CFA Level III Fixed-income Portfolio -1

dd neutral 答案-阶梯方法2-回到原来dd**

Solution 2-只调整一个bond,一般调整duration 最大的, 通过delta portfolio dollar duration 算 delta bond one DD old- DD new = 162658-107143 delta P bond1 x 4.1 x 0.01 = DD old - DD new 债卷价值要增加这么多才能让我portfolio duration增加这么多 delta P bond1=1354024, dd增加都放在一个bond上面 MV'bond 1 = Mv bond1 +delta=958000+1354024=2312524

Bums problem

capitalization weighted bond indices give more weight to issuers that borrow the most, increase risk compared with an equally weighted index

Classic Immunization-1

creation of a fixed income portfolio that produces an assured return for a specific time horizon irrespective of any parallel shifts in the yield curve 特点-specified time horizon / assured rate of return / insulation from the interest rate change 让两大风险互相抵消 利率变化不对价格产生影响，锁定回报率不论利率如何变化 两个风险中赚到的钱要大于亏损的钱 担心利率上升，持有时间要大于mocD, 持久时间越长，reinvestment risk越大 Immunization offsets interest rate risk and reinvestment risk - interest rate上升bond价格下降但是利息也上升，所以你最后总共得到的价格可能不变，这就是所谓duration matching

Two basic approaches to global credit bond portfolio managment

top-down approach and bottom-up approach. The top-down approach focuses on high-level allocations among broadly defined credit asset classes. The goal of top-down research is to form views on large-scale economic and industry developments. These views then drive asset allocation decisions (overweight certain sectors, underweight others). The bottom-up approach focuses on individual issuers and issues that will outperform their peer groups.

Multifactor model technique

use a set of factors that drive bond returns, focus on most important or primary risk factors 1.duration-effective duration measures the sensitivity of index's price to a relatively small parallel shift in interest rates 2. key rate duration and present value distribution of cash flows-measuring the effect of shifts in key points along the yield curve, holding spot rates constant for all points along the yield curve but one. another method is match the portfolios present value distribution of cash flows to that of the index (a-project cash flow for each issue for specific periods, and pv of total cash flow b-each period pv divide by total pv for a percentage of each period c-calculate the contribution of each periods cash flow to portfolio duration time period times the periods percentage of total PV, add each period duration contribution tgt 3.sector and quality percent 4.sector duration contribution 5.quality spread duration contribution -bonds price will change as a result of spread change-spread duration, match amount of the index duration comes from various quality categories 6. sector coupon maturity cell weights 7.issuer exposure

Key rate duration

yield curve risk - changing spot rate for a particular key maturity rate duration-sensitivity of the change in value to a particular change in spot rate 短期利率变化激烈，长期几乎不变 找关键时间点的收益率变化， key rate, 人为定 change in rates between two key rates are calculated using linear approximation, 线性差值（时间差距要一样才行） 题目不难算，表格难看，尽量把表格看清楚 这两个portfolio duration一样，但是convexity不一样， convexity 1> convexity2,两者不能完全对冲

三个duration， portfolio duration局限性

yield curve平行移动-可以近似算出 deltap= -D.P.deltaY,但是可以不平移，S1+1%, S2+2%, S3+0.5%, 这里delta y 处处不等，你不能用duration, 三个现金流各个影响一笔一笔算 portfolio duration 局限性-key rate duration你要一笔一笔算 Δvalue = (effective duration)(decimal change in interest rates)(price) dollar duration = (effective duration)(0.01)(price) Portfolio dollar duration is the sum of the dollar durations of the individual bonds in the portfolio

Chris Dialynas in "The Active Decisions in the Selection of Passive Management and Performance Bogeys" (in Frank J. Fabozzi (ed.), Perspectives on Fixed Income Portfolio Management, Volume 2) wrote: Active bond managers each employ their own methods for relative value analysis. Common elements among most managers are historical relations, liquidity considerations, and market segmentation. Market segmentation allegedly creates opportunities, and historical analysis provides the timing cure. A.What is meant by "historical relations, liquidity considerations, and market segmentation" that Chris Dialynas refers to in this passage? B.What is meant by: "Market segmentation allegedly creates opportunities, and historical analysis provides the timing cure?"

•Historical relations help a portfolio manager identify opportunities when current spreads are out of line and relative-value opportunities may be available. Liquidity considerations affect spreads and the ability to trade. Market segmentation means factors affecting supply and demand within sectors of the bond market due to impediments or restrictions on investors from reallocating funds across those bond sectors. •Market segmentation may create relative value opportunities when spreads get out of line due to obstructions that prevent or impede investors from allocating funds to certain sectors due to regulatory constraints and asset/liability constraints. Market segmentation may affect the supply of bonds in a sector for the same reasons. In pursuit of the optimal timing to move into or out of a sector (industry category, maturity neighborhood, or structure) or individual issuer, historical analysis of spreads, based on mean-reversion analysis can help identify when spreads might revert to some "normal" equilibrium.

credit risk 相关

很多情况下比如immunization和option pricing都假设了没有credit risk这个前提 Analytical models for valuing bonds with embedded put options assume the issuer will fulfill the obligation to repurchase an issue if the bondholder exercises the put option. For high-yield issuers, there is the credit risk associated with the potential inability to satisfy the put obligation. Thus for high-yield issuers, the credit risk may override the value for a putable issue derived from a valuation model.

credit risk的问题

很多时候这些题目问题的假设都是说没有credit risk， analytic pricing就说没有credit risk,

dd neutral经典例题***-一定很熟做

怎么让dollar duration回归 re-balancing-保证duration 一样 原生品underlying 变化，对冲品要变，不然没法100% hedge

Contingent immunization ××

我的资产可以cover 负债还可以cover 收益 Contingent immunization is the combination of active management with passive immunization techniques. Like immunization, there must be a defined liability or liabilities for known amounts on known dates allowing a present value of liabilities to be computed. Unlike immunization, the beginning value of the portfolio must exceed the PV of the liabilities. The difference is called an economic surplus or surplus. The initial surplus is related to and can only exist if the investor will accept a floor return less than the available immunization rate. The immunization rate available in the market minus the investor's minimum floor return is called the cushion spread. The basic steps in contingent immunization consist of determining the PV of the liability and comparing this to the PV of the assets (their market value) to determine the value of the surplus. As time and/or market conditions change, the PV of assets and liabilities will change as well. The surplus must be continually recomputed. As long as the surplus is positive the portfolio can be actively managed.

