还是低估。否则上来直接假设它的价格是合理的，这个游戏就没法玩了。
Pathwise valuation
n period, 2的n-1次方paths
算术平均
蒙特卡洛模拟
Adv: 解决路径依赖
适用MBS
例题
Porter also analyzes Government-guaranteed mortgage backed securities (MBS). He considers the appropriate method to value those MBS, and the interest rate term structure model he should use to generate interest rates. Porter decides to use a model that avoids the generation of negative rates. Which of the following methods is most appropriate for valuing the government-guaranteed MBS that Porter is examining? A. Pathwise valuation based on a binomial tree B. Pathwise valuation based on Monte Carlo Simulation C. Backward induction valuation based on a binomial tree
正确答案：B B.Correct because the Monte Carlo simulation paths are different enough such that path-dependent securities, such as mortgage-backed securities, can be analyzed in ways that provide insights not possible in binomial trees, because Monte Carlo techniques provide greater flexibility to change parameters over time. The Monte Carlo method is an alternative method for simulating a sufficiently large number of potential interest rate paths to discover how the value of a security is affected Monte Carlo methods are often used when a security's cash flows are path dependent. For example, the valuation of mortgage-backed securities depends to a great extent on the level of prepayments and prepayments tend to increase when interest rates fall, because borrowers are more likely to pay off mortgage loans and refinance at lower interest rates.
利率二叉树只有2个分支，但是MBS可能有很多分支，所以只能蒙特卡洛模拟
如果利率低，大家可能提前归回，影响MBS剩下的本金，进一步影响MBS剩下的现金流，所以MBS是前面影响后面。
Pathwise是说路径，比如2%(t1)->3%(t2)->4%(t3)
二叉树：backward induction
适用callable，putable
例题
Zhang adds: "While your example represents good practice, we also need to be able to value bonds with embedded options where expected cash flows of bonds with options change depending on the path of future interest rates. We typically construct an interest rate tree as a visual representation of the paths of future interest rates, with the average of possible future values being centered on the current yield curve. The following three steps can be employed to construct an interest rate tree for valuing a particular bond: Step 1 Using prices of the benchmark bonds, determine the current par curve. Step 2 Estimate interest rate volatility, and calculate the potential paths of future rates. Step 3 Starting with the current market price, calculate each successive node's value.” The interest rate tree must then be calibrated to fit the actual yield curve while being consistent with an underlying interest rate model. Which of Zhang's three steps to value bonds with embedded options is least likely correct? A. Step 1 B. Step 2 C. Step 3
答案：C 解析：C is correct. Step 3 (“Starting with the current market price, calculate each successive node’s value.”) is incorrect. To find the value of a bond at a particular node in a binomial tree, the backward induction methodology is used. Starting with the known bond valuation at maturity (barring default), preceding values can be calculated backwards using the interest rate model generated. A and B are incorrect. Steps 1 and 2 are correct steps in constructing a binomial interest rate tree
这里要注意，虽然step 1说的是par curve，没有spot curve那么好，但是也并不是错的。确定了par curve还可以继续确定spot rate。而step 3明显和backwardation不一致。选择题选择一个最佳选项，所以选C，错的最厉害。
M3 Valuation and Analysis of Bonds with Embedded Options
Callable & Putable Bond
Option value
V(callable) = V(s) - V(call)
V(putable) = V(s) + V(put)
r
callable
利率下降价格升的少
例题
Samuel & Sons is a fixed-income specialty firm that offers advisory services to investment management companies. On 1 October 20X0, Steele Ferguson, a senior analyst at Samuel, is reviewing three fixed-rate bonds issued by a local firm, Pro Star, Inc. The three bonds, whose characteristics are given in Exhibit 1, carry the highest credit rating. A fall in interest rates would most likely result in: A. a decrease in the effective duration of Bond #3. B. Bond #3 having more upside potential than Bond #2. C. a change in the effective convexity of Bond #3 from positive to negative.
B is correct. A fall in interest rates results in a rise in bond values. For a callable bond, such asBond #2, the upside potential is capped because the issuer is more likely to call the bond. Incontrast, the upside potential for a putable bond, such as Bond #3, is uncapped. Thus, a fall ininterest rates would result in a putable bond having more upside potential than an otherwiseidentical callable bond, Note that A is incorrect because the effective duration of a putable bondincreases, not decreases, with a fall in interest rates, the bond is less likely to be put and thusbehaves more like an option-free bond,C is also incorrect because the effective convexity of a putable bond is always positive. It is the effective convexity of a callable bond that will change from positive to negative if interest rates fall and the call option is near the money.
