The Yield Model provides bond investors with four tools needed to navigate the fixed income markets successfully. First, we provide bond investors with direction. The first question most bond investors ask is: Where are interest rates going? In the Forecast & Results section the Yield Model provides interest rate forecasts on 31 different fixed income financial instruments. Using this information we then can guide investors as to how they can best allocate their bond portfolio over the next quarter and calendar year. We also provide the prior quarter’s forecast results so bond investors can evaluate how effective our forecasting is.
Second, we provide information. Each day we provide a dozen or more links to articles that relate to bond investing. The sources range from the most well known financial publications to government agencies to global economic organizations. Third, we give investors an understanding of what is occurring with their fixed income investments in our Weekly Commentary (as well as various Featured Model issues). With our Weekly Commentary we can give bond investors a summary of the prior week’s bond market events and performance (as well as key events that will affect bond markets and interest rates in the coming week). We can explain how our forecast is performing in response to these weekly events as well. For the more advanced quantitative analyst our various Featured Model issues use econometric models to explain topics currently making headlines in fixed income news. Lastly, we educate bond investors by proving a full explanation in our Forecast Methodology section. Here we fully explain how we use an econometric, time series model to forecast these 31 different interest rates.
July 24, 2010
The Yield Model's forecast has had rather disappointing results quarter to date. As of Thursday's close Barclay's Municipal Bond Index (which we have recommended over-weighting) had returned 1.05% quarter to date while the U.S. Aggregate Index had returned 0.66%. However, the U.S. Treasury 3-7 Year, U.S. Treasury 10-20 Year and 1-3 Year Credit Indices have trailed the Aggregate Index by a few basis points. The U.S. Treasury 20+ Year Index declined 0.33% quarter to date, consistent with the slight rise in longer term Treasury bond yields. High Yield and longer term credit have been the best performing bond asset classes quarter to date while TIPS, short term Treasuries and MBS have under-performed. Below is a summary of the week's key events.
On Monday Builder Confidence declined to the lowest level since April 2009 due to the expiration of the home buyer tax credit. The report attributed the decline to hesitancy of home buyer, tighter lending criteria and competition among distressed properties. The FDIC, the Federal Reserve and other government agencies held hearings in regard to the Community Reinvestment Act (there was some speculation that this act may have contributed to the financial crisis by forcing banks to make loans to borrowers they normally would not have). President Obama gave remarks in regard to Unemployment Insurance and that benefits need to be extended at the upcoming vote tomorrow. Some key points included more lending for small businesses and business hiring, but the focus was the necessity of keeping this program in place with so many Americans out of work. The FDIC selected a group of investors as the winning bidders on $898 Million of non-performing residential loans. The FDIC will retain a 60% stake. HAMP will be provided to eligible loans in the portfolio. Moody's announced they downgraded another $7.4 Billion backed by sub-prime RBS. The Moody's commercial property price index was up 3.6% in May but they noted prices would remain "choppy" in coming months.
On Tuesday the Reserve Bank of Australia's board released the minutes of their July 6th meeting where they decided to leave the Cash Rate at 4.5%. The focus on Europe's credit conditions was the biggest concern of the Reserve Bank and the coming months will determine whether or not the bank should change policy given what happens in Europe. The bank expects inflation to be above 3% at year end. The Federal Reserve and the Treasury agreed to reduce the amount of credit protection for the Term Asset-Backed Securities Loan Facility (TALF) from $20 Billion to $4.3 Billion as many of the loans have been repaid early due to market level interest rates being more attractive for ABS and CMBS borrowers. The TALF has had no losses to date and is well collateralized. Federal Reserve Bank Governor Daniel K. Tarullo spoke before the Subcommittee on Security and International Trade and Finance on Tuesday. His testimony covered the U.S.'s role in international regulation, financial market reform (including Basel III) and the impact of the Dodd-Frank Act. Governor Tarullo said the goals of the international cooperation are to increase stability, to prevent competitive imbalances, to promote the availability of information flows and to share information to mitigate financial instability. Treasury Secretary Brainard spoke at the Federal Reserve Bank of San Francisco on Asia's role in the economic recovery. He noted the three objectives of partnering with Asia are assuring recovery in financial flows and international trade, promotion of stable growth policies and support of integration among Asian countries. He also discussed the affects of the various U.S. and international programs that prevented a total global economic meltdown which included projected global growth changing from 1.9% to 4.2%, G-20 exports returning to 86% of their peak levels and stronger balance sheets for banks. Housing Permits rebounded in June, but the overall U.S. housing market picture is grim as housing starts came in 31,000 lower than estimates. A Fitch survey of senior fixed income investors (a semi-annual survey) showed there has been "resiliency" in the recovery of credit markets, but the U.S. outlook is clearly better than that of Euro-area debt markets. Less than 10% of those surveyed expect credit deterioration across asset classes. June 2010 unemployment data was released by the BLS. Unemployment rates dropped in 39 states and the District of Columbia, but at the same time last year the national Unemployment Rate was at the same level of 9.5%.