Spread duration

所以说你看spread duration是和treasury比较，所以treasury 是没有spread duration measure how the market value of a risky bond will change with respect to a parallel 100 bps change in its spread above the comparable benchmark security Spread duration is a measure of a non-Treasury security's price change as a result of a change in the spread between the security and a Treasury. The portfolio spread duration is the weighted average duration of those securities in the portfolio that have a yield above the default-free yield (i.e., non-Treasuries). In this problem, the agencies, corporates, and mortgage-backed securities have a spread. Using their original weights in the portfolio, the spread duration is (0.1479 × 5.80) + (0.1235 × 4.50) + (0.2512 × 4.65) = 2.58165. Round to 2.58. *Nominal spread-spread of a bond or portfolio above the yield of a certain maturity treasury *static spread-constant spread above the treasury spot curve that equates the calculated price of security to the market price *option adjusted spread-current spread over the benchmark yield minus component of spread attributable to embedded optionality

Yield curve/spot rate, YTM,forward rate

根据具体公司来平移yield curve, spread 来自于信用和流动性

dd neutral答案-解题方法一-回到原来DD**

每一个bond都一样改 现在的dd小了，要变大，把现在的每一个价值×1.52 re-balancing ratio 这种计算一定要严谨规范，注意细节 1.t=0, DD old = 162658 2. t=1, DD new ration=DD old/DD new = 1.52 3. MV'=MV1*1.52 - 每一个bond增加

Multiple liability cash flow matching

用多个资产来配出来-用多个0息债卷匹配， 现金流同时发生的可以抵消 the conditions that must be satisfied to assure multiple liability immunization in the case of parallel rate shifts. The necessary and sufficient conditions are: 1.The present value of the assets equals the present value of the liabilities. 2.The (composite) duration of the portfolio must equal the (composite) duration of the liabilities.35 3.The distribution of durations of individual portfolio assets must have a wider range than the distribution of the liabilities

contingent immunization答案

看清楚你的liability pv是多少，根据liability算出来required future value 然后根据discount rate算出来present value 资产变化负债不变化，资产可能不cover负债 不能cover,结论-new dollar safety margin =现有价值 15870551-17839999<0 Contingent immunization不行-classic immunization 才行（资产等于负债） dollar safety margin = current PV - required PV

dd-neutral 答案-solution 3**

算出bond one 目标dd，，根据比列算相应价值，简单做法不容易错 delta DD = DD old - DD new =55515 DD bond 1' = DD bond1+ delta DD=39299+555115=94814 多买一些bond 用比例来算 DD bond1/MV1 = DD bond'/MV1' 39299/958500=94814/MV1' MV1'=2311300 三级计算都是套路，把考试的之前计算典型过一遍

Contingent immunization-cushion spread

要求的回报率8%,提供的9%（immunization rate of return)，cushion spread 1%

market price risk/ reinvestment risk 收益率和价格以及再投资收益的矛盾

零界时间t*,小于market price risk 主导，大于reinvestment risk 主导 临界时间 Macaulay duration, 债卷不受利率影响，免疫了 Schweser explains that the Mac Duration is the point at which the market price risk equals reinvestment risk Yes, one of the interesting characteristics of Macaulay duration is that it gives the point of indifference: if interest rates change and the Macaulay duration is, say, 8 years, then 8 years after the interest rate change, the portfolio value (value of the bond plus the value of the coupons with reinvested interest) is the same as it would have been had interest rates not changed. If your holding period is shorter than the Macaulay duration, then you'll lose more on the value of the bond than you'll gain via the additional interest from reinvesting the coupons. If your holding period is longer than the Macaulay duration, then you'll gain more via the additional interest from reinvesting the coupons than you lose on the value of the bond.

combination matching advantage disadvantage

These approaches can also be combined and blended together. Combination matching, also known as horizon matching, is a combination of multiple-liability immunization and cash flow matching that can be used to address the asset cash flow/liability matching problem. This strategy creates a portfolio that is duration matched. During the first few years, the portfolio would also be cash flow matched in order to make sure that assets were properly dispersed to meet the near-term obligations. Combination matching offers the following advantages over multiple-liability immunization:•Provides liquidity in the initial period.•Reduces the risk associated with nonparallel shifts in the yield curve. The initial cash needs are met with asset cash flows. There is no rebalancing needed to meet the initial cash requirements. The primary disadvantage of combination matching is that it tends to be more expensive than multiple-liability immunization.

Contribution of bond

wi X Di W - Weight bond计算很爱考

Dollar duration value 计算

(Dollar Duration) = (Market value of bond) * (Bond duration) * (Par value of bond) * (0.01) Dollar duration用portfolio market value

Treasury spread duration

0 Treasuries are the benchmarks against which spreads are measured

债卷最主要还是看credit and interest risk

interest risk

Contingent immunization典型例题解答

变量和不变的计算 rate， 注意n的不同

例题 reinvest and match dollar duration Alonso has done further analysis of the current US Treasury portion of the portfolio and has discovered a significant overweight in a 5-year Treasury bond ($10 million par value). He expects the yield curve to flatten and forecasts a six-month horizon price of the 5-year Treasury bond to be $99.50. Therefore, Alonso's strategy will be to sell all the 5-year Treasury bonds, and invest the proceeds in 10-year Treasury bonds and cash while maintaining the dollar duration of the portfolio. US Treasury bond information is shown in Exhibit 2. Using Exhibit 2, the par value of 10-year bonds to be purchased to execute Alonso's strategy is closest to:

计算方法就是算出一个dollar duration,然后除以另一个duration, 0.01,算出来需要多少钱，这个是你现在要得钱，然后除以现在价格和par价格的区别，就是par value (Dollar Duration) = (Market value of bond) * (Bond duration) * (Par value of bond) * (0.01) Dollar duration用portfolio market value A is correct. Alonso is not simply going to reinvest the entire proceeds of the sale into 10-year Treasuries because his stated desire is to maintain the dollar duration of the portfolio. The sale price of $10 million par value of the 5-year bond is found by multiplying $10,000,000 × 1.0040625 = $10,040,625. The dollar duration of the 5-year is 4.53 × $10,040,625 × 0.01 = $454,840.31. Now divide $454,840.31 by the product of the duration of the 10-year and its quoted price and 0.01 to get the par value of the 10-year. The result is $454,840.31/(8.22 × 1.0909375 × 0.01) = $5,072,094.

Classic Immunization-2

资产价值变化抵得上负债价格变化 最好是资产负债同时到期 Portfolio assets duration is less so they r maturing before the liabilties dates. To fund the liabilities thru assets we will have to make an assumption about the reinvestement of these assets which exposes our portfolio to reinvestment risk. Since future reinvestment rates are unknown, the total future value of a bond portfolio's coupon payments plus reinvested income is uncertain. "if interest rates are decreasing, the losses from reinvestment income would be greater than the gain in the value of the bonds." (this will hold good if duration of assets are less than duration of liabilities ) So reinvestment risk If Int rate are increasing, so the gain from reinvestment income would be lower than the losses from the losses in value of bond. When duration of assets are greater than liabilities. (Price risk) So to immunize you choose classical single period immunization (stands good for a single period & 1 time change in interest rate) . That is your reinvestment risk & price risk should exactly offset each other 但hedge 很麻烦，两边delta y不一样，左右两边delta y不平行移动，不一定能完美hedge

Structuring Analysis

长期短期流动性很好，中期相对更加Popular但是长期债越来越少，短期债收益少

Critique the use of bond market index as benchmarks

1. Benchmark should be invest-able. bond market securities are more heterogeneous and illiquid. 2.Index from different vendors appears the same but are different 3.Risk characteristics can change quickly over time new issues of bond are added 4. Bum problem-capital weighted indexes carry increased exposure to credit downgrades 5.It is difficult for investors to find index match their risk profiles

五大技术优缺点** 五大策略名字要背，记住优缺点走势

1. PBI-不改变 追踪指数 优点： 没有tracking error, same risk,管理费低（administrative cost) 缺点：昂贵难执行**(交易费用昂贵,trading cost）,收益略低于index (不可能像index一样高效） 2. Enhanced indexing by matching promary risk factors(sampling) 优点：1.相对便宜 2.renturn相对高一点 3. 主要风险因素和index一致 缺点： 1. increased management fee 2. lowered ability to track index 3. lower expected return than the index 3.Enhanced indexing by small risk factor mismatches 优点：1. same duration 2. increased expected return 3.reduced manager restriction 缺点：1. increased risk 2. increased tracking error 3.increased management fees 前三个不能改duration,第四个才可以. managment fee 1-5递增 4.Active management by larger risk factor mismatches 优点：1.abbility to tune the portfolio duration 2. increased expected return 3.reduced manager restrictions 缺点：1. increased risk 2. increased tracking error 3.increased management fees 5.Full blown active management by larger risk factor mismatches 优点1.increased expected return 2.few if any manager restriction 3. no duration limit 缺点： 1. increased risk 2. increased tracking error 3.increased management fees

Bond portfolio benchmark

1. Using bond index benchmark (Passive, active) 2. using liability as benchmark (single and set of liability)

Scenario analysis-why useful

1. assess the distribution of possible outcomes 2. analysis can be reversed, begining with a range of acceptable outcomes and then calculate the range of interest rate movements 3.can evaluate the contribution of individual components to the total return 4.can use to evaluate the relative merits of entire trading strategies

Strategies to enhance index

1. lower cost enhancement 2.issue selection -select securities that are undervalued relative to a valuation models theoretical value 3. yield curve positioning - long term bonds are popular investments for many and tend to be overvalued, weighting the undervalued areas of the curve and under-weighting the overvalued areas the manager can enhance the portfolios return 4.sector and quality positioning ( yield tilt toward short duration corporate-those tend to have best yield spread per unit of duration risk, periodic over or underweight of sectors-overweight treasuries when spreads are expected to widen like before a recession) 5. call exposure positioning - underweight callable bonds that will retire early and have drop in price

Three spread duration measures

1. nominal spread - spread between nominal yield on a non treasury bond and a treasury of the same maturity, represents the approximate percent price change for 100 basis point change in nominal spread 2. zero volatility spread - spread that must be added to the treasury spot rate curve to force equality between PV of bond cash flows and market price of bond plus accrued interest 3.option adjusted spread - approximate percentage change in price for 100 basis point change in OAS

小总结1-manage fund against index benchmark

1.benchmark构建，思想 ×bond index *liabilities 2.Index *pure indexing *full blown 那些上升下降×consideration-stable, liquidity, credit 3.Risks *interest rate risks (mocD, MD, ED,DD,PVBP, Dport, KRD-非平行) *re-balancing-计算 a.rebalancing ratio b. D max 调整 *Nonparallel Shift - KRD *Credit Risk-Spread, spread duration

immunization总结

1.classic immunization - 目标切断y p关联 三个匹配方法，注意现金流也要Match 优点-安全，缺点-没有收益 2. contingent immunization - 一定会让你算cushion margin, 今天知道liability 0,后来算liability t, liability t 倒过来算，根据rate of asset算required asset, required asset<asset OK, 如果大于，classical 计算量：L0， lt会算，ra告诉你，今天实际asset也可能用定价公式算 3. Multi liability -每一笔liability cashflow要求都不一样 cashflow matching-用好几笔资产来抵消 重点说了债卷风险，re-balancing ratio-dollar duration, 免疫技术等

Active manager extra activities

1.identify which index mismatches are to be exploited 2. extrapolate the market's expectations or inputs from the market data 3. independently forecast the necessary inputs and compare these with the market's expectations 4.estimate the relative values of securities in order to identify areas of under or overevaluation

Safety net return-SNR

1.给safety return和immunization rate of return 2.required terminal value-三年后负债会要求达到多少，这个负债要求多少现在的资产多少 3.liability未来资产immunization rate折现 只要能还得起就可以了，不用20， 4.initial dollar safety margin (名字） = 20m - 19432661=567339

Rebalancing cost calculation算方法 dollar duration, rebalancing ratio计算，dollar duration and portfolio duration difference?