Callable bond的convexity会变，但是putable bond的convexity永远是正的
例题
The one-yeai; two-yearf and three-year par rates are 2.250%, 2.750%, and 3.100%, respectively. Based on an estimated interest rate volatility of 10%,Ferguson constructs the binomial interest rate tree shown in Exhibit 2. The value of Bond #2 is closest to: A. 102.103% of par. B. 103.121% of par. C. 103.744% of par.
A is correct
务必自己亲手算一次
putable
利率上升价格跌的少
Volatility
interest rate volatility
影响binomial tree: spread out
波动变大，option的价值上升
volatility change -> option value change -> bond price/value change
valuation of risky callable/putable bonds
OAS
二叉树（试错法）
计算
Callable OAS = Z - |call|
Putable OAS = Z + |put|
可以对比不含权和含权债券
例题
Hsu selects two corporate bonds that are callable at par and have same characteristics in term of maturity, credit quality, and call dates. Hsu finds that the option-adjusted spread (OAS) is 25.5 bps for Bond 1 and 30.3 bps for Bond 2. He would most likely conclude that relative to Bond 1, Bond 2 is A. overpriced. B. fairly priced. C. underpriced.
答案： C 解析： 两个债券的特征相同， 信用质量一致， OAS应该相同。 如果OAS不相同， OAS越大， 债券价格越低， 即债券被低估。 因此选项C正确。
送分题，选这题是为了了解下OAS的考法。
Effect of interest rate volatility on OAS
Capped and Floored Floating-Rate Bonds
计算binomial tree
Option-free floater: price = par
Cap: coupon>cap，只取cap
例题
A Floating-rate bond reset coupon annualy, capped at 5.00%. Given the following binomial intetest rate tree, the value of the bond is closest to: A. 99.697% of par. B. 99.936% of par. C. 101.153% of par.
送分题，必须熟练掌握。一定要自己算一次。
Floor: coupon<floor，只取floor
V(capped) = V(S) - V(embedded cap)
V(floored) = V(S) + V(embedded floor)
Option bond types
Simple
Callable
Putable
Extendible bond
Complex
Estate put
Sinking fund bond
例题
Exhibit 4: Selected Data for Rl Convertible Bond Straight bond value: 978 Value of embedded issuer call option: 43 Value of embedded investor put option: 26 Value of embedded call option on issuer's stock: 147 Conversion price: 12.50 Current common stock share price: 11.75 Based on Exhibit 4 the arbitrage-free value of the RI bond is closest to: A. €814., B. €1,056. C. €1,108.
C is correct. The value of a convertible bond with both an embedded call option and a putoption can be determined using the following formula. Value of callable putable convertible bond= Value of straight bond + Value of call option on theissuer's stock- Value of issuer call option + Value of investor put option. Value of callableputable bond=€978+€147-€43+€26=€1.108.
送分题
Interest rate risk
Duration
Effective duration = (P(-) - P(+)) / (2 * Delta(Curve) * P(0))
r上升，ED Putable下降
r下降，ED callable下降
含权债券的ED小于S bond的ED
One-side duration
Callable: lower one-sided down-duration
例题
For embedded option bonds, one-side duration is more commonly used to measure interest rate risk rather than effective duration. Which one of the following statements about one-side duration is correct? A. One-sided up-duration is applied only when price rises. B. One-sided up-duration is larger than one-sided down-duration for a callable bond. C. One-sided up-duration is larger than one-sided down-duration for a putable bond.
答案： B 解析： 对于可赎回债券而言， 当利率下降时债券有可能被发行人提前赎回， 所 以利率下降时债券价格上涨幅度很有限， 因此利率下降时债券价格对利率变化 的敏感度相比于利率上升时债券价格对利率变化的敏感度更低， 因此利率上升 时的单边久期（one-sided up-duration） 大于利率下降时的单边久期（one-sided down-duration） 。 因此正确选项为B。
要理解one side duration是针对利率的变化
Putable: lower one-sided up-duration
Key rate duration
Callable/putable: exercise date和maturity date最大
Effective convexity
EC = (p(-) + p(+) - 2p(0)) / (P(0) * Delta(Curve)^2)
Callable: r下降 -> negative convexity
Putable: r上升 -> more convexity
Effect of yield curve changes
Level
r下降 -> callable比straight下降的少
r上升 -> putable比straight上升的少
Shape
call: r下降 -> value of call 上升
put: r上升 -> value of put上升
Convertiable bond
Calc
Conversion price
bond issue price / conversion ratio
例题
On 19 October 20X0, Ferguson analyzes the convertible bond issued by Pro Star given in Exhibit 3. That day, the option-free value of Pro Starf s convertible bond is $1,060 and its stock price $37.50. The conversion price of the bond in Exhibit 3 is closest to: A. $26.67. B. $3226. C. $34.19.
B is correct. The conversion price of a convertible bond is equal to the par value divided bythe conversion ratio that is,$1,000/31=$32.26 per share.