On Wednesday, with the passage of the Dodd-Frank reform bill, the FDIC permanently raised deposit insurance coverage to $250,000 per depositor. The amount was temporarily increased to $250,000 from $100,000 in October 2008, but the new legislation made this permanent. The coverage applies to CDs as well as regular bank accounts (and will be applied retroactively to six banks that failed in the first three quarters of 2008). The BIS released their first quarter Provisional International Banking Statistics report. The report showed there was a $700 Billion increase in international banking activity in 1Q10. This was the first increase since 3Q08. In a research note Moody's stated liquidity was worsening for speculative grade credit according to an index that measures liquidity stress. This could be attributed to the large amounts of high yield bonds maturing in the next two to three years (some investors refer to this as a "maturity wall"). The White House released a statement from Vice President Joe Biden about the new financial reform. In his statement he noted the Bureau for Consumer Financial Protections is the primary agency that will look out for consumers, there will be reduced incentives for mortgage brokers to make risky loans, there will be greater credit score visibility and tax payers will no longer foot the bill for large firm failures. The Federal Reserve Bank of New York released a report on the bank stress test results (The Information Value of the Stress Test and Bank Opacity). The study found that markets had already reflected the information revealed by the stress tests but that the study did help to stop financial panic by making information about the viability of banks more transparent. Federal Reserve Chairman Ben Bernanke testified before Congress on Wednesday. Chairman Bernanke noted the economy appears to be growing at a moderate pace largely due to fiscal and monetary stimulus. The biggest concerns of the Fed appear to be the building foreclosure inventory and the length of time many Americans have been unemployed as this is time workers could have acquired new skills during (half of the unemployed have been out of work for more than six months). The good news is the slack in the labor market has kept inflation low. Chairman Bernanke reiterated rates will be kept low for an "extended period" given the uncertainty of the future of the current economic conditions.
On Thursday Existing Home Sales, the FHFA House Price Index and Leading Indicators were released. Existing Home Sales were expected to fall with the expiration of the home buyers tax credit, but still fell a full 5.1%. Supply rose to 8.9 months. The FHFA House Price Index rose 0.5% on the month at a seasonally adjusted rate. The Index of Leading Indicators declined by the consensus change of 0.2%. The number actually would have been lower, but with the Fed keeping rates so low the yield curve (which is 10.2% of the index calculation) is kept artificially steep. The CFTC announced they will be issuing a new report titled Traders in Financial Futures. The report now separates large traders into four categories to increase the transparency of futures markets: Dealers (Sell side), Asset Managers & Institutional (Buy side), Leveraged Funds (Buy side) and Other Participants. New York Federal Reserve President Dudley spoke about the regional economy on Thursday. He noted manufacturing growth has been from businesses replenishing inventories and if we are at the peak of the cycle "we will lose restocking as an impetus for growth."
On Friday the Committee of European Banking Supervisors released the results of the bank stress test (seven banks failed the test). The purpose of the test was to see how Euro-area banks would respond to any types of market or sovereign shocks. The test covered 65% of European bank assets which includes 91 banks. The study, conducted over a two year time frame, showed that under severe stress seven banks would have Tier 1 Capital Ratios that would fall below 6% where 4% is the required floor. Next week's key economic releases include New Home Sales, Case-Shiller HPI, Consumer Confidence, Durable Goods, Beige Book, GDP, Consumer Sentiment and the Employment Cost Index.