1.计算两个Portfolio dollar duration Dollar duration = duration × portfolio dollar value × 0.01 portfolio duration is just the weighted average duration of portfolio's different assets 2. rebalancing ratio = benchmark dollar duration / portfolio dollar duration 3. cash required = ( rebalancing ratio -1) × market value of the current portfolio amount

contingent immunization步

1.计算要点n，半年一年 2.有的时候不告诉你手里资产，要多一步算资产

Contingent immunization-图解

1.负债liability-算出来terminal value （根据safety rate) 2.terminal value / (1+immunization rate)^year = asset required

spread vs duration spread understanding

A portfolio's duration, which is a weighted average of the individual bond durations, measures the percentage change in the total value of the portfolio for a 100 bps change in the required return on the portfolio. Duration assumes a one-time parallel shift in the yield curve, which causes the yields on all bonds to increase or decrease the same amount. Spread duration measures the percentage change in the total value of the portfolio given a parallel 100 bps change in the spread over Treasuries. In the former (duration), the parallel shift in the yield curve could be caused by a change in inflation expectations, which causes the yields on all bonds, including Treasuries, to increase/decrease the same amount. In the latter (spread duration), the shift is in the spread only, indicating an overall increase in risk aversion (risk premium) for all bonds in a given class.

Most likely has the least immunization risk

C 最好，cash flow在一起

"When managing the risks of a schedule of liabilities, multiple liability immunization and cash flow matching approaches do not have the same risks and costs. Whereas cash flow matching generally has less risk of not satisfying future liabilities, multiple liability immunization generally costs less."

Cash Flow Matching eliminates immunization risk (which includes only investing in US Treasuries and/or laying off your credit risk). It is also expensive to properly time the cash flows and periodically maintain large cash balances with conservative ROR assumptions. Multiple liability immunization minimizes (but does not eliminate) immunization risk and requires less money to fund liabilities. [My editorial] Perhaps cf matching is "technically inferior to immunization (p. 46)" because the cost of a properly cash flow matched portfolio is greater than even a poorly executed multiple liability immunization. (CFAI, vol 4, pg 45-46)

Primary market analysis

Centers on new issue supply and demand new bound issue goes up, secondary market perceived risk goes down, spread goes down, price goes down, return goes up new bound issue goes down, return goes down

contingent immunization总结

Classic immunization- minimize risk Contingent immunization-maximize return

Price risk vs reinvestment risk duration issue

Dp<Dl-reinvestment risk Dp>Dl-price risk "If portfolio duration is less than liability duration, the portfolio is exposed to reinvestment risk" On total return basis : Coupon income+reinvestment income+ change in price Coupon are fixed, so we are exposed to change in reinvestment income (reinvestment risk) & change in price (price risk) Portfolio assets duration is less so they r maturing before the liabilties dates. To fund the liabilities thru assets we will have to make an assumption about the reinvestement of these assets which exposes our portfolio to reinvestment risk. Since future reinvestment rates are unknown, the total future value of a bond portfolio's coupon payments plus reinvested income is uncertain.

Contingent immunization注意点

For the Exam: A contingent immunization strategy is a complex time value of money strategy. The data can be presented in a variety of ways so examine the information carefully to determine how to solve the question. Determining the surplus or what has happened to surplus is generally important. Surplus is a concept that pervades any form of asset liability management and contingent immunization is a form of ALM. To compute surplus be prepared to calculate the PVA and PVL if not given directly. A couple of hints:•Assume semiannual compounding as in the example unless directed otherwise.•If asset duration and convexity match those of the liability the surplus will be relatively stable (essentially this means the portfolio is immunized). If duration and convexity of assets and liability do not match, the surplus will change as market conditions change and time passes.•Before the surplus becomes negative, the portfolio must be immunized and active management is no longer allowed. If the surplus becomes negative, it is no longer possible to immunize and reach the target value because the current value of assets is not large enough to reach the terminal value at the prevailing market immunization rates.

Liquidity and trading analysis

How are portfolio management decisions influenced by, say, short-term liquidity needs? Some fixed-income managers are willing to give up additional return by investing in issues that possess greater liquidity such as larger-sized corporate issues (>$1bn) and government issues. By contrast, other managers are willing sacrifice liquidity for issues which offer a greater yield such as smaller-sized issues and private placements. And, how about the influence of long-term liquidity needs? Liquidity will ebb and flow with factors such as the economic cycle, credit cycle, yield curve shape, supply, seasonality and market shocks such as a wave of defaults. However, the overall trend is towards greater liquidity as new technologies are adopted and markets become truly global as evidenced by decreasing bid/ask spreads - especially for large, well-known corporate issuers.

免疫-immunization

Immunization aims to construct a portfolio that over a specific horizon will earn a predetermined return regardless of interest rate changes p对Y脱离关系 The purpose of immunization is to identify the portfolio for which the change in price is exactly equal to the change in reinvestment income at the time horizon of interest

Bond Index Investability Issue

Most bond indices will not be easily replicated. Issues that prevent bond index investability include the small size of bond issues, their heterogeneity, and infrequent trading. Additionally, bond indices may have unexpected risk exposures, risk that changes over time, or be overweighted by bums. Investors may also have trouble finding an index that matches the portfolio's desired risk exposures.