注意辨析conversion price和market conversion price
例题
Armand Gillette, a convertible bond analyst, stops by Bimnchi' s office to discuss two convertible bonds. One is issued by DeLille Enterprises (DE), and the other is issued by Raffarin Incorporated (RI). Selected data for the two bonds are presented in Exhibits 3 and 4. Gillette makes the following comments to Bianchi: ■ "The DE bond does not contain any call or put options, but the RI bond contains both an embedded call option and put option. I expect that DeLille Enterprises will soon announce a common stock dividend of €0.70 per share." ■ "My belief is that, over the next year, Raffarin’s share price will appreciate toward the conversion price but not exceed it." Based on Exhibit 3, if DeLille Enterprises pays the dividend expected by Gillette, the conversion price of the DE bond will: A. be adjusted downward. B. not be adjusted. C. be adjusted upward.
A is correct The conversion price would be adjusted downward because Gillette's expecteddividend payment of€0.70 is greater than the threshold dividend of 0.50.
这里要了解threshold dividend的作用。如果超过的话，因为bond价格是有变低的，所以conversion price也需要做相应的下调
Market conversion price
market price of bond / conversion ratio
Conversion value
market price of stock * conversion ratio
Straight value
value of bond if not convertible
Minmum value
max(conversion value, straight value)
Market conversion premium
market conversion price - market price
Armand Gillette, a convertible bond analyst, stops by Bimnchi's office to discuss two convertible bonds. One is issued by DeLille Enterprises (DE), and the other is issued by Raffarin Incorporated (RI). Selected data for the two bonds are presented in Exhibits 3 and 4. Based on Exhibit 3, the market conversion premium per share for the DE bond on 17 September 20X5 is closest to: A. €0.90. B. €2.13. C. €2.53.
B is correct. The market conversion premium per share is equal to the market conversionprice minus the underlying share price. The market conversion price is calculated as follows. Convenible bond priceMarket conversion price =1123/1000*10=11.23 per share. The market conversion premium per share is then calculated as follows: Market conversion premium per share = Market conversion price - Underlying share price =11.23-9.10=2.13.
注意这里是market - market
Market conversion premium ratio
market conversion premium pre share / market price of stock
Downside risk of convertible bond
downside risk of bond
Upside potential of convertible bond
prospectives of underlying common stock
Valuation
convertible bond = s bond + value of call
例题
Jerome Powell, an investment consultant, is analyzing a convertible bond issued by Bank of ICBR with a conversion price of $40 for his client. And he tells the client that the current risk and return characteristics of this bond are similar to those of ICBR 's common stock. If Jerome Powell’s statement is correct, the current stock price of ICBR is most likely to be? A. $42 B. $34 C. no enough information to infer the stock price
答案： A 解析： 当可转换债券的转换价格小于标的股票的价格时， 可转换债券的风险收 益特征与该债券发行方的股票相似。 因此正确选项为A。 对于选项B， 当ICBR公司股票价格为$34时， 可转换债券的转换价格大于标的股 票的价格， 此时可转换债券的风险收益特征与该债券发行方的不含权债券相似。 因此， 该选项错误。 对于选项C， 基于题目中可转换债券呈现出与标的股票相似的风险收益特征， 可 以判断出当前股价应大于转换价格。 因此， 该选项错误。
这题要领会出题人意图，考点是stock一般是高于转换价格。不要纠结是42还是43。
characters
fixed-income equivalent
market stock price < conversion price
common stock equity
market stock price > conversion price
hybrid security
Analysis
stock price volatility下降 -> value of call 下降 -> convertible bond value下降
stock price下降 -> return on convertible bonds exceed stock
stock price上升 -> bond will underperform
例题
The Busan Fund, based in South Korea, invests in Asian corporate bonds, including convertible bonds. One of the convertible bonds in the fund was issued on 15 June 2015 by Soyang, Ltd., an electronics manufacturer, when Soyang’s common stock was selling for KRW3,245 per share. Each bond has a par value of KRW1,000,000. The initial conversion price was KRW4,500. The bonds have a threshold dividend of KRW300 and a change of control conversion price of KRW3,500. At the end of trading on 2 September 2015, the market conversion price for Soyang bonds was KRW5,025 and its common shares closed at KRW2,985. The next day, Soyang, which had never previously paid a dividend to common shareholders, paid a dividend of KRW400 per share. At the close of trading on 2 September 2015, the risk–return characteristics of Soyang’s bonds most closely resemble those of: A. shares of common stock B. busted convertibles C. hybrid securities
正确答案：B A.Incorrect because the embedded options are very out of the money, so a change in the price of the common stock will not have a substantial impact on the value of the convertible bonds. B.Correct. At the close of trading, the market conversion price of the bonds was KRW5,025, which represents a conversion premium of 68.3% = (KRW5,025/KRW2,985) – 1. The embedded call option is so far out of the money that a small change in the price of Soyang’s common stock will have a minimum impact on the value of the convertible bonds. Therefore, the bonds will resemble option-free bonds, also known as busted convertibles. C.Incorrect because the embedded options are very out of the money, so a change in the price of the common stock will not have a substantial impact on the value of the convertible bonds.
