Kamakura Blog: Fixed Income Performance Attribution

We can briefly summarize the key causes of the cultural differences between fixed income investment managers and bankers in a few bullet points:

• Nature of assets managed: The overwhelming majority of the assets held by fixed income fund managers is publicly traded.  The overwhelming majority of assets held by banks, at least by number of transactions, is not publicly traded.
• Nature of performance measurement: In fixed income fund management, performance measurement is based on market valuation and both absolute returns and returns versus a benchmark portfolio.  In spite of more than 40 years of debate in banking, that industry remains largely driven by financial accounting-based performance measurement, not market value based performance measurement
• Granularity of performance measurement: The CFA Institute, formerly known as the Association for Investment Management and Research, has long recommended calculating performance using daily time periods. Outside of the trading floor, banks are largely driven by monthly or quarterly time frames. The performance attribution recommendations are available at this link:

https://www.cfainstitute.org/ethics/Documents/Codes%20Documents/redraft_aimrpps.pdf

• Volume of transactions: Most investment managers would have no more than 5,000 or 10,000 positions, and many would have far less. Among Kamakura’s clients is one of the world’s 5 largest banks, with more than 700 million assets and liabilities. This creates a much bigger information technology footprint in banking by necessity.
• Staff count: Staffing in investment management is lean and mean, because very little retail business is done, at least relative to banking.  The largest banks in North America, by contrast, have a staff count in the hundreds of thousands.
• Analytical rigor: There are brilliant people in both banking and fixed income investment management who are well beyond best practice in their analysis.  That being said, it is much more tempting to manage risk with a spreadsheet or risk analysis that is not much more powerful than a spreadsheet when the portfolio has a relatively small transaction count, something very common in the hedge fund industry in particular.

I recently came across a European paper on fixed income performance attribution that relied heavily on standard yield to maturity calculations and duration as the basis for improved fixed income performance attribution.  The purpose of this blog, in an introductory way, is to explain why it is particularly important in fixed income portfolio attribution to apply much more accurate and modern techniques than the duration concept, because the errors embedded in the yield to maturity concept and duration are large and can result in wildly inaccurate assessments of fixed income performance attribution:

• Yield to maturity discounts cash flows at all payment dates at the same interest rate
• If the same issuer has two bonds outstanding with different yields to maturity, interest payments on the same dates will be discounted at different rates for each bond
• Common spread calculations are usually the simple difference between the yields to maturity on two bonds with similar but not identical maturity dates

For a complete account of the errors embedded in the yield to maturity and duration calculations, see van Deventer, Imai and Mesler, Advanced Financial Risk Management (John Wiley & Sons, 2004).

Now we can see the benefits of cross-pollenization of risk management between bankers and fixed come fund managers:

• We take the mark to market orientation of fund managers
• We take the exact day count “matched maturity transfer pricing” concept from banking
• We take the yield curve smoothing concepts that are essential to transfer pricing in banking
• We take the macro factor driven stress testing approach from banking and bank regulators that has come out of the 2007-2010 credit crisis
• We then use this technology to analyze the reasons for mark to market performance changes in a way already familiar to fixed income fund managers but with greater accuracy.

We know that changes in a large number of macro-economic factors affect performance of fixed income portfolios.  A small sample of them is listed here:

• Level and shape of the risk free yield curve
• Home prices
• Commercial real estate prices
• Oil prices
• Other commodity prices
• Foreign exchange rates
• Market volatility
• Unemployment rates
• Changes in real gross domestic product
• Government surpluses or deficits

Kamakura clients are increasingly measuring the impact of each of these factors on mark to market performance by tracing their impact on credit spreads, prepayment and default risk of borrowers from retail to small business to major corporations to sovereigns.  In today’s example, we keep it simple.

• We analyze the performance of one bond
• We assume that we only need to analyze 3 drivers of performance: changes in the risk free yield curve and the credit spread for the bond issuer, along with the passage of time.
• We look from the perspective of July 15, 2010 and ask the question, “how much did these risk factor movements contribute to the gain or loss in the value of our bond since April 15, 2010?”  We could just as easily do the analysis for a portfolio versus a benchmark.  We keep it very simple here for expository purposes.

A more complete analysis has a much longer list of drivers of performance that includes all of the macro factors above plus many more.

A Worked Example of Modern Fixed Income Performance Attribution

We now go through a worked example of a more modern approach to fixed income performance attribution with one bond issued by “ABC Company” and three drivers of performance: the risk free yield curve, the spread and the passage of time.

We assume the ABC bond has a par value of 1000, a 10% coupon, semiannual coupon payment dates of June 30 and December 31, and a maturity on June 30, 2019.  We observe in the market place these prices:

April 15, 2010: $1532.60 (net present value=price plus accrued interest)
July 15, 2010: $1580.18

We ask this question: What factors have caused the net present value of the bond to change from $1532.60 to $1580.18? How much was due to the passage of time, how much to changes in the risk free rate, and how much to spread changes?