PVD

Present value distribution of cash flow of the index used as portfolio benchmark Measures the proportion of the index's total duration attributable to cash flows falling in selected time periods

Bond indexing strategy

Pure bond indexing Enhanced indexing by matching primary risk factors (duration-senstivity to interest rate risk, credit, maturity一样）主要风险指标吻合 Enhanced indexing by small risk factors mismatched 小因素mismatch while matching duration Active management by larger risk factors mismatches-大因素mismatch Full blown active management The primary risk factors to match are the portfolio's duration, key rate duration and cash flow distribution, sector and quality percent, sector duration contribution, quality spread duration contribution, sector/coupon/maturity/cell weights, and issuer exposure 这种只要是有一些明显的不同那就是大不同，比如reading 20课后第六题Exhibit 1 makes clear that the portfolio weights differ and for some sectors quite dramatically from those of the index and that the durations of the portfolio components differ from their respective durations in the index. Thus the manager is using active management because he had both duration and sector mismatches and not on a small scale.

Discount rate and spread概念

Rf-宏观经济因素，spread,微观因素，spread就是风险溢价，risk free一段时间内稳定，spread变化，信用流动性变，价格变，YTM是一个平均利率 P=CF1/（1+S1) + CF2/(1+S2)^2 + .....,每一年spot rate在一起年化的平均利息， 实际中spot rate boot strap出来的，出来每年spot rate就是yield curve

Yield curve risk例题答案

Scenario 1-平移 Scenario 2，3- 一个一个正负号带进去算

Enhanced Indexing Strategies The Board of Directors of the Teachers Association of a Canadian province has asked its chairman, Jim Reynolds, to consider investing C$10 million of the fixed-income portion of the association's portfolio in the Reliable Canadian Bond Fund. This index fund seeks to match the performance of the Scotia Capital Universe Bond Index. The Scotia Capital Universe Bond Index represents the Canadian bond market and includes more than 900 marketable Canadian bonds with an average maturity of about nine years. Jim Reynolds likes the passive investing approach of the Reliable Canadian Bond Fund. Although Reynolds is comfortable with the returns on the Scotia Capital Universe Bond Index, he is concerned that because of the expenses and transactions costs, the actual returns on the bond fund could be substantially lower than the returns on the index. However, he is familiar with the several index enhancement strategies identified by Volpert (2000) through which a bond index fund could minimize the underperformance relative to the index. To see if the fund follows any of these strategies, Reynolds carefully reads the fund's prospectus and notices the following. "Instead of replicating the index by investing in over the 900 securities in the Scotia Capital Universe Bond Index, we use stratified sampling. The fund consists of about 150 securities. ... We constantly monitor the yield curve to identify segments of the yield curve with the highest expected return. We increase the holdings in maturities with the highest expected return in lieu of maturities with the lowest expected return if the increase in expected return outweighs the transactions cost. Further, the fund manager is in constant touch with traders and other market participants. Based on their information and our in-house analysis, we selectively overweight and underweight certain issues in the index." 1.Which of the index enhancement strategies listed by Volpert are being used by the Reliable Canadian Bond Fund? 2.Which additional strategies could the fund use to further enhance fund return without active management?

Solution to 1: By investing in a small sample of 150 of over 900 bonds included in the index, the fund is trying to reduce transactions costs. Thus, the fund is following lower cost enhancements. The fund is also following yield curve positioning enhancement by overweighting the undervalued areas of the curve and underweighting the overvalued areas. Finally, the fund is following issuer selection enhancements by selectively over- and underweighting certain issues in the index. Solution to 2: The fund could further attempt to lower costs by maintaining tight controls on trading costs and management fees. Additional strategies that the fund could use include sector and quality positioning and call exposure positioning.

Portfolio Immunization The Managers of Reliable Life Insurance Company are considering hiring a consultant to advise them on portfolio immunization. Following are some of the statements that were made during these presentations: 1.A great thing about immunization is that it is a set-and-forget strategy. That is, once you have immunized your portfolio, there is no subsequent work to be done. 2.The immunization target rate of return is less than yield to maturity. 3.If a portfolio is immunized against a change in the market yield at a given horizon by matching portfolio duration to horizon, the portfolio faces no risk except for default risk. 4.The liquidity of securities used to construct an immunized portfolio is irrelevant. 5.In general, the entire portfolio does not have to be turned over to rebalance an immunized portfolio. Furthermore, rebalancing need not be done on a daily basis. Critique the statements.

Solution to 1: This statement is incorrect. One needs to rebalance the portfolio duration whenever interest rates change and as time elapses since the previous rebalancing. Solution to 2: This statement is only true if the yield curve is upward sloping. If the yield curve is downward-sloping, then this statement is not true as the immunization target rate of return would exceed the yield to maturity because of the higher reinvestment return. Solution to 3: The statement is incorrect. The portfolio described would be exposed to the risk of a change in interest rates that results in a change in the shape of the yield curve. Solution to 4: The statement is incorrect because immunized portfolios need to be rebalanced; the liquidity of securities used to construct an immunized portfolio is a relevant consideration. Illiquid securities involve high transaction costs and make portfolio rebalancing costly. Solution to 5: The statement is correct. The entire portfolio does not have to be turned over to rebalance it because shifting a small set of securities from one maturity range to another is generally enough. Also, to avoid excessive transactions costs, rebalancing is usually not done on a daily basis, which could involve excessive transaction costs.