June 30, 2010
Our forecast indicates that an overweight to medium and long term Treasuries, Municipal bonds and Adjustable Rate Mortgages in 3Q09 and through to year end should outperform Barclays Aggregate Index. Fixed income asset classes to avoid include Treasuries of maturities two years and shorter and TIPS.Treasuries in the medium to long term maturity
(Barclays U.S. Treasury 3-7 Year Index appears to be the most under-valued part of the curve followed by the U.S. Treasury 7-10 Year Index and the Treasury indices with 10+ Year maturities) still have room to rally before year end. Corporate bonds at the higher and lower rated ends of the investment grade spectrum should see some widening in their spreads relative to Treasuries (but given shorter term Swap yields should fall, short term credit should be over-weight). Municipal bonds should see yields fall about 20 basis points between now and year end indicating they are one of the most attractive asset classes, so Barclays Municipal Bond Index should outperform the aggregate index between now and year end as well. We also show rates on ARMs will decline, so a portfolio exposure here would be beneficial. We continue to show the Fed as holding rates at their current level though year end. Our hypothetical portfolio is shown below with our rate forecast. Ideally we hope to outperform the Barclay's U.S. Aggregate Index by 20 to 30 basis points per quarter:
Our forecast for 2Q09 yielded some mostly successful results. We were correct in our suggested overweight allocation to Barclays U.S. Long Credit A and U.S. Credit indices, but the U.S. Intermediate Credit and U.S. Corporate High Yield indices continue to lag the aggregate index year do date (as of June 30, 2010). We were also correct in our overweight to the U.S. Treasury 7-10 Year and U.S. Treasury 10-20 Year indices (though an allocation to the U.S. Treasury 20+ Year Index would have earned the greatest excess returns year to date and was the best performing part of the Treasury curve). Our Municipal Bond recommendation was incorrect, but we feel this is an undervalued asset class that should rally before year end.
January 2010
One of the most important variables in all of finance and economics is the interest rate (or yield) on a given asset or financial instrument. Yields provide a way to gauge the current economic climate, to measure investors’ expectations, to determine the risk-reward trade off of an investment and even to indicate what markets anticipate inflation to be in coming years. Yields are used by economists to evaluate financial conditions, they are used by equity analysts to calculate a company’s cost of capital and they are used by CFOs to decide whether or not it is an appropriate time to issue new corporate debt. The Yield Model provides forecasts for the level of interest rates of various asset classes in future quarters. The rates forecasted by the Yield Model are typically considered to be the most important indicators of investor outlook and overall economic health. The Yield Model uses readily available, public financial and economic data for all forecasts. The instruments on which the Yield Model forecasts include Commercial Paper (one month financial and non-financial), the Fed Funds rate, one month CDs, one month Eurodollar deposits, U.S. Treasuries of various maturities, TIPS (Treasury Inflation Protected Securities), Swaps of various maturities, Fixed and Adjustable Rate Mortgages, Municipal bonds and Corporate bonds (AAA and BBB rated) .
There are numerous ways to forecast interest rates. For government bonds analysts use economic reports and releases. For corporate bonds credit analysts scrutinize balance sheets and financial ratios. Quantitative analysts use prepayment models to evaluate reinvestment risk for mortgage backed securities. Technical analysts use moving averages and trading volume to gauge the momentum of interest rate futures. Investors even factor in variables like the political climate and the quality of corporate governance when investing in foreign bonds. All of these are sound, well established and widely used techniques to forecast interest rates that thousands of investment professionals use in their analysis. The Yield Model takes a different approach. Using regressions, or econometrics, the Yield Model combines the fundamentals behind these kinds of analysis to model and forecast interest rates.
As an example, we can look at how a fixed income investor might derive the yield on a corporate bond. Most fixed income investors would agree the yield on an index of corporate bonds is largely a function of perceived credit, liquidity and interest rate risk in the economy. A truly seasoned bond trader probably has an idea of which direction the TED spread will be moving in over the coming quarter (and what that implies for any bonds they are considering buying or selling). Econometrics, however, can give us empirical evidence as to what these relationships have been in the past and allows us to forecast what they will be in the future. The Yield Model has identified 16 different financial time series that explain 85% to 99% of the variation in the 30 different rates we forecast.
