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fixed income performance attribution
FIXED INCOME PERFORMANCE ATTRIBUTION ANALYSIS OF A MULTI-CURRENCY BOND PORTFOLIO Diploma thesis submitted to Swiss Federal Institute of Technology, Zürich University of Zürich, Swiss Banking Institute for the degree of Master of Advanced Studies in Finance presented by BLAISE RODUIT lic sciences éco Supervisors Dr Nils Tuchschmid Dr Anna Holzgang DECEMBER 2005 ABSTRACT Abstract The two key asset classes available to investment managers are equities and bonds Equity attribution has been around for a while and well-established methods of attribution have been developed It is therefore tempting to generalize these methods to fixed income attribution However, in doing this the performance analyst ignores essential characteristics of fixed income investments In many points, risk factors in fixed income investments are fundamentally different from those in equity Some of them not even have an equivalent in the equity attribution universe – these include yield curves and credit spreads Furthermore, the effect of yield curve moves and spread changes on bond value is non-trivial This paper proposes in the first part to review the different factor decompositions and methodologies used in the fixed income industry A special emphasis is put on the yield curve shift effects (parallel, twist, butterfly, reshape) which play a central role in performance attribution In the second part we discuss the practical problems of data quality that usually occur when implementing a fixed income performance attribution Then we will run a Fixed Income Performance Attribution analysis (FIPA) on a real portfolio and interpret the results obtained We finish by checking which FIPA factors are the main driver of excess returns and if excess returns identified are still present under a risk-adjusted basis -I- FIXED INCOME PERFORMANCE ATTRIBUTION CONTENTS Introduction 1.1 Performance attribution 1.2 Fixed income performance attribution Theoretical framework 2.1 Fixed income return decomposition 2.1.1 Carry return – Coupon income 2.1.2 Carry return - Roll-down 2.1.3 Market return – Yield curve 2.1.4 Market return – Spread 2.1.5 Market return – Volatility 2.1.6 Market return – FX rate 2.1.7 Timing return 2.2 Yield curve construction 2.2.1 Yield to maturity (YTM) curve 2.2.2 Zero coupon yield curve 2.3 Yield curve decomposition 10 2.3.1 Principal component analysis method 10 2.3.2 Empirical method 13 2.3.3 Polynomial method 16 2.3.4 Duration based method 17 2.4 Linking return effects to multiple periods 18 2.4.1 The arithmetic model 18 2.4.2 The geometric model 19 Issues in practice 20 3.1 Data quality 21 3.1.1 Assets without price or with an incorrect price 21 3.1.2 Corporate actions 21 3.2 Cash flows and management fees 22 3.2.1 Management fees 22 3.2.2 Accounting of reclaimable withholding taxes 22 3.2.3 Reinvestment of coupons 22 3.3 Gross / Net basis 22 3.4 Replicating the benchmark in general 23 Characteristics of the portfolio analyzed 24 4.1 Constraints on the portfolio 24 4.2 Style of the portfolio manager 24 4.3 Set up of the fixed income performance analysis 25 4.3.1 The yield curve 25 4.3.2 The YC decomposition factors 26 4.3.3 Linking method 26 The results 27 5.1 The FIPA attribution for the global portfolio 27 5.1.1 Global return (TWR) 28 5.1.2 Direct return 28 5.1.3 Roll-down 28 - II - CONTENTS 5.1.4 YC shift (parallel shift) 29 5.1.5 YC reshape 29 5.1.6 Sector spread return (credit spread) 30 5.1.7 YC spread return (issue spread) 31 5.1.8 Fixed income timing 31 5.1.9 Fixed income currency return 32 5.2 The key ratios 32 5.2.1 The Alpha 32 5.2.2 The Beta 33 Interpretation 34 6.1 Excess returns and FIPA factors 34 6.1.1 Distribution of excess returns 34 6.1.2 Interaction between FIPA factors and excess returns 34 6.1.3 Multivariate analysis 37 6.2 Performance on a risk-adjusted basis 39 6.2.1 Alpha and FIPA factors 39 6.2.2 Excess returns on a risk-adjusted basis 40 Conclusion 44 Acknowledgments 46 References 47 10 Appendix 48 Appendix 1: US government yield curve principal component analysis 48 Appendix 2: Multivariate analysis of the FIPA factors 49 - III - INTRODUCTION INTRODUCTION 1.1 Performance attribution A manager has a return of 8% for the year 2005 while the benchmark only performs 6% How did he get it? What could have caused an excess return of 2%? Hopefully it has something to with the manager’s conscious decisions That is, with something the manager meant to But, in reality, a whole lot of the return might have to with things the manager didn’t do, right? Like, the effects of the market at large The economy The overall