busted convertibles这个单词建议混个眼熟
M4 Credit Analysis Models
valuation based on non-arbitrage
fixed rate
float rate
impact on interest rate volatility
volatility上升，CVA下降
Credit risk and CVA
Concept
Default risk & credit risk
Expected exposure to default loss
RR & LGD
POD
Calc
VND & CVA
fair value of bond =VND - CVA
例题
Daniela Ibarra is a senior analyst in the fixed-income department of a large wealth management firm. Marten Koning is a junior analyst in the same department and David Lok is a member of the credit research team. The firm invests in a variety of bonds. Ibarra is presently analyzing a set of bonds with some similar characteristics, such as four years until maturity and a par value of €1r000. Exhibit 1 includes details of these bonds. Ibarra asks Koning to assist her with analyzing the bands. She wants him to perform the analysis with the assumptions that there is no interest rate volatility and that the government bond yield curve is flat at 3%. The market price of Bond B1 is €875. The bond is: A. fairly valued. B. overvalued. C. undervalued.
The value of the bond if it were default free would be 1,000 × DF for Date 4 = €888.49. Fair value of the bond considering CVA = €888.49 – CVA = €888.49 – €36.49 = €852.00. Because the market price of the bond (€875) is greater than the fair value of €852, B is correct.
核心题，必须手动算次，公式必须熟练掌握
credit spread
只四求一算I/Y，减去rf得到利差
POD & RR
例题
Lena Liecken is a senior bond analyst at Taurus Investment Management. Kristel Kreming, a junior analyst, works for Liecken in helping conduct fixed-income research for the firm1 s portfolio managers. Liecken and Kreming meet to discuss several bond positions held in the firm' s portfolios. Bonds I and II both have a maturity of one year; an annual coupon rate of 5% of and a market price equal to par value. The riskfree rate is 3%. Historical default experiences of bonds comparable to Bonds I and II are presented in Exhibit 1. Exhibit 1:Credit Risk Information for comparable Bonds Bond: I Recovery Rat: 40% Percentage of Bonds ThatSurvive and Make FullPayment: 98% Based on Exhibit 1, the expected future value of Bond I at maturity is closest to: A. 98.80. B. 103.74. C. 105.00.
B is correct. In the event of no default, the investor is expected to receive 105. In the event ofa default, the investor is expected to receive 105-[105x(1-0.40)]=42. The expected futurevalue of the bond is, therefore, the weighted average of the no-default and default amounts, or(105x0.98)+(42x0.02)=103.74.
送分题
这题相当于把CVA拆了出来，只让你求一期的FV。需要看懂题目到底是在问什么
Risk-neutral default probability
例题
Lena Liecken is a senior bond analyst at Taurus Investment Management. Kristel Kreming, a junior analyst, works for Liecken in helping conduct fixed-income research for the firm1 s portfolio managers. Liecken and Kreming meet to discuss several bond positions held in the firm' s portfolios. Bonds I and II both have a maturity of one year; an annual coupon rate of 5%, and a market price equal to par value. The riskfree rate is 3%. Historical default experiences of bonds comparable to Bonds I and II are presented in Exhibit 1. Exhibit 1:Credit Risk Information for Comparable Bonds Bond | Recovery Rate | Percentage of Bonds That Survive and Make Full Payment I | 40% | 98% II | 35% | 99% Based on Exhibit 1, the risk-neutral default probability for Bond I is closest to: A. 2.000%. B. 3.175%. C. 4.762%.
因为题目提到market price = par，所以不能直接用2%。等价公式应该为： 100 * (1+3%) = 105 * p + 105 * 40% * (1-p) -> p = 3.175%。
【PS1】Percentage of Bonds That Survive and Make Full Payment不等于risk-neutral default probability。
【PS2】等号左边的利率把面值折算到未来时点不要忘记。
Expected yield
例题
Anna Lebedeva is a fixed-income portfolio manager Paulina Kowalski, a junior analyst, and Lebedeva meet to review several positions in Lebedeva' s portfolio. Lebedeva begins the meeting by discussing credit rating migration. Kowalski asks Lebedeva about the typical impact of credit rating migration on the expected return on a bond. Lebedeva asks Kowalski to estimate the expected return over the next year on a bond issued by Entre Corp. The BBB rated bond has a yield to maturity of 5.50% and a modified duration of 7.54. Kowalski calculates the expected return on the bond over the next year given the partial credit transition and credit spread data in Exhibit 1. She assumes that market spreads and yields will remain stable over the year. Based on Exhibit 1, the one-year expected return on the Entre Corp, bond is closest to: A. 3.73%. B. 5.50%. C. 7.27%.