The first step in designing our forecasting model is to hypothesize which time series’ drive our observed interest rate. We use multiple linear regression to do this. As an example, the Yield Model has created a model for the yield on the Moody’s Seasoned Corporate Bond All Industry BBB index using monthly data which can be found on the Federal Reserve’s web site. We regress the yield on the Moody’s BBB index on four different variables: a liquidity risk measure, a credit risk measure, a measure of credit spread (or interest rate) risk and an economy-wide measure of financial market volatility. Each variable contains 75 observations and the data spans from January 2003 to March 2009. We can then evaluate our results using an ANOVA (Analysis of Variance) table generated with Eviews software:
We can start by looking at a few basic statistics to decide whether or not we have modeled the yield of our index appropriately. After using some basic intuition as to what drives the risk and return of our given yield, typically we want the R-squared to explain a significant amount of its variability. Most econometricians hope to explain 90% to 95% of the variance (at a minimum) with their models. Clearly our model is on the right track as we have explained 97% of the variance of our index with only four variables.
The next check is to see if our variables are statistically significant at the individual and joint levels. To do this we look at the “p-value” for each coefficient. All four of our variables and the constant term are highly significant. In most cases any variable falling outside of 90% confidence should be taken out of the model. However, the size of the coefficient and the modeler’s rationale for including the variable should be considered as well. For example, were the “spread” variable significant at less than 90% we might still choose to include it as the coefficient is large (a 1% change in our spread measure would result in a 1.25% change in our BBB index yield all else being held constant) and we know most investors would agree that the spread variable has a fundamental economic relationship with the yield we are trying to explain. We then evaluate the p-value for the F-statistic. With 99.99% confidence we can say that all coefficients jointly affect the variability of the yield on our BBB index. One final check with the F-statistic and t-statistics is for the presence of multicollinearity. A common issue when modeling financial time series is so much of the data is highly correlated. When the S&P 500 rises, so does the Dow Jones index. When the ten year treasury yield declines, so do the yields on conforming mortgage backed securities (give or take some spread widening or tightening). When multicollinearity is present the result can be inaccurate coefficient estimates. Multicollinearity is typically present when none (or few) of the regressors are statistically significant, yet the model has a high R-squared. Clearly this is not the case . Were multicollinearity present, we could simply drop or replace the variables with the high correlation and re-run the model.
Even though our model explains 97% of the variance in our interest rate, there is the possibility there is a key driver of this rate we have excluded from our model (econometricians call this omitted variable bias). We can observe this when our error term is not constant and has some correlation with our dependent variable (i.e. it is heteroskedastic and not homoskedastic). The result is that regressors (independent variables) can have their variability understated so a variable that is actually not statistically significant is included in the regression model. To see if hetereoskedasticity is present we can simply view a time series of the residuals from our model:
Clearly the error term is heteroskedastic and does not follow a white noise process as the error term has a significant amount of variability . There were multiple quarters where the model over or underestimated the actual yield consistently. To correct for heteroskedastcicity we use White-corrected standard errors (which shift the confidence intervals) which adjust for the inconsistency in our error term.
Another check we use our error term for is for the presence of autocorrelation. This can also result in inaccurate coefficient estimates. Positive autocorrelation means that if the error term increases in one period, it is highly likely it will increase in the following period (inflation is a good example of a variable with positive autocorrelation). Negative autocorrelation means that a positive increase is typically followed by a decrease in the following period. This is less likely to be found in most types of financial data. To test for autocorrelation we use the Durbin-Watson (DW) statistic which is included in our ANOVA table. The interpretation is fairly simple. A DW of 2 indicates no autocorrelation, a DW of 0 indicates highly positive autocorrelation and a value of four indicates negative autocorrelation. With a DW of 0.86 there is clearly some positive autocorrelation. Autocorrelation can cause the same problem as heteroskedasticity: Coefficient variance is underestimated so we conclude variables are statistically significant when in fact they are not. The Hanson method is used to adjust the standard errors when autocorrelation is present.