movement of industries relative to actions of the Federal Reserve or other bodies Even some unintended consequences of the manager’s actions! Performance attribution tries to answer these questions The purpose of performance attribution is to understand realized excess returns and to relate this information to the active decisions made in the investment organization, in order to understand the sources of out-performance and identify the active decisions that have generated the excess returns Attribution models are designed to identify the relevant factors that impact performance and to asses the contribution of each factor to the final result This information can then be communicated to clients, management and (not least) the portfolio managers that conducted the active bets In doing so the performance analysis can over time add value by assisting in the identification of the investment management particular skills and of the areas where skills appear to be lagging 1.2 Fixed income performance attribution The slump in equity markets during the last couple of years has changed many investors attitude towards fixed income From being a low returning low volatile asset class bond investments are now considered more than just a safe-haven Measured on a risk-adjusted basis the long-term returns from bond investments compare favorably with equity returns In order to understand the active decisions made during the investment process it is essential to understand the characteristics of the underlying asset classes and relevant risk factors that drive the investments, since it is these assets classes and risk factors that the portfolio manager analyzes when designing portfolios Two key asset classes available to investment managers are equity and bonds Equity attribution has been around for a while and well-established methods of attribution have been developed It is therefore tempting to generalize these methods to fixed income attribution However, in doing this the performance analyst ignores essential characteristics of fixed income investments In many points, risk factors in fixed income investments are fundamentally different from those in equity Some of them not even have an equivalent in the equity attribution universe – these include yield curves and credit spreads Furthermore, the effect of yield curve moves and spread changes on bond value is non-trivial For all these reasons, Fixed Income Attribution has been one of the key challenges in the portfolio management industry; though there is now an extensive set of research into differing methodologies, there is still no agreed industry standard -1- FIXED INCOME PERFORMANCE ATTRIBUTION This paper proposes in its first part to review the different factor decompositions and methodologies used in the fixed income industry A special emphasis is put on the yield curve shift effects (parallel, twist, butterfly, reshape) which play a central role in performance attribution In the second part we will discuss briefly the different problems that usually occur in practice when implementing the attribution Then we will run a Fixed Income Performance Attribution analysis (FIPA) on a real portfolio and interpret the results obtained We finish by checking which FIPA factors are the main driver of excess returns and if the excess returns identified are still present under a risk-adjusted basis THEORETICAL FRAMEWORK 2.1 Fixed income return decomposition It is generally admitted that the value generated by holding bonds is composed of three different components Unlike the case for equities, the return generated from periodic cash flows is significant In addition to the periodic return, bond returns are sensitive to changes in the fundamental market variables or fixed income risk factors Finally the return is affected by timing of trades These three different sources of return are usually denoted by carry, market and timing return: rTotal = rCarry + rMarket + rTiming Fig Fixed income return components 2.1.1 Carry return – Coupon income The carry return is composed of two components The central component is the (typically annual) coupon being paid out to the investor – we denote this component direct return This component is always positive This direct return is theoretically defined as: -2- THEORETICAL FRAMEWORK rDirect = C ⋅ ∆t = yCurrent ⋅ ∆t P where C is the annual coupon, t is time passed, P is the initial price and y denotes yield More generally a direct return is computed as follows within a “end of the day cash-flow / geometric model”: r Direct t −1, t ∑ (N ⋅ (P + AI ) + C )⋅ X = ∑ N ⋅ (P + AI ) ⋅ X t −1 t −1 Coupon t t t −1 t −1 t −1 t −1 t −1 where t: time, N: nominal