A is correct. The expected return on the Entre Corp. bond over the next year is its yield to maturity plus the expected percentage price change in the bond over the next year. In the following table, for each possible transition, the expected percentage price change is the product of the bond’s modified duration of 7.54, multiplied by –1, and the change in the spread, weighted by the given probability: Expected percentage price change = (0.0002 × 6.786%) + (0.0030 × 4.524%) + (0.0480 × 3.016%) + (0.8573 × 0.000%) + (0.0695 × –14.326%) + (0.0175 × –37.700%) + (0.0045 × –60.320%) = –1.76715%. So, the expected return on the Entre Corp. bond is its yield to maturity plus the expected percentage price change due to credit migration: Expected return = 5.50% – 1.77% = 3.73%.
必须自己多算几次，熟练掌握
因为大概率降级，所以期望回报可能更低，肯定由5.5下调，考试可以直接选A，插旗子，检查的时候再好好算。
Securitized debt credit analysis
Covered bonds
dual recourse
Credit analysis
assets
homogeneity
granularity
counterparty analysis
structure and credit enhancement
例题
Lebedeva and Kowalski next discuss the drivers of the term structure of credit spreads. Kowalski tells Lebedeva the following: Statement 1 The credit term structure for the most highly rated securities tends to be either flat or slightly upward sloping. Statement 2 The credit term structure for lower-rated securities is often steeper, and credit spreads widen with expectations of strong economic growth. Which of Kowalski' s statements regarding the term structure of credit spreads is correct? A. Only Statement 1 B. Only Statement 2 C. Both Statement 1 and Statement 2
A is correct. For investment-grade bonds with the highest credit ratings, credit spreads areextremely low, and credit migration is possible only in one direction given the implied lowerbound of zero on credit spreads. As a result, the credit term structure for the most highly ratedsecurities tends to be either flat or slightly upward sloping. Securities with lower credit qualityhowever, face greater sensitivity to the credit cycle. Credit spreads would decrease, not increase.with the expectation of economic growth, There is a countercyclical relationship between creditspreads and benchmark rates over the business cycle. A strong economic climate is associatedwith higher benchmark yields but lower credit spreads because the probability of issuersdefaulting declines in such good times.
直接记结论： 1. 投资级，期限结构平坦或者上升 2. 垃圾债，陡峭 3. 经济变好，利差变小
Approach
load-by-load
RE
portfolio-based
Auto
statistics-based
Credit card
例题
Lebedeva ends the meeting by asking Kowalski to recommend a credit analysis approach for a securitized asset-backed security (ABS) held in the portfolio. This non-static asset pool is made up of many medium-term auto loans that are homogeneous, and each loan is small relative to the total value of the pool. Given the description of the asset pool of the ABS, Kowalski should recommend a: A. loan-by-loan approach. B. portfolio-based approach. C. statistics-based approach.
B is correct. The auto ABS is granular, with many small loans relative to the size of the totalportfolio. The auto loans are also homogeneous. These characteristics support using theportfolio-based approach. A loan-by-loan approach would be inefficient because of the largenumber of basically similar loans, this approach is best for a portfolio of discrete, large loans thatare heterogeneous. A statistics-based approach would work for a static book of loans, whereas theauto loan portfolio would be dyamic and would change over time.
如果不理解3者的区别，直接记典型案例就可以
credit spread adjustment
micro
expected loss from default
liquidity
taxation
risk aversion
macro
expected inflation rate
expected real rate of return
risk aversion
models
Reduced-form model
nature
when default
exogenous variable
Adv
inputs are observable variables
Reflect the business cycle
all information available in financial market
Disadv
not explain why default
assume default can happen anytime
例题
Bond IV is an AA rated bond that matures in five years, has a coupon rate of 6%,and a modified duration of 4.2. Liecken is concerned about whether this bond will be downgraded to an A rating, but she does not expect the bond to default during the next year. Kreming constructs a partial transition matrix, which is presented in Exhibit 3, and suggests using a model to predict the rating change of Bond IV using leverage ratios return on assets, and macroeconomic variables Kreming's suggested model for Bond IV is a: A. structural model. B. reduced-form model. C. term structure model.
B is correct. A reduced-form model in credit risk analysis uses historical variables, such asfinancial ratios and macroeconomic variables, to estimate the default intensity. A structural modelfor credit risk analysis, in contrast, uses option pricing and relies on a traded market for theissuer's equity.