One final check is for the stability of the parameters in our regression. If we are going to use our regression as a forecasting tool, it is imperative the relationships between our independent variables and our dependent variable have been stable in the past (and are likely to continue to be in the future). To confirm parameter stability we use the cumulative sum of the standardized recursive residuals (or “CUSUM”) test. If the CUSUM calculation falls within the 5% confidence bands, we can say with 95% confidence that our parameters are stable over our regression sample. Clearly our parameters are stable as the CUSUM calculation lays well within the 5% bands:
Once we have verified our model meets these requirements (or the proper correction measures are put in place), we can be confident our model has a minimal level of validity when explaining the variability of our given interest rate.
While multivariate regression can help us identify which financial time series explain the variability of a given interest rate, this type of regression can only take us so far in terms of forecasting. To improve our model’s accuracy we construct a vector autoregression (VAR) from our original multivariate model. The VAR has two basic advantages over our initial multivariate model. One, the VAR accounts for current and historical values of independent and dependent variables while the multivariate regression did not use historical values. Second, the VAR captures the interdependencies of each variable (independent and dependent) which are cross-variable dynamics that improve the explanatory power of the regression. Financial markets are highly efficient and the information contained in our explanatory variables is mostly reflected in our BBB yield almost instantaneously, but the VAR will account for any influence prior observations have over the current BBB yield and will capture the magnitude of how much these explanatory variables have changed over a given time period. Below is the basic algebraic comparison of a multivariate regression and a vector autoregression (using three lags) that we use for the BBB index yield: 
Below is the Eviews output of a VAR for the BBB index with the independent variables we used in our original regression:
The output is similar to our original ANOVA table, but there are more coefficients and some additional descriptive statistics. Both the R-squared and adjusted R-squared have increased (meaning the increase in explanatory power has outweighed the statistical “cost” of including lagged variables). The Sum of Squared Residuals has declined from 0.98 to 0.76. If our model continues to fit the data this well in the future, this will reduce the errors of our model significantly . As we have already confirmed the independent variables model the interest rate well with our original multivariate regression, our final decision when evaluating the VAR is the number of lags to include in our model. In any kind of time series analysis the relationship between a variable’s current and past values diminish the further away from the past value you are. For example, many economists believe the slope of the yield curve is an indicator of economic growth (and sometimes recession). Though the slope of the curve 12 months ago will have some relationship with the current state of the economy, clearly the slope of the curve one month ago will have a stronger relationship with current economic conditions than the slope of the curve twelve months ago. The question is: What is the most efficient number of lags to include in our VAR (i.e. what is the “order” of the VAR?)? To answer this we use the AIC (Akaike Information Criterion) and the SIC (Schwarz Information Criterion). The calculation of the AIC is:
AIC(p) = ln[SSR(p)/T] + (p + 1)2/T
The intuition behind the AIC is relatively simple. The goal of a regression is to minimize the sum of squared residuals (SSR). The SSR generally falls as we increase the number of lags in the model, but the “p” term in the equation penalizes the model for each time the number of lags included is increased. The concept is similar to that of the adjusted R-squared. The adjusted R-squared will decline at a certain point as more regressors are added which indicate a statistical cost of expanding the model. Essentially the AIC measures the trade off between reducing the residuals and adding lags (only this metric will decline or become more negative if including more lags adds value). The optimal model is the one with the smallest AIC. The SIC is a similar calculation, but the second term is (p + 1)lnT/T. Below are the AIC and SIC of VARs of orders one through six for our BBB index yield model:
Before we select the order of our model, it is generally a good idea to be realistic as to how many lags of a variable actually affect its current value. Financial markets reflect information relatively quickly. It is highly unlikely that lags of a variable affecting BBB corporate bond yields will have any real affects more than a quarter or so later. Ideally the AIC and SIC will select the same model, but often times they will indicate a different number of lags to include for the same model. The basic difference between the two measures is the AIC overestimates the number of lags in large samples and the SIC tends to select models with too few lags (as it penalizes more harshly for the change in degrees of freedom). There is no rule of thumb as to which information criteria works best. For our BBB index yield model 3 lags seems to fit best. Our model is on the smaller side, but clearly the AIC has not over-estimated the model as it has selected only 3 lags. Though the SIC selects the model of order one, we know it traditionally selects models with too few lags. We now have an efficient, highly explanatory and parsimonious regression that is consistent with what most investors would agree explains the majority of the variability in the BBB index yield. We can now make an estimate as to what our given yield will be at the next quarter or calendar year end.