amount, AI: accrued interest, P: price, C: coupon, X: FX rate Redemption + Coupon days interest earned Coupons Fig Direct return 2.1.2 Carry return - Roll-down A less pronounced component of carry is the passage of time Bonds usually not trade at par, but they are eventually redeemed at par, therefore at maturity the market price must converge towards par For longer-dated bonds this effect is minor, whereas it can be significant for shorter-dated bonds trading away from par This return component is called roll-down return The effect is positive for discount bonds (the roll effect will pull the price up towards par) and negative for premium bonds (the roll effect will pull the price down towards par) The roll-down return can be interpreted as: r RollDown t −1, t ∑ (N ⋅ (P (YC , YCS ) + AI ) + C )⋅ X = ∑ (N ⋅ (P + AI ) + C )⋅ X t −1 t −1 t t −1 t −1 t −1 t −1 Coupon t −1 t Coupon t t −1 t −1 where t: time, N: nominal amount, P: price, X: FX rate, YC: yield curve, YCS: yield curve spread Remark: The artificial price “Pt(.)” is calculated by a function of different factors like yield curve, yield curve spread, volatility for example (the number of factors depends on the model complexity) Artificial prices are needed to sequentially calculate and decompose return effects (see Fig 1.) -3- FIXED INCOME PERFORMANCE ATTRIBUTION Zero rate YCt-1 Day Time Fig Roll-down return when the bond is overvalued 2.1.3 Market return – Yield curve In contrast to the carry return components the market return is less predictable The market return is driven by the market variables on which bond value depends In fixed income the yield curve is the central market variable Traditionally the yield curve is based on bonds issued by government entities The rationale has been that this provides a default free yield curve per country Therefore the market value of government bonds are normally driven entirely by movements in this curve The basic approach to modeling yield curve movements is to calculate the difference between the final and the initial yield curve for the period for which performance is measured Fig Yield curve movements Often portfolio managers decompose yield curve shifts further into basic movements Typically the number of basic movements vary between and This number is arbitrarily chosen by the portfolio manager who constructed the portfolio and who did bets on yield curve moves The number of basic movements is consequently a trade-off between the explanation power of the model and the complexity of the interpretation Recent studies suggest that most of the yield curve shift can be explained pretty well by essentially three factors: parallel shift, slope (or twist) and curvature (or butterfly) The unexplained shift left is normally statistically small and put in a residual factor called reshape -4- THEORETICAL FRAMEWORK Of course in market crisis situations these three first factors might be insufficient to leave the reshape small and to a good performance attribution a) Parallel shift A parallel shift appears when the rates at standard maturities move uniformly Note that parallel shifts in yields are captured directly by the bond duration as rParallel ≅ − D ⋅ ∆ycParallel where r denotes return, D is modified duration and YC is the yield curve b) Twist (steeping / flattening) We can see a twist effect when short term and long term rates move in opposite direction but proportionately in relation to the distance from some “pivot point” maturity (usually defined at years) c) Curvature The curvature or butterfly effect occurs when short term and long term rates move in same direction while medium term rates move in an opposite direction, still proportionately By decomposing the yield curve movements into contributions from these shifts the bond fixed income portfolio return that is due to the yield curve moves can be decomposed into: rYieldCurve = rParallel + rTwist + rCurvature + rReshape Fig Example of parallel, slope (steepness) and curvature shifts The financial literature identifies several methods to extract these factors and quantify them Four, at least, can be mentioned: -5- INTERPRETATION 6.1.3 Multivariate analysis According to Fig 30 only a few effects should play an important role in the creation of excess return This is confirmed by a multiple regression: Call: lm(formula = Excess.return ~ Direct.return + Roll.down + YC.shift.1 + YC.reshape + Sector.spread + Issue.spread + FI.timing + FI.currency) Residuals: Min 1Q Median 3Q Max -0.02253 -0.004074 -0.001135 0.003012 0.03395 Coefficients: (Intercept) Direct.return Roll.down YC.shift.1 YC.reshape Sector.spread Issue.spread FI.timing FI.currency Value Std