Spread duration definition

Spread duration is a measure of how the market value of a risky bond (portfolio) will change with respect to a parallel 100 bps change in its spread above the comparable benchmark security (portfolio). Spread duration is an important factor influencing a portfolio's total return because spreads do change frequently.

general cash flow immunization

Suppose a manager has a given obligation to be paid at the end of a two-year horizon. Only one-half of the necessary funds, however, are now available; the rest are expected at the end of the first year, to be invested at the end of the first year at whatever rates are then in effect. Is there an investment strategy that would guarantee the end-of-horizon value of the investment regardless of the development of interest rates? Under certain conditions, such a strategy is indeed possible. The expected cash contributions can be considered the payments on hypothetical securities that are part of the initial holdings. The actual initial investment can then be invested in such a way that the real and hypothetical holdings taken together represent an immunized portfolio. We can illustrate this using the two-year investment horizon. The initial investment should be constructed with a duration of 3. Half of the funds are then in an actual portfolio with a duration of 3, and the other half in a hypothetical portfolio with a duration of 1. The total stream of cash inflow payments for the portfolio has a duration of 2, matching the horizon length. This match satisfies a sufficient condition for immunization with respect to a single horizon.

Dollar duration

The dollar duration measures the dollar change in a bond's value to a change in the market interest rate. The dollar duration is generally used by professional bond fund managers as a way of approximating the portfolio's interest rate risk. Dollar duration is one of several different measurements of bond duration. 计算是duration *1% * market value

General cashflow understanding "Let's assume the manager expects to receive a cash flow in six months. Treating this like a zero, the duration of 0.5. To construct the portfolio to immunize a liability due in 1.5 years with a duration of 1.0, the managers could combine the cash to be received with an appropriate amount of bonds with duration greater than 1.0, so that the conditions for immunization are met, including weighted average portfolio duration of 1.0" Please help with this puzzle?

The dur of zero coup bond is time till its maturity. if its is one year till maturity, the dur is 1. since cash is expected to come in six months, which is half of one year, that is why cash dur in this example is 0.5. 1) meet the condition that Aggr dur of liability = aggr dur of assets. As per this you have to construct PF with aggr duration =1. Why a zero has duration equal to its maturity is 1 ? because you do not receive anything in between apart from its maturity. If you receive any cashflow in between, the duration would be less than 1. What the example says is that to make aggr duration 1, you can take a bond with duration greater than 1 say 1.5 (say this bond does not pay any cash flows in between). Now you add the exapected cash with duration 0.5 and treat this expected cash coming from the above bond with duration 1.5. Since you are receiving cash in between the duration would drop.

Multiple liability conditions

The key to immunizing multiple liabilities is to decompose the portfolio payment streams in such a way that the component streams separately immunize each of the multiple liabilities. Multiple-liability immunization is possible if the following three conditions are satisfied (assuming parallel rate shifts):1.Assets and liabilities have the same present values.2.Assets and liabilities have the same aggregate durations.3.The range of the distribution of durations of individual assets in the portfolio exceeds the distribution of liabilities. This is a necessary condition in order to be able to use cash flows generated from our assets (which will include principal payments from maturing bonds) to sufficiently meet each of our cash outflow needs.

Relative-Value Methodologies-重要

The main methodologies for credit relative-value maximization are: ◾total return analysis; ◾primary market analysis; ◾liquidity and trading analysis; ◾secondary trading rationales and constraints analysis; ◾spread analysis; ◾structure analysis; ◾credit curve analysis; ◾credit analysis; ◾asset allocation/sector analysis.

Explain tracking error The target tracking risk of the fund is 1 percent. Interpret what is meant by this target.

The target tracking risk of 1 percent means that the objective is that in at least two-thirds of the time periods, the return on the Star Bond Index Fund is within plus or minus 1 percent of the return on the benchmark Barclays Capital Global Aggregate Bond Index. The smaller the tracking risk, the more closely the fund's return matches the benchmark's index return. Assume that the tracking risk for a portfolio is calculated to be 30 bps. Statistically, the area that is one standard deviation either side of the mean captures approximately 2/3 of all the observations if portfolio returns approximately follow a normal distribution. Therefore, a tracking risk of 30 bps would indicate that, in approximately two-thirds of the time periods, the portfolio return will be within a band of the benchmark index's return plus or minus 30 bps. The smaller the tracking risk, the more closely the portfolio's return matches, or tracks, the benchmark index's return.

Rebalancing相关

Without re-balancing, classic immunization only work for one time change in interest rate But interest rate fluctuates, and time passes all change the duration and balance To keep a portfolio immunized, we have to re-balance all the time Characteristics of bond to consider 1.credit rating-assume that none of the bonds will default 2.embedded options-difficult to estimate duration 3.liquidity-re-balancing requires sale

I don't understand one of the requirements to immunize mutliple liabilitites. In particular, why does the range of durations of assets have to be greater than the range of duration of liabilities?

You are reading too much into it, and way beyond what is necessary. I don't understand much of your question, so answer with general explanations in hope that it answers your concerns: Let's step back. 1. To ensure that there is necessary CF (without too much selling), you need a wider distribution of assets than distribution of liabilities. 2. But you don't want TOO MUCH distribution since it will increase your immunization risk, so you want minimum maturity variance, subject to the above condition. So what you'll do is to run a linear program (LP) with the following Min (maturity variance,M2) with constraints: o Weighted duration = average duration of liabilities. o Necessary duration dispersion (i.e., > dispersion of the liabilities). There is always reinvestment risk (unless you have a bullet portfolio meeting each CF precisely, but it is not often feasible), so you want to minimize this risk. Besides, as you see at the constraints, you don't aim to meet the precise date of each CF, but only aim to meet the AVERAGE duration of all liabilities, relying on partly on selling off when you need as well as coupon and principals repayments to meet the liabilities. The portfolio is therefore always fully invested. CF matching on the other hand, aims to meet the individual CF as precisely as possible. When not possible, it will aim to have cash available BEFORE each deadline. The cash available then just put into bank (or CD) to be readily available. This is all you need to know for the exam. When you make the duration of the assets to go to the far end, you minimize the impact of lowered interest rates. If rates drop dramatically and you have asset durations that extend from the near end and stop short of the longest liability duration, this will expose the risk of the immunization not matching the liabilities. The liability will rise faster more than the asset and will cause an erosion of value but with a longer asset duration, you will have at least one security rising in price faster than the longest liability duration.