Our BBB index model (run with data as of March 2009) indicated the yield would fall to 7.73% from 8.45% in 2Q09 (it actually reached 7.17%) and then continue to fall to 6.70% in 3Q09 (it actually reached 6.17%). Most investors would consider both forecasts as successes as the direction of the yield move was correct and the forecast errors (56 basis points and 53 basis points) were within one standard deviation of that of the BBB sample (71 basis points). The model has forecasted the BBB yield to be 6.43% at year end (and was actually at 6.41% at year end). The forecasted yield and the actual yield are displayed graphically below:
April 2010
When constructing an econometric model for a given interest rate, it does not take much of an imagination to determine which variables will drive that given interest rate. Cash flow and leverage for a company will determine the spread on its bond yields when it issues new debt. Inflation will determine the yield at which investors wish to buy bonds in the Treasury market. Tax revenues are a large determinant of the yield on a state or local government’s general obligation municipal bonds (if tax revenue is declining there is a larger probability bond holders won’t receive timely interest and principal payments so yields will rise). The one thing that cash flow, leverage, inflation and tax revenue all have in common is they are all highly observable, measurable variables that we can use to model a given yield. With a little bit of basic investor intuition (and even data mining) an econometrician can develop a highly useful model in only a few minutes. However, for some financial instruments it can be difficult to find variables that explain enough of the variation in a given rate to develop a forecast. Part of the reason is that a certain asset’s yield may not be entirely determined by a set of observable financial and economic variables. Sometimes an econometrician must use a latent variable model to find a regression that is sufficient enough to explain the changes in a given interest rate.
A latent variable is a variable that is not directly measurable but is inferred from a group of variables that are directly measurable (the concept is similar to using an index to measure an economic or financial variable…i.e. to measure the return of a given sector of the stock market a company like Standard & Poor’s uses a group of companies that are considered to be most representative of that sector). As mentioned earlier, it isn’t difficult to find out which variables determine Treasury rates through some basic trial and error. Models of Treasury rates can include explanatory variables like inflation, GDP, the budget deficit, the slope of the yield curve, foreign purchases of Treasury bonds, the Fed Funds rate and implied interest rate volatility. The list is limitless for Treasuries. However, when we developed a model for Treasury Inflation Protected Securities (TIPS) after trying numerous variations of these variables we simply could not find a parsimonious model that could explain more than 50% of the variability in TIPS rates. This was clearly reflected in our forecast for 1Q10 as TIPS was where our forecast had the largest error. This was likely due to over-specification in an effort to explain a high enough percent of the variance of TIPS.
To understand what drives TIPS yields, a basic understanding of how TIPS work is needed. TIPS differ from nominal Treasury bills, notes and bonds as their principal is adjusted with movements of inflation while nominal Treasuries do not have any adjustment to their principal (remember that par value and market value are two different things). The inflation adjustment is based on the Consumer Price Index Urban Non-Seasonally Adjusted (CPI-U NSA) calculation. It should be noted that in the event of deflation TIPS actually have their principal adjusted downward, but have a floor, or deflation put, of their par value at their actual redemption. There are a few key points to understand here. One, TIPS pay a fixed coupon on a semi-annual basis. This means as inflation goes up (and thus the principal value of the TIPS) so too does the actual interest payment. For example, if a TIPS has a par value of $1,000 and has a 5% coupon and it is a month interest is to be paid out the investor will receive an interest payment of $25 ($1,000 x 5% ÷ 2 = $25). Now lets assume (and this is an extreme assumption just so we can see the affect of inflation on a TIPS) that inflation three months prior to this interest payment of $25 was 2.5% and is 2.5% of the next three months. The principal will be adjusted upward by 5% (in daily increments) to a value of $1,050 on the next payment date. At an interest rate of 2.5% the amount of the interest payment will be $26.25 ($1,050 x 5% ÷ 2 = $26.25). However, if the reverse were true and prices had actually fallen by 2.5% the prior three months and then an additional 2.5% in the next three months the principal would have been adjusted downward to $950 and the interest payment would have declined from the prior period to $23.75 (the point here is that even though the TIPS has a floor of $1,000, the interest payments will be smaller until inflation moves upward again). The point should also be made that were this TIPS trading at a par of $1,100 and deflation occurred over the rest of the term of the bond as much as $100 of principal (about 9% of the bond’s value ) could be eroded. Typically TIPS trading at a significantly greater par value than their par value at issuance will trade at a discount to those closer to their floor (or original par value) to compensate for this deflation risk. It should be noted that many of these risks are mitigated by holding a basket of TIPS and simply over or under-weightings TIPS holdings based on The Yield Model’s forecast.