Error t value 0.0036 0.0010 3.6181 0.9954 0.0059 167.7317 1.0019 0.0014 723.8494 1.0014 0.0015 657.4042 0.9972 0.0012 855.2926 1.0009 0.0007 1338.1940 1.0004 0.0004 2637.4455 1.0056 0.0048 210.8842 0.9985 0.0014 702.8091 Pr(>|t|) 0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Residual standard error: 0.00766 on 164 degrees of freedom Multiple R-Squared: F-statistic: 1083000 on and 164 degrees of freedom, the p-value is Correlation of Coefficients: (Intercept) Direct.return Roll.down YC.shift.1 YC.reshape Direct.return -0.8036 Roll.down 0.0431 0.0807 YC.shift.1 0.1088 -0.0938 0.1424 YC.reshape -0.2148 0.1646 0.0006 -0.1453 Sector.spread 0.0353 -0.0496 0.1317 0.0926 0.0902 Issue.spread -0.0346 0.0279 0.1453 0.0350 0.0458 FI.timing -0.0250 -0.0051 -0.0297 0.0154 -0.0513 FI.currency -0.0367 0.0433 0.0698 0.0259 0.0037 Sector.spread Issue.spread FI.timing Direct.return Roll.down YC.shift.1 YC.reshape Sector.spread Issue.spread FI.timing FI.currency 0.5435 0.0185 0.0031 -0.0127 0.0093 -0.1611 Fig 32 Results of the multivariate analysis The first observation is that the multiple R-squared sum to one indicating that no residuals were generated This is a nice property of the geometric model (see chapter 2.4.2.) The second observation is that the factor coefficients are close to one This is as well the value expected as we obtain excess return by “adding geometrically” each factor As expected the most important coefficients are: • • • Issue spread (specific spread or picking ability) Sector spread (credit spread) Reshape Finally the impression we had with Fig 30 was correct: the correlation between coefficients are pretty low except for issue spread and sector spread If we add the more important factors we obtain a multiple R-squared of more than 84% with all the coefficients being highly significant Issue.spread: Multiple R-Squared: 0.5911 Issue.spread + Sector.spread: Multiple R-Squared: 0.7364 Issue.spread + Sector.spread + YC.reshape: Multiple R-Squared: 0.8405 - 37 - FIXED INCOME PERFORMANCE ATTRIBUTION So we think that the most appropriate model for this particular portfolio would be the following: Call: lm(formula = Excess.return ~ Issue.spread + Sector.spread + YC.reshape) which consists of a multiple linear regression of three factors The next stage of the analysis should be an examination of the residuals from fitting the chosen model to check on the normality and constant variance assumptions If the residuals are nicely distributed we will be able to validate this three factor model The analysis consists of comparing the residual distribution to a standard normal We made the analysis more informative by supplementing it with a confidence interval, as suggested in Atkinson (1987) and Weisberg (1982) In essence, the procedure involves the generation of m pseudo-residual vectors, e, from yi = β + β1 xi1 + + β p xip + ε i y = Xβ + ε ( H = X XTX )X T ek = (I − H )ε k , T k = 1, , m and I being the identity matrix On the following graph you can see the 95% (solid line) confidence interval and the 90% confidence interval (dotted line): Fig 33 Scatter plot of the FIPA factor residuals - 38 - INTERPRETATION The residuals pass the test of the 90 percent interval, but fail the test of the 95% interval Confidence interval 95% Confidence interval 90% Points outside Total 15 17 173 173 Percentage Test passed 8.7% No 9.8% Yes Fig 34 90% and 95% confidence interval of the residuals We then can argue that for normal days (90% of the time) our model with three factors describe very well the excess return So we can conclude that the issue spread effect, which is definitely the main factor in our model, plays a central role in the generation of overperformance relative to the benchmark This proves that, at least for the period taken into consideration and after transaction costs but before management fees and bank account returns, it is the portfolio manger’s credit analysis ability that has generated an excess return (on average to 6bps per month) We repeated the same process after management fees and bank account returns which are both very small compared to the portfolio size Therefore the “net” excess return gives similar results (on average an excess return of to 5bps per month) So the portfolio manager did really create excess return for its client That’s fine But one could now ask this embarrassing question: “Do you still have the same picture under a risk-adjusted basis?” We answer this question in the next session 6.2 Performance on a risk-adjusted basis 6.2.1 Alpha and FIPA factors We have shown that the portfolio does produce excess return More, we showed thanks to the FIPA decomposition that it is the