有宏观，无脑简约模型
Structure model
nature
depend on B/S structure
explain why default
例题
David Lok has estimated the probability of default of Bond B1 to be 1.50%. He is presenting the approach the research team used to estimate the probability of default. Which of the following statements is Lok likely to make in his presentation if the team used a reduced-form credit model? A. Option pricing methodologies were used, with the volatility of the underlying asset estimated based on historical data on the firm' s stock price. B. Regression analysis was used, with the independent variables including both firm-specific variables, such as the debt ratio and return on assets, and macroeconomic variables, such as the rate of inflation and the unemployment rate. C. The default barrier was first estimated, followed by the estimation of the probability of default as the portion of the probability distribution that lies below the default barrier
B is correct. Statement B is correct because a reduced-form credit model involves regressionanalysis using information generally available in the financial markets, such as the measuresmentioned in the statement.Statement A is incorrect because it is consistent with the use of a stnictural model and not areduced-form model. It is a structural model that is based on the premise that a firm defaults on itsdebt if the value of its assets falls below its liabilities and that the probability of that event has thecharacteristics of an option. Statement C is incorrect because it is consistent with the use of a structural model and not areduced-form model. A structural model involves the estimation of a defauit barrier, and defaultoccurs if the value of fim's assets falls below the default barrier.
这里要注意，default barrier也是结构化模型的一部分，因为我们一般会得到违约的具体参数，然后判定每个公司是否达到门槛，导致违约
例题
Johnson is trying to use a structural model to estimate the probability of default of some bonds in his portfolio and write a research report. Which of the following statements may appear in the description of the credit analysis models used in his report? A. The core idea of this model is that the company may default if the value of its assets is lower than its liabilities, and the probability of this occurrence presents the same features as options. B. This model assumes that default is an exogenous variable and occurs randomly. C. Regression analysis is used on both macroeconomic and company-specific variables.
答案： A 解析： 结构模型（structural models） 的核心思想是， 如果一家公司的资产价值 低于其负债额， 那么该公司就会违约， 而且该事件发生的概率具有期权的特征。 因此正确选项为A。 对于选项B， 结构模型（structural models） 假设违约是内生变量（endogenous variable） ， 简约式模型（reduced form models） 则是假设违约是外生变量（exogenous variable） 。 因此， 该选项错误。 对于选项C， 简约式模型（reduced form models） 中使用回归分析， 而结构模型 （structural models） 中并不使用回归分析。 因此， 该选项错误。
送分题
Adv
straightforward
reflect nature of credit risk
Disadv
inside information
assume trade actively
limitations in available data
Calc
P(risky) = P(rf) - Put
例题
Johnson is trying to use a structural model to estimate the probability of default of some bonds in his portfolio and write a research report. Which of the following statements may appear in the description of the credit analysis models used in his report? A. The core idea of this model is that the company may default if the value of its assets is lower than its liabilities, and the probability of this occurrence presents the same features as options. B. This model assumes that default is an exogenous variable and occurs randomly. C. Regression analysis is used on both macroeconomic and company-specific variables.
这题问的是structural model，其核心是，如果资产小于负债，会违约。A是对的。B说反了，structural models假设违约是endogenous，而reduced form model假设是exogenous。C中回归分析也是reduced form的特点。
【PS】structural model觉得原因都是内部，所以一个缺点是需要inside information。改模型的出发点是公司的B/S，相对缺点是可能找不到主动的交易，也不考虑商业周期。一个常见模型是BSM。
【PS2】reduced form觉得原因是外部，所以用回归分析。也会考虑商业周期，但是缺点是假设随时会破产，以及没法解释为什么破产。
Credit ratings
target: company and government
Agency
notching
issuer -> senior unsecured debt
stable
Transition matrixes
下调概率高
降级影响大
Credit scores
target: SME or personal
M5 Credit Default Swaps
Definition
Settlement
Cash settlement
Payout amount = LGD * Notional
Loss given default = 1 - Recovery rate (%)
例题
On 1 January 20X2f Deem Advisors purchased a $10 million six-year senior unsecured bond issued by UNAB Corporation. Six months later (1 July 20X2), concerned about the portfolio' s credit exposure to UNAB, Doris Morrison, the chief investment officer at Deem Advisors, buys $10 million protection on UNAB with a standardized coupon rate of 5%. The reference obligation of the CDS is the UNAB bond owned by Deem Advisors. UNAB adheres to the ISDA CDS protocols. On 1 January 20X3, Morrison asks Bill Watt, a derivatives analyst, to assess the current credit quality of UNAB bonds and the value of Deem Advisors' CDS on UNAB debt. Watt gathers the following information on UNAB' s debt issues currently trading in the market: Bond 1: A two-year senior unsecured bond trading at 40% of par Bond 2: A five-year senior unsecured bond trading at 50% of par Bond 3: A five-year subordinated unsecured bond trading at 20% of par If UNAB experienced a credit event on 1 July, Watt should recommend that Deem Advisors: A. prefer a cash settlement. B. prefer a physical settlement. C. be indifferent between a cash or a physical settlement.