Now that we have a fundamental understanding of how TIPS work, we can hypothesize as to what investment environment is the best for owning TIPS. There are numerous opinions as to when it is best to invest in TIPS. One of the more popular strategies is to look at the break even rate between a TIPS and a nominal Treasury of comparable duration. The yield of the nominal Treasury is typically greater than the TIPS yield as the holder of the nominal Treasury requires a higher interest rate to compensate them for the inflation risk inherent in a Treasury bond. TIPS require a smaller yield as their principal is adjusted upward as inflation occurs (so normally the nominal yield less the TIPS yield is positive and the difference is somewhere around the 2% range depending on what the market’s view of inflation is ). If an investor believes the average annual inflation rate will be greater than this difference until the maturity of the two bonds the TIPS will outperform the comparable nominal Treasury bond. There are two problems with this analysis: One, it does not take into account which of the two yields will move as the market adjusts to actual inflation levels. For example, if the break even rate is currently at 1.5% and an investor believes actual inflation will be 3% over the coming year they would choose to buy TIPS rather than Treasuries. If inflation trends toward the 3% level, the break even rate between these two securities will adjust to market expectations and expand to 3%. But this could be from either the nominal Treasury yield rising, the TIPS yield falling or some combination of the two. If yields are at high levels, the rise in the Treasury yield may not necessarily mean the Treasury will under-perform as the change in price will not be as large in a higher yielding environment so the Treasury security could just as easily have a greater total return even though actual inflation was higher than the break even rate reflected. Essentially this analysis falls short because it does not account for the actual level of the two rates. The second problem is this analysis ignores other fixed income asset classes. TIPS might outperform nominal Treasuries over a given time period, but this does not help an investor if mortgage backed securities, high yield bonds and municipal bonds all produce significantly higher returns than both TIPS and nominal Treasuries. Another strategy aims to exploit the fact that the CPI index used to adjust the principal of TIPS is not seasonally adjusted so TIPS will outperform over the first half of the year and under-perform in the second half of the year. Below we show the total return of the Barclays TIPS Index less the total return of the Barclays 3-7 Year Treasury Bond Index by half for the last ten calendar years . The green bars represent the difference between the two funds (the TIPS less Treasury total return) for the first half of the year and the blue bars represent the second half of the year. The solid bars represent when the hypothesis that TIPS outperformed or underperformed nominal Treasuries was correct. The hollow bars represent when that hypothesis was wrong. Though the strategy would work in thirteen out of twenty half year periods (a 65% success rate) the strategy is not perfect.