manager’s ability (issue spread) that is the main driver of the excess return With FIPA, we were able to decompose excess return into different factors The interesting property of the portfolio we are analyzing is that it only takes bet on credit spread while being “neutral” in interest and currency risk Therefore for this portfolio, the issue spread must play the same role of the alpha because they both try to measure the value added or subtracted by the portfolio manager We remind you that alpha measures the difference between a fund's actual returns and its expected performance, given its level of risk (as measured by beta) A positive alpha figure indicates the fund has performed better than its beta would predict In contrast, a negative alpha indicates a fund has underperformed, given the expectations established by the fund's beta Some investors see alpha as a measurement of the value added or subtracted by a fund's manager Those investors seeking higher return from their portfolios can take on more alpha risk and/or more beta risk There are numerous alpha-seeking strategies In this paper, we focus on an alpha strategy that makes use of the issue spread between bonds with different ratings It is generally admitted that the management of such a strategy requires a significant amount of fundamental research on credit and specific risk analysis Superior research is likely to generate greater alpha The three largely independent sources of alpha are: - 39 - FIXED INCOME PERFORMANCE ATTRIBUTION • • • higher expected returns from the strategic allocation into the higher credit risk high active management opportunities with bonds with lower ratings additional returns from the active tactical shifts across the different fixed-income sectors The combination of multiple independent alpha sources creates the opportunity for higher return with relatively small increase in risk The skills required in the successful management of credit spread portfolios can be used to capture all three sources of alpha described above We would like here to test if our issue spread calculated by FIPA is correlated or not with the alpha Unfortunately, we only dispose of eight months of complete data We are then forced to a weekly comparison in order to have enough data to an acceptable correlation analysis But the quality of the alpha will of course suffer from the very short period Here are the results: Issue spread and alpha (by week) 14 12 10 Pasis points Issue spread (Bps.) Alpha RC (Bps.) -2 -4 -6 08/2005 07/2005 06/2005 05/2005 04/2005 03/2005 02/2005 01/2005 -8 Fig 35 Comparison between issue spread and alpha on a weekly basis On a weekly basis the correlation is 0.63 and on average the alpha is around 1.4bps per week while the issue spread is around 0.6bps per week This indicates that a strong link between alpha and issue spread exists reflecting the manager’s ability to analyze credits and pick up the right bonds Unfortunately the history is much too short to perform a robust analysis and we are stuck there We however think that it is a good way for identifying the part of the risk-adjusted return, measured by the alpha, which has been created by the portfolio manager It would be interesting to redo this analysis on a monthly basis to improve the alpha quality and with to 10 years of data to improve the correlation analysis This being said, the Fig 35 gives us a first hint: it seems that the portfolio does generate some alpha after costs and that a good part of it is captured by the issue spread 6.2.2 Excess returns on a risk-adjusted basis Another way to adjust the excess returns to risk would be to adapt the benchmark in order to remove all the beta-returns We remind you that the three main factors that explain the returns of the portfolio analyzed are in order of importance: - 40 - INTERPRETATION • • • Issue spread (specific spread or picking ability) Sector spread (credit spread) Reshape with a multiple R-squared of 84% Furthermore, we know that the portfolio only takes bets on credit spread and is neutral on currency and interest risk That is the reason why, for this particular portfolio, issue spread and sector spread play the central roles Note that the portfolio is constructed to be neutral on interest risk but only in the first order (duration) It is then logic that the reshape is the third most important factor We know that the portfolio is 10% underweighted in AAA and overweighed in A and BBB The sector spread shows us how much return the portfolio manager has generated by being a bit riskier than the benchmark, but it does not tell us if the returns were fairly compared to the risk taken So how could we adjust