cash flow matching

alternative multiple liability immunization , 一笔一笔看cash flow requirement,从最后一笔开始看， 往前面慢慢配平， http://www.investopedia.com/articles/investing/022615/portfolio-immunization-vs-cash-flow-matching.asp

Delta neutral 两个portfolio value

alue不一定相等,我们只关心价值的变化是0，没有要求价值相等， 只要求PV1*D1=PV2*D2 时间变化duration 要变化，随时都要调控， 加上减掉一个value,让dollar duration相等 PV看market value

calculate tracking risk的方法例题，给你portfolio return, 给你benchmark return,算tracking risk

benchmark return - portfolio return得到active return, active return平方加在一起，除以N-1由于你是sample standard deviation,然后开方

如何实现YTM

hold to maturity, no default, reinvest at YTM,持有到期收益率 reinvestment risk-没有办法按照ytm reinvest

Risk Spread duration

default downgrade spread goes up (credit, liquidity) spread duration-spread变1%， price of spread变多少 Delta YTM=Delta(Rf + Spread) 短期Rf很小，所以 Delta YTM = Delta Spread

Dollar duration hedge爱考 DD neutral

delta P = -D*P*delta Y Duration-inherent, not 0 delta Y-market dependent not equal 0 P not equal 0 要让dd neutral, delta p = 0, 必然要两个，一个原来的，一个对冲的,债卷期货，债卷期权，另一个债卷 delta=0就是两个债券组合起来delta p=0 两个债卷的DD一定要一致，考计算考两种解题方法

Total Return analysis

detailed dissection of past returns and a projection of expected returns. Rate of return that equates the future value of the bond's cash flows with the full price of the bond, takes into account all three sources of potential return-coupon income, reinvestment income and change in price 但是这个看不到risk, thats why you have scenario analysis risk adjusted total return -扣掉风险以后的 在危机的时候收益会相对于国债更差，经济不好国债好，经济好国债不好, thats why during recessions, increasing default risk widen spreads and reduce credit returns relative to treasuries, economic prosperity reduces bankruptcies and tighter spreads boosts credit returns relative to treasuries 通过cds 看未来forward probability of default

Cash flow matching

future funding of a liability stream from the coupon and matured principal payments of the portfolio

Duration概念

interest变化对price的影响， 三个计算macaulay, modified (最有效）, effective (option)-考effective duration Dollar duration-收益率变化1%，价格怎么变化， PVBP，收益率变0.01% price变动=-D.P.delta Y, 这个是平行移动，如果不是平行移动就用key rate duration

Tracking risk/tracking error

measure of variability with which a portfolios return tracks the return of a benchmark index. STD of portfolios active return, active return = portfolio's return - benchmark index's return

market capitalization of bond and stock

nts and government entities issue bonds but not stocks. In addition, most issuers have only one type of common stock outstanding but several bond issues of different maturity, seniority, and other features. As a result, the total market capitalization of the global bond market was almost twice as large as the global equity market, estimated as of 2011 at $93 trillion compared with $54 trillion for global equities.

理解-In general, for an upward-sloping yield curve, the immunization target rate of return will be less than the yield to maturity because of the lower reinvestment return. Conversely, a negative or downward-sloping yield curve will result in an immunization target rate of return greater than the yield to maturity because of the higher reinvestment return.

reinvestment return is lower because reinvestments are being done at a shorter duration of the YTM curve than the original investment . If the curve stays the same shape and is upward sloping , the shorter end has a lower YTM than the far end. So reinvestments fetch lower yield ( and that is assumed to mean lower total return as well ) you are reevaluating what will be achievable a year later. at that time - with a upward sloping yield curve you have higher reinvestment income, but lower price income (because at a higher yield - price falls). So now your YTM is not achievable. What you can achieve is a lower number since what you decided to immunize with was set a year earlier (and not changeable). So with an upward sloping yield curve your target rate of return will be lower then the YTM. key thing to remember - Price change trumps the reinvestment of coupon. So with an upward sloping -> you would have lower. This has been discussed many times here; the search function may help locate the other threads. In fact, the coupons are reinvested at a lower rate, not a higher rate. Suppose that the yield curve is: 1-year (par) rate: 1% 2-year (par) rate: 2% 3-year (par) rate: 3% To make things simple, imagine that the yield curve doesn't change for the next 3 years. If you own a 3-year bond, your YTM is 3%, but your actual yield will be lower. A coupon you receive today will be invested at 3%, but the coupons received next year and the year after that will be invested at, respectively, 2% and 1%.

reinvestment risk or interest rate risk determines immunization risk

reinvestment risk determines immunization risk. The portfolio that has the least reinvestment risk will have the least immunization risk. When there is a high dispersion of cash flows around the horizon date, as in the barbell portfolio, the portfolio is exposed to high reinvestment risk. When the cash flows are concentrated around the horizon date, as in the bullet portfolio, the portfolio is subject to minimal reinvestment risk. reading 20 11题目 A is a zero-coupon bond and thus has no reinvestment rate risk. Portfolio B has lower dispersion in maturities than Portfolio C. Therefore, Portfolio C has more reinvestment rate risk than Portfolio B.

Statement #1 "To use a portfolio of bonds to immunize a single liability, and remove all risks, it is necessary only that 1) the market value of the assets be equal to the present value of the liability and 2) the duration of the portfolio be equal to the duration of the liability." 为什么这句话不对

statement #1 is incorrect because what she describes does not remove all risks. Credit risk destroys the immunization match; therefore, the statement is incorrect. The risk to immunization comes from non-parallel shifts in the yield curve. Immunization of a single-liability only immunizes against one time parallel change in interest rates, so against interest rate risk. It doesn't immunize the portfolio against any other type of risk.