To accurately forecast what direction and with what magnitude a TIPS yield will move we need to consider what the optimal investment environment is for TIPS. Clearly we know that a highly inflationary environment will drive the yield on TIPS, but we have to consider other factors that will affect TIPS yields relative to other asset classes. We need a measure of what will have a positive impact on the return of TIPS and a mostly negative impact on other fixed income securities. The answer is stagflation. The definition of stagflation varies, but most economists would agree it includes some combination of high inflation, high unemployment and stagnant growth (i.e. inflation and stagnation result in stagflation). If you think about this environment, it’s easy to see why investors would want to be holding TIPS. Positive inflation actually increases the principal of TIPS, but for just about every other security inflation erodes the value. Inflation is bad for nominal Treasuries, it offsets any yield an investor gets from a money market fund and it even eats into the principal value of corporate bonds. What is most important about the stagnation part of stagflation is that it has no affect on TIPS. If the United States needs cash to pay off maturing Treasuries it can simply issue more debt, regardless of the strength of the U.S. economy. Stagnation, however, does affect other fixed income securities. As the economy slows and unemployment rises, people find it harder to pay bills. As consumers get squeezed banks tighten lending standards and require higher interest rates to compensate them for the risk of consumers not being able to pay their debts. The end result: rising interest rates on mortgages and other securitized asset classes (like credit cards, small business loans and auto loans). This puts downward pressure on the value of these types of securities already outstanding. The implications are the same for corporate bonds. As growth slows so does business activity. Banks have fewer customers opening accounts. Manufacturing companies see sales decline. Shipping companies see activity slow as consumers and businesses purchase less. These companies see less business so their cash flow and their equity values decline (thus pushing their leverage upward). This raises the yields on their existing debt as the chance of them failing to make timely interest and principal payments increases. Slowing growth will push municipal bond yields higher too as tax revenue declines. Clearly stagflation is the optimal environment to have exposure to TIPS.
As we have now identified when we want to invest in TIPS, this brings us back to the concept of what a latent variable is. As noted earlier, there are various definitions of how to measure stagflation as it is not directly observable thus making it a latent variable. Two of the more common “back of the envelope” measures of stagflation include the Simplified Stagflation Index (SFI) and the Misery Index. The SFI is calculated by taking the difference between the monthly percent changes in Average Hourly Earnings and the CPI-U NSA and multiplying by 100 (this index was at -28.76 as of January 2010). When the index is negative this means prices are rising faster than income. When this occurs people have less disposable income as a larger portion of their income is allocated to purchases of food, utilities and gasoline. The result is less economic activity. The Misery Index is simply the unemployment rate plus the annual inflation rate (this index was at 12.33% as of January 2010). As most economists agree that the equilibrium rate of unemployment is 5% and the target rate of inflation is around 2% to 2.5%, any reading over 8% would be considered stagflationary. We show the results when we regress each of the variables against the five year on the run TIPS yield from January 2003 to January 2010 below:
Our two TIPS models give us some mixed results when we use the different stagflation measures. On the positive side the stagflation coefficients and the constant terms are statistically significant for both models. The coefficients also have the sign we would expect them to have. The SFI Index coefficient implies that for every increase of one point in this index results in a rise in the five year TIPS yield of 0.0034% putting downward pressure on the price (which makes sense as the more positive this index the more wages and the economy grow relative to inflation where other bonds tend to outperform TIPS). The Misery Index coefficient makes sense as well. This coefficient implies for every 1% rise in the Misery Index the result is a decline in the five year TIPS yield of 0.22%.
It appears as though we are on the right track, but we are simply not fully capturing stagflation (or some expectation of the measure). There appear to be two key factors we are missing here: the expected level of inflation and a risk premium associated with TIPS of various maturities. What The Yield Model does is use a variation of the Misery Index. We can still use the unemployment rate, but rather than using the CPI-U NSA (which only gives us what inflation has been in the past) we use the five year breakeven inflation rate which tells us what markets anticipate inflation will be, on average, over the next five years . In addition to using expected inflation, we add a risk premium dimension which is the difference between the ten and five year on the run TIPS yields giving us an idea of how much short term inflation expectations are seeping into long term expectations. Below we display the results of our original two regressions along with the regression with our new latent variable that accounts for expected inflation and the inflation term premium:
Clearly our latent variable version of the Misery Index is superior to both back of the envelope stagflation measures. The constant term and the Latent coefficient are statistically significant at the highest confidence levels. The sign of our coefficient also makes sense as it implies for every 1.0% move upward in the latent variable the result is a decline of the five year TIPS yield of 0.33% (we also see TIPS have a greater sensitivity when we account for expected inflation and how much short term inflation expectations are flowing into long term expectations). Lastly, our latent variable explains 55% of the variability in the five year TIPS yield which is far greater than what the SFI and Misery indices explain. When we combine our latent variable with some of the more traditional variables that explain nominal Treasury yields, we have a model that explains as much as 95% of the variability in TIPS yields.