excess returns to risk? If we could artificially increase the benchmark credit risk and equalize it to the portfolio credit risk, we could get rid of the return generated by taking more risk on credits Then, excess return could be computed on a riskadjusted basis and compared with the “usual” excess return To implement this process the necessary condition is to be able to extract the credit spread from the benchmark An easy and dirty way would be to take a AAA benchmark and a BBB benchmark and compute the theoretical spread But if we could split up the benchmark into different ratings and use the weights of the portfolio to compute the overall performance, we could directly adjust the benchmark risk to the portfolio risk Unfortunately the main problem with security-level benchmark data supplied by most vendors is that rates of return are not available on security-level (see point 3.4.) However, after a huge work of data quality improvement, we are totally free with FIPA to decompose a benchmark according to our wishes because the benchmark is treated as a “normal” security-level portfolio We propose here to decompose the benchmark by ratings and weight each bucket by the portfolio weights to adjust the benchmark credit risk This kind of decomposition is pretty similar to the well-established Brinson, Hood and Beebower (BHM) model13 for top-down equity performance attribution We have rExcess = wPF ⋅ rPF − wBM ⋅ rBM Adj rExcess = wPF ⋅ rPF − wPF ⋅ rBM where rExcess is the excess return, rExcess is the risk-adjusted excess return, wPF and wPM are respectively the weights of the portfolio and the benchmark and finally we have the terms rPF and rPM which are respectively the return of the portfolio and the benchmark Adj Then we can calculate: Adj Credit risk = rExcess − rExcess = (wPF ⋅ rPF − wBM ⋅ rBM ) − (wPF ⋅ rPF − wPF ⋅ rBM ) = wPF ⋅ rBM − wBM ⋅ rBM = rBM ⋅ (wPF − wBM ) 13 See for example [14] Splaulding D., “Investment Performance Attribution”, McGraw-Hill, 2003 - 41 - FIXED INCOME PERFORMANCE ATTRIBUTION which is similar to the Asset Allocation (AA) formula in the top-down BHM model And, Adj Selection = rExcess = rExcess − Credit risk = wPF ⋅ (rPF − rBM ) would be the return generated by the portfolio manager’s picking ability In the BHM model this is described as the Stock Selection effect (SS) As the weights in the portfolio are larger in BBB bonds compared to the weights of the BBB BBB benchmark wPF − wPM > , we expect the formula of credit risk to be positive because ( ) BBB bonds give on average higher returns than AAA bonds Credit risk explains the fair part of the excess return coming from the fact that the portfolio is riskier than its benchmark Here are the results for the portfolio analyzed: Date 01/2005 02/2005 03/2005 04/2005 05/2005 06/2005 07/2005 08/2005 10.19 3.51 4.11 7.11 1.91 5.74 -2.31 6.28 Excess return on a risk adjusted basis (Selection) 8.08 -3.81 22.86 8.70 1.85 2.14 -3.49 3.72 Return due to credit risk (Credit risk) 2.11 7.32 -18.76 -1.59 0.06 3.60 1.18 2.55 Excess return calculated by FIPA (r excess) Fig 36 BHM decomposition in bps The results are a priori surprising but in fact really interesting It seems that we can split the period in two: the first bucket would be January, February, May, June, July and August 2005 where the risk premium is positive The second bucket would be March and April 2005 with a negative risk premium For the first bucket an interpretation is straightforward The pure credit risk generates about 2bps per month So, in the excess return computed by FIPA we should remove about 2bps per month from the “normal” excess return to get a return on a risk-adjusted basis So on the 5bps that are on average generated every month by the portfolio (see 5.1.1.), 2bps are coming only from credit risk These 2bps of pure credit risk are simply added along the decomposition factors of the FIPA analysis (principally on credit spread and issue spread) The second bucket, March and April 2005, is trickier to analyze It seems that the premium to credit risk was negative (-18bps in March)! In fact, the bond market was pretty shaky in March/April 2005 because of the US auto-sector issue For example GM, one of the major auto-motive company, got downgraded from BBB- to BB in spring 2005 On the following graph you can see the disastrous effect of downgrading rumors on the GM Swap Relative Value Curve A very similar example could be given for Ford Fig 37 Effects on the Swap Relative Value of GM bonds after the downgrading - 42 - INTERPRETATION The erosion of credit quality in US auto-sectors companies caused a widening in credit spreads especially for the spread of the BBB