A is correct. Deem Advisors would prefer a cash settlement Deem Advisors owns Bond 2(trading at 50% of par), which is worth more than the cheapest-to-deliver obligation (Bond 1, alsoa senior secured bond, trading at 40% of par). Based on the price of this cheapest-to-deliversecurity, the estimated recovery rate is 40%6. Thus, Deem Advisors can cash settle for $6 million[=(1 -40%)x $10 million] on its CDS contract and sell the bond it ows, Bond 2, for $5 million,for total proceeds of $11 million. IfDeem Advisors were to physically settle the contract, only $10million would be received, the face amount of the bonds, and it would deliver Bond 2.B isincorrect because if Deem Advisors were to physically settle the contract, it would receive only$10 million, which is less than the $11 million that could be obtained from a cash settlement. C isincorrect because Deem Advisors would not be indifferent between settlement protocols as thefirm would receive $1 million more with a cash settlement in comparison to a physical settlement.
关键是先找到同一类的债券是哪些，然后再做判断
Physical settlement
Types
Single-name CDS
CTD
例题
Assume that a company with several debt issues trading in the market files for bankruptcy (i.e., a credit event takes place). What is the cheapest-to-deliver obligation for a CDS contract where the reference bond is a fiveyear senior unsecured bond? A. A subordinated unsecured bond trading at 20% of par B. A five-year senior unsecured bond trading at 50% of par C. A two-year senior unsecured bond trading at 45% of par
C is correct. The cheapest-to-deliver, or lowest-priced,instrument is the two-year seniorumsecured bond trading at 45% of par. Although the bond in A trades at a lower dollar price, it issubordinated and, therefore, does not qualify for coverage under the CDS. Note that even thoughthe CDS holder holds the five-year bonds, he will receive payment on the CDS based on thecheapest-to-deliver obligation not the specific obligation he holds.
关键是先找到同一类的债券是哪些，然后再做判断
Index CDS
multiple issures
Tranche CDS
only up to pre-specified levels of losses
Characters
ISDA Master Agreement
Notional principal
CDS spread and CDS coupon
upfront payment
Credit event
bankcrupt
restructure
failure to pay
Application
Credit exposure
Lender: reduce credit exposure
CDS seller: add credit exposure
Naked CDS
a party with no exposure to reference entity
Long/short trade
Curve-steepening trade
Curve-flattening trade
卖相对好的标的的CDS，买相对差的标的的CDS
例题
Chris Murphy,a derivative investment fund manager, recently finds that the credit spread of Northern Airlines and comparable Southern Airlines have a large and abnormal deviation. Through in-depth research, he also finds that the credit quality of Northern Airlines is constantly improving, while the credit quality of Southern Airlines is declining. If he wants to take advantage of the current situation to make a profit, what kind of strategy is suitable for him to manage credit exposure? A. long/short credit trade B. curve trade C. basis trade
不同债券/CDS，低买高卖，属于long/short credit trade，选A。
【PS1】curve trade指通过不同maturity套利。
【PS2】basis trade指通过bond和CDS的价差套利。
Valuation differences and basis trading
Basis trade
exploit difference in credit spread between bond markets and CDS market
Leverated buyout
purchase both stock and CDS protection
Valuation
Credit curve
credit spreads for a range of maturities
Coupon rate
1%
5%
例题
Mosica wants to purchase a CDS with a duration of 4.5 years to hedge his $1 million position in ABC corporate bond which is high-yield bond. If the current credit spread of this bond is 800bps of the amount of upfront premium will be ? A. $30,000 B. $135,000 C. $315,000
答案:B 解析:该题主要考点为 CDS的定价。由于 ABC公司债券为高收益债券，因此相应 CDS的标准票息率为 5%。又由于当前 ABC公司债券的信用利差为 8%，CDS的久期为4.5年，因此Mosica应向CDS卖方支付的预付保费(uprontpremium)为 $135,000=(8%-5%)x4.5 x$1 million因此正确选项为 B。
1%和5%这2个参数，题目不告诉你，也要知道会用
CDS pricing
upfront payment = PV(protectioin leg) - PV(premium leg)
upfront premium % = (CDS spread - fixed coupon) * duration
例题
Recently, Marsha is analyzing a 6-year CDS on EIS debt to hedge its current portfolio position. Marsha asks Hanse to calculate if an upfront payment would be required and, if so, the amount of the premium. The information for the CDS is in Exhibit 1. Exhibit 1 Data for 8-year CDS on ElS Credit spread: 400 basis points Duration: 5 years Coupon rate: 3% Based on Exhibit 1, the upfront premium as a percent of the notional for the CDS protection on EIS would be closest to: A. 5.0%. B. 8.0%. C. 10.0%.