We answer this question by using the maximum smoothness forward rate approach to yield curve smoothing outlined in Chapters 8 and 18 of Advanced Financial Risk Management and explained in these recent blog entries:

van Deventer, Donald R. “Basic Building Blocks of Yield Curve Smoothing, Part 10: Maximum Smoothness Forward Rates and Related Yields versus Nelson-Siegel,” Kamakura blog, www.kamakuraco.com, January 5, 2010.  Redistributed on www.riskcenter.com on January 7, 2010.

van Deventer, Donald R. “Basic Building Blocks of Yield Curve Smoothing, Part 12: Smoothing with Bond Prices as Inputs,” Kamakura blog, www.kamakuraco.com, January 20, 2010. Redistributed on www.riskcenter.com on January 21, 2010.

van Deventer, Donald R. “Basic Building Blocks of Yield Curve Smoothing, Part 13: Smoothing Credit Spreads,” Kamakura blog, www.kamakuraco.com, April 7, 2010. Redistributed on www.riskcenter.com, April 14, 2010.

We apply these techniques to the risk free yield curve and to the ABC bonds outstanding to derive a “risk free” and “risky” yield curve on April 15, 2010 and July 15, 2010.  As a substitute for a risky yield curve derived from all ABC bonds outstanding, we assume that, by coincidence, the yield curve for ABC is identical to the US dollar libor-swap curve.

For example, here are the zero coupon bond yields for the risk-free and risky (ABC curve or swap curve) on April 15, 2010 as reported in Kamakura’s “Friday Forecast” available on www.kamakuraco.com or via www.riskcenter.com:

Note that, on this day, the risk-free yield curve’s zero coupon yields were actually higher than the ABC Company/swap curve zero yields at the longer maturities.  This is an increasingly common phenomenon that recognizes that the risk free or sovereign yield curve is not, in fact, risk free.  For more on that issue, see the following commentary on the Kamakura forecasting process:

van Deventer, Donald R. “The Kamakura Corporation Monthly Forecast of U.S. Treasury Yields,” Kamakura blog, www.kamakuraco.com, March 31, 2010. Redistributed on www.riskcenter.com on April 1, 2010.

We also take the zero coupon yields for the risk free and risky ABC/swap yield curve on July 15, 2010:

Over this three month period, we can see that the risk free zero coupon yield curve has fallen substantially:

Risky zero coupon yields, with the exception of the short maturities, have also moved downward, as this graph shows:

The zero coupon credit spread for ABC company/swap curve have moved as shown below:

Many researchers have found that it is common for credit spreads to rise when risk-free yields fall, and that is consistent with yield curve movements between these two dates. We extract the following zero coupon bond prices from both yield curves on both dates and apply it for performance attribution to the cash flows on the ABC bond:

We want to understand the drivers of changes in bond value so we analyze these specific combinations of changes in the key ‘macro factors’ that we have chosen to analyze:

The first two scenarios use the real inputs for April 15 and July 15, 2010.  The next three scenarios shift one of our three key drivers of returns, one at a time.  The “risk-free shift only” scenario can be explained as follows: “Assume we are at April 15, 2010 and the risk free curve took July 15, 2010 levels but the credit spread was the April 15 spread.” The “spread shift only” scenario means “Assume we are at April 15, 2010 and risk free curve is the April 15 curve, but the spread is the July 15 spread.” In the final scenario, the “date shift only” scenario applies the April 15 risk-free curve and spread on the July 15, 2010 value date, when all cash flows are 3 months closer than they were on April 15.

In each case, the ABC bond’s present value is the sum of the relevant zero coupon bond times the cash flow on that particular date.  Those zero coupon bonds are shown here:

When we apply these scenarios, we get the following components of performance:

Note that we first deduct from the actual April 15, 2010 “gross bond value” or net present value the present value of the June 30, 2010 coupon payment of $50.  This adjustment is necessary to insure we are comparing the value of two securities (ABC bond on April 15 and July 15) with the same attributes.  This adjustment would not be necessary if we were using the daily return intervals that the CFA Institute recommends, since the coupon payment would just be an element of daily total return. In this case, we deduct the present value of that first coupon rather than speculate on reinvestment returns from June 30 to July 15.

The analysis shows that, after adjusting for the first coupon, our ABC bond returned a total of 6.579% from April 15, 2010 to July 15, 2010.  The downward shift in the risk-free curve contributed 6.123% to this total return.  The widening of credit spreads by itself reduced return by 0.480%. The passage of time, which moved all cash flows 3 months closer, contributed 1.141% to total return.  A final component, the impact of all factors moving together, reduced total return by 0.204%.

In this fashion, we have a complete and accurate understanding of the contribution of the risk factors we have chosen to analyze to total absolute return.  Return relative to a benchmark index, or tracking error, is analyzed in the same way.  We have avoided the serious performance attribution errors that can arise from the simplifying assumptions embedded in yield to maturity and simple credit spread calculations by using modern yield curve and credit spread smoothing on an exact day count basis. The process is simple and straightforward when using modern enterprise risk management software like Kamakura Risk Manager.

For more details on today’s example or how to apply Kamakura Risk Manager to a richer analysis using macro factors like home prices, real GDP or unemployment, please contact us at info@kamakuraco.com.

Donald R. van Deventer
Kamakura Corporation
Honolulu, July 21, 2010