segment It is the first time in the recent history – at least since 1997 – that only a segment (BBB) widens so much while other segments remain flat This widening was huge in March and induced large losses for people having GM bonds in their portfolios Additionally, most of them were forced sellers On 31.5.2005 this effect disappears because GM was downgraded to BB the 05.05.2005 and consequently jumped out of the BBB benchmark segment Difference of yields - rating class vs government bonds USD Bonds in basis points, August 1997 - Sept 2005 (Morgan Stanley) 440 AAA AA A 390 BBB 31.05.2005 340 290 14.03.2005 240 190 140 90 40 27.06.2005 10.01.2005 26.07.2004 09.02.2004 25.08.2003 10.03.2003 23.09.2002 08.04.2002 22.10.2001 07.05.2001 20.11.2000 05.06.2000 20.12.1999 05.07.1999 18.01.1999 03.08.1998 16.02.1998 01.09.1997 -10 Fig 38 Effects caused on the BBB yields by the downgrading of GM (in bps) Now it becomes easy to interpret the negative premium in March 2005 As we use the weights of the portfolio to weigh the benchmark, the BBB segment is consequently overweighed So the widening of the BBB curve in March induces large losses for the risk-adjusted benchmark In the opposite, all positions in GM in the portfolio were already sold in December 2004 Consequently, in the portfolio, we not have such big losses due to the BBB curve widening This reflects a good picking ability of the portfolio manager who has been able to remove GM position soon enough This is captured in our BHM model by the Selection effect And therefore this explains why we get a negative risk premium in March 2005 To summarize, if we remove the GM effect from the calculation, the “normal” excess return should be corrected of to bps per month to be risk-adjusted But if we keep the GM effect in the calculation, there is almost no differences between the “normal” excess return computed by FIPA (4.57bps) and the risk-adjusted excess return (5.01 bps) Mean Mean without GM effect (wihout March and April 2005) Excess return calculated by FIPA (r excess) 4.57 4.22 Excess return on a risk adjusted basis (Selection) 5.01 1.42 -0.44 2.80 Return due to credit risk (Credit risk) Fig 39 Mean of the BHM decomposition in bps (with and without GM effect) To conclude, we would like to make the reader attentive that normally the Brinson, Hood and Beebower (BHM) model is usually applied on equity The BHM model only splits the return - 43 - FIXED INCOME PERFORMANCE ATTRIBUTION into Asset Allocation and Stock Selection effect With bonds portfolios the BHM model is far too simple because it does not take into account important effects like the yield curves and the carry of the bonds However we have been able to apply this BHM model on the portfolio analyzed because we proved in the former chapters that the single main driver of the portfolio is the credit spread So a BHM decomposition on the credit spread only has been therefore possible for this particular portfolio CONCLUSION The Fixed Income Performance Attribution analysis (FIPA) is for sure an unbelievable powerful tool to decompose the performance of a bond portfolio The advantages of this method are numerous and include: a systematic identification of the basic sources of return in terms of bets and market variables via the FIPA factors; a flexible and consistent interpretation of attribution numbers; an easy measurement of different investment strategies within the same framework The main difficulties to perform such an analysis are certainly the set up and the data quality The set up is rather complex, especially when defining accurate yield curves and replicating the benchmark on a security-level In addition, data quality is for sure the most sensible point of the whole process Our experience has showed that one single mistake in a bond might make the system collapse and make the attribution difficult to interpret because some factors are very sensitive to any mistake With the FIPA decomposition we have also been able to identify the main driver of the portfolio excess return – in our case the issue spread We also showed that the portfolio generates on average some alpha and a decent excess return of to 6bps per month after costs but before management fees and cash returns (bank accounts) After fees and cash returns, the excess return is between to 5bps a month Under risk-adjusted basis, about basis points should be removed from excess return This being done, the portfolio always generates a net excess return of to 3bps a month for the client which emphasis the portfolio manager’s ability to analyze credits and generate some alpha This could be interpreted as the beginning of the proof that alphas