Benchmark criteria selection

•Market value risk. The desired market value risk of the portfolio and the index should be comparable. Given a normal upward-sloping yield curve, a bond portfolio's yield to maturity increases as the maturity of the portfolio increases. Does this mean that the total return is greater on a long portfolio than on a short one? Not necessarily. Because a long duration portfolio is more sensitive to changes in interest rates, a long portfolio will likely fall more in price than a short one when interest rates rise. In other words, as the maturity and duration of a portfolio increases, the market risk increases. •Income risk. The chosen index should provide an income stream comparable to that desired for the portfolio. Many investors (e.g., foundations and retirees) prefer portfolios that generate a high level of income while conserving principal. Investing in a long portfolio can lock in a dependable income stream over a long period of time and does not subject the income stream to the vagaries of fluctuating interest rates. If stability and dependability of income are the primary needs of the investor, then the long portfolio is the least risky and the short portfolio is the most risky. •Credit risk. The average credit risk of the index should be appropriate for the portfolio's role in the investor's overall portfolio and satisfy any constraints placed on credit quality in the investor's investment policy statement. The diversification among issuers in the index should also be satisfactory to the investor. •Liability framework risk. This risk should be minimized. In general, it is prudent to match the investment characteristics (e.g., duration) of assets and liabilities, if liabilities play any role. The choice of an appropriate index should reflect the nature of the liabilities: Investors with long-term liabilities should select a long index.6 Of course, bond investors that have no liabilities have much more latitude in the choice of an index because of the lack of this restriction.

RELATIVE VALUE MAXIMIZATION OBJECTIVE AND METHOD

•The objective of relative value analysis is to identify the sectors with the most potential upside, populate these favored sectors with the best representative issuers, and select the structures of the designated issuers at the yield curve points that match the investor's outlook for the benchmark yield curve. •The main methodologies for credit relative value maximization total return analysis primary market analysis liquidity and trading analysis secondary trading rationales constraints analysis spread analysis structure analysis credit curve analysis credit analysis asset allocation/sector analysis.

收益率曲线平移不平移

一个三年债卷S加上1%，但如果y变得不同每一期，就要分开算 KRD-KEY RATE DURATION用在非平行移动 只有平行移动的时候才能一起算

Relative value analysis

两个价值作比较，买高卖低 In the bond market, relative value refers to the ranking of fixed-income investments by sectors, structures, issuers, and issues in terms of their expected performance during some future period of time.

Contingent immunization典型例题 If a firm has a three-year investment horizon over which it must earn 3% and it can immunize its asset portfolio at 4.75%, the manager can actively manage part or all of the portfolio until it reaches the safety net rate of return of 3%. The difference between the 4.75% and 3% safety net return is called the cushion spread. If the manager started with a $500m portfolio, after three years the portfolio needs to grow to: $500 * (1+3%/2)6 = $546.72 At time 0, the portfolio can be immunized at 4.75%, which implies that the required initial portfolio amount: 546.72 / (1+4.75%/2)6= $474.90 The manager therefore has an initial dollar safety margin of $500m - $474.90m = $25.10m

今天的liability算出未来的值， 根据ASSET收益率算出asset 现有价值，注意两个的n会不一样，一个根据bond的20个，一个根据liability的，算出来后减

immunization什么事后bond price change什么时候不变

你如果一直等到Maturity,bond price doesnt change, you pay par, 只有在你maturity之前卖，才会有这个问题，这个是你在use longer duration时候会有可能遇到的情况

Contingent immunization计算cushion当利率变化的时候什么变什么不变来计算NPV

你的coupon不变，按照之前的coupon rate，只是你的discount rate变了所以你的Portfolio value变，你的liability需求折现也变了，根据现在的利率折现 If the manager invests the entire $500 million in 4.75 percent, 10-year notes at par and the YTM (yield to maturity) immediately changes, what will happen to the dollar safety margin? If the YTM suddenly drops to 3.75 percent, the value of the portfolio will be $541.36 million.( pmt=4.75%*500, n=10, I/Y=3.75, PV=541.36) The initial asset value required to satisfy the terminal value of $546.72 million at 3.75 percent YTM is $489.06 million so the dollar safety margin has grown to $541.36 million − $489.06 million = $52.3 million. The manager may therefore commit a larger proportion of her assets to active management. If rates rise so that the YTM is now 5.80 percent, the portfolio value will be $460.55 million and the initial asset value required will be $460.52 million. The dollar safety margin has gone to zero, and thus the portfolio must be immunized immediately.

怎么样选择benchmark-criteria

债卷index很难，差别太大了，千差万别，流动性不好，交易不经常，难估值，风险类型变，指数集中在交易量活跃的债卷，有的风险类型特殊找不到index

Structure trade

利率上升不要持有duration高债卷，会跌价 利率下降，买高duration

Combination matching

前几年用duration hedge 难 A popular variation of multiple liability immunization and cash flow matching to fund liabilities is one that combines the two strategies. This strategy, referred to as combination matching or horizon matching, creates a portfolio that is duration-matched with the added constraint that it be cash flow-matched in the first few years, usually the first five years. The advantage of combination matching over multiple liability immunization is that liquidity needs are provided for in the initial cash flow-matched period. Also, most of the curvature of yield curves is often at the short end (the first few years). Cash flow matching the initial portion of the liability stream reduces the risk associated with nonparallel shifts of the yield curve. The disadvantage of combination matching over multiple liability immunization is that the cost to fund liabilities is greater.

Barbell and bullet strategy

对冲时候尽量用bullet不用barbell When interest rates change in an arbitrary nonparallel way, however, the effect on the value of the two portfolios differs—the barbell portfolio is riskier than the bullet portfolio. Suppose, for instance, short rates decline while long rates go up. Both the barbell and bullet portfolios would realize a decline of the portfolio value at the end of the investment horizon below the target investment value, because they would experience a capital loss in addition to lower reinvestment rates. The decline would be substantially higher for the barbell portfolio, however, for two reasons. First, the barbell portfolio experiences the lower reinvestment rates longer than the bullet portfolio does. Second, more of the barbell portfolio is still outstanding at the end of the investment horizon, which means that the same rate increase causes much more of a capital loss. In short, the bullet portfolio has less exposure to changes in the interest rate structure than the barbell portfolio.