A is correct An approximation for the upfront premium is the (Credit spread –Fixed coupon rate) × Duration of the CDS. To buy 6-year CDS protection, AKC Wealth Management would have to pay an approximate upfront premium of 500 basis points [(400 – 300) × 5], or 5% of the notional.
基本公式，必须熟练掌握
例题
Mosica wants to purchase a CDS with a duration of 4.5 years to hedge his $1 million position in ABC corporate bond which is high-yield bond. If the current credit spread of this bond is 800bpsf the amount of upfront premium will be ? A. $30,000 B. $135,000 C. $315,000
公式：Upfront premium (%) = (credit spread - fixed coupon) * Duration 1000000*(0.08-0.05)*4.5=135000，选B。
【PS1】CDS coupon rates，默认投资级1%，投机级5%。
CDS quoted price = 100 - upfront premium (%)
Valuation changes in CDS
Profit for protection buyer = Delta(spread) * duration * notional principal
Profit for protection buyer (%) = change in spread (%) * duration
例题
Bond 1 has a yield to maturity of 2.57% and Zu believes it will not default within the next year. He estimates the expected 1-year return on Bond 1 using the transition probabilities and credit spreads for different credit rating groups in Exhibit 2 The expected 1-year return on Bond 1 is closest to: A. 1.59% B. 2.39% C. 2.82%
B is correct stimate the expected return of Bond 1 over the next year, Zu needs to adjust for the possible credit spread change by taking into consideration the adjustment amount from the bond's yield to maturity. To breakdown the calculation, the adjustment is the sum of the expected % price change multiplied by transition probability for each rating category, for the time period of the next year. Expected % change for each rating category: AAA, AA, A = –2.77 × (0.0110 – 0.0275) = 0.0457 BB, B = –2.77 × (0.0450 – 0.0275) = –0.0485 CCC, CC, C, D = –2.77 × (0.0950 – 0.0275) = –0.1870 Therefore the adjustment is calculated by multiplying the probability to each expected % change: 0.0457 × 0.0433 + (–0.0485 × 0.0560) + (–0.1870 × 0.0057) = –0.1801% The expected return = yield to maturity + adjustment = 2.57% −0.1801%=2.3899% closest to 2.39%. Note for internal consistency check. To derive the modified duration of 2.77, I have used discount rate at (1.5% risk free rate + 2.75% credit spread = 4.25%) to account for the credit spread of 2.75 at BBB. YTM is calculated by adjusting for CVA by 3.21 per item 03 from value assuming no default (VND) at risk free rate of 1.5%.
这题是credit tranition matrix的一个变形。一般基础的题目会让你算credit spread change。进阶点不直接问这个，而是问expected return。关键难点在于理解expected return背后的含义。
例题
Anna Lebedeva is a fixed-income portfolio manager Paulina Kowalski, a junior analyst, and Lebedeva meet to review several positions in Lebedeva' s portfolio. Lebedeva begins the meeting by discussing credit rating migration. Kowalski asks Lebedeva about the typical impact of credit rating migration on the expected return on a bond. Lebedeva asks Kowalski to estimate the expected return over the next year on a bond issued by Entre Corp. The BBB rated bond has a yield to maturity of 5.50% and a modified duration of 7.54. Kowalski calculates the expected return on the bond over the next year given the partial credit transition and credit spread data in Exhibit 1. She assumes that market spreads and yields will remain stable over the year. Exhibit 1: One-Year Transition Matrix for BBB Rated Bonds and Credit Spreads - | AAA | AA | A | BBB | BB | B | CCC,CC,C Probability(%) | 0.02 | 0.30 | 4.80 | 85.73 | 6.95 | 1.75 | 0.45 Credit spread | 0.60% | 0.90% | 1.10% | 1.50% | 3.40% | 6.50% | 9.50% Based on Exhibit 1, the one-year expected return on the Entre Corp, bond is closest to: A. 3.73%. B. 5.50%. C. 7.27%.
Mod duration = - Delta(p) / Delta(i)，所以Delta(p) = Mod duration * delta(i) BBB -> AAA: delta(p) = -7.54 * (0.6%-1.5%) = -7.54*-0.009=6.786% 考虑概率和所有变化: Total Delta(p) =-7.54*0.0001*(-0.9*0.02-0.6*0.3-0.4*4.8+1.9*6.95+5*1.75+8*0.45)=-0.017671 所以expected return = 0.055-0.0177=0.0373。选A
【PS1】预期的回报可以粗略的用现在的回报直接加减价格的变化百分比来得到粗略估计。
【PS2】注意mod duration是负的，利率降低，价格升高，反向变化。
【PS3】计算每一个预期价格变化，需要用新的spread减去老的spread。
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