can be generated after all costs have been taken into account Unfortunately data have been cleaned only back to 31.12.2004, so we not dispose of a sufficient time period to have robust results We can only conclude that during the period analyzed the portfolio over-performed its benchmark on a risk-adjusted basis However we can say nothing about the persistence over time of the over-performance For an academic point of view, FIPA analysis brings a huge variety of new data that have not been analyzed yet For instance, it would be interesting to the same analysis on a 10 or 15 year period to improve the robustness of the results and check the persistence of the overperformance Unfortunately, the time and the costs of a data cleaning are enormous Furthermore, we doubt that large banks or asset management companies will make the heart of their fixed income strategies available for an external analysis In the near future, we think that major players in the bond market will use FIPA analysis to analyze ex-post their bets and active strategies because a well set up FIPA analysis produces a mine of detailed and directly analyzable information Of course the same model could be easily extended for simulating ex-ante scenarios like a yield curve shift or a change in FX - 44 - CONCLUSION rates The FIPA analysis will therefore become also an active management tool which will help in the construction of an efficient portfolio When writing this thesis, at the opposite of the equity side, no standard attribution models for fixed income are well-established on the market yet This is certainly due to the complexity of the risk factors driving fixed income performance We believe that in the next few years Fixed Income Performance Attribution will remain a very hot topic in the bond industry Unfortunately we not think that so sensible data will be published very easily for academic researches and we are therefore a bit more reserved concerning the future benefits of FIPA for the academic world - 45 - FIXED INCOME PERFORMANCE ATTRIBUTION ACKNOWLEDGMENTS This paper was sponsored by Swisscanto Asset Management and conducted as a part of an internal project in the bond team I first would like to thank my two supervisors, Dr Nils Tuchschmid for his guidance throughout the work and Dr Anna Holzgang for her precious support on the FIPA project I also would like to thank Mr Alex Schöb for the confidence he gave me as well as all the bond team, the reporting team, the back office team and the Business Application team of Swisscanto for their support throughout the project I owe a special thank to Mr Matthias Zimmermann who helped me set up the FIPA module I would like also to thank Ms Doreen Roduit for the spelling correction Finally I am grateful to my family for the support and encouragements - 46 - REFERENCES REFERENCES [1] Atkinson A.C., “Plots, Transformations, and Regression”, Oxord Statistical Science Series, 1988 [2] Chambers J.M & Hastie T.J., “Statistical Models in S”, Wadsworth and Brook/Cole, 1988 [3] Colin A., “Fixed Income Attribution”, Wiley Finance Series, 2005 [4] Cook R.D & Weisberg S., “Residuals and Influence in Regression”; CRC/Chapman & Hall, 1982 [5] Dynkin L., Hyman J & Konstantinovsky V., “A return Attribution Model for Fixed Income Securities”, Handbook of Portfolio Management, 1998 [6] Esseghaier Z., Lal T., Cai P & Hannay P., “Yield Curve Decomposition and Fixed Income Attribution”, DST international, 2003 [7] Everitt B.S., “A Handbook on Statistical Analyses using S-Plus”, Chapman & Hall/CRC, 2002 [8] Fong G., Yoo D., & Zelaya Z.M., “Global Performance Attribution, Perspectives on International Fixed Income Investing”, 1998 [9] Hughston L., “Vasicek and Beyond: Approaches to Building and Applying Interest Rate Models”, Risk Books, 1997 [10] James J & Webber N., “Interest Rate Modelling”, Ed J Wiley, 2001 [11] Knott G.D., “Interpolating cubic splines”, Birkhäuser, 2000 [12] Søgaard-Andersen P., “Fixed Income Performance Attribution, a flexible approach”, SimCorp Dimension, Knowledge-sharing, 2005 [13] Sørensen O., “FIPA calculations in SimCorp Dimension”, SimCorp Dimension, 2005 [14] Spaulding D., “Investment Performance Attribution”, McGraw-Hill, 2003 [15] Vasicek O., “An equilibrium characterisation of the term structure”, Journal of Financial Economics, 5: 177-187, 1977 - 47 - FIXED INCOME PERFORMANCE ATTRIBUTION 10 APPENDIX Appendix 1: US government yield curve principal component analysis # -# Fixed Income Performance Attribution # Principal Component Analysis # by Blaise Roduit # module(finmetrics) # Construct appropriate return data # -# Loading data in a time series with business days USD.GOV.YC