Predicting Fixed Income Credit Spread Movements
Global Strategic Management
March 1st, 2001
Abstract:
The goal of this exercise was to come up with a multi-factor model to forecast changes in credit spreads. The models produced significant results for two credit spreads. We then tested our BBB model with a trading strategy. Compared to benchmark (30-day Euro$), annualized alpha was 1.01%. We suggest that further work could seek to implement a trading strategy that capitalizes on our model's predictive power.
Conclusions/Future paths of study
Introduction
In this exercise, we used various financial variables to predict the direction and magnitude of credit spread movements. We focused on the US market, specifically 3 spreads: the 10-year swap spread, the spread between the AAA 7-10 year maturity corporate bond and the 10-year Treasury Bond, and the spread between BBB 7-10 year maturity corporate bond and the10-year Treasury Bond.
After identifying variables that we thought would have predictive power, we identified the models that did the best job of predicting credit spreads. We used the predictions to implement a trading strategy. Our strategy was to take a long position in the spread (i.e. buying the BBB and selling the10-year U.S. Treasury Bond in equal weights) when our model predicted a decrease in the spread and to take a short position in the spread (i.e. selling the BBB and buying the10-year U.S. Treasury Bond in equal weights) when our model predicted an increase in spreads. We chose the BBB-10Yr Treasury spread to test our predictions based on the findings of research reported by Fabio Alessandrini [Sept 1999]. Alessandrini’s research finds that the Baa credit spread has inherent predictability. His model demonstrated a significant relationship between the lagged change in 10Yr Treasury and a lagged change in the value of the firm (proxied by the change in the DJIA). Additionally, his findings state that this spread is sensitive to the business cycle. These variables become more statistically significant and the coefficients larger during a recession. Based on these findings we chose to test the models predictive power for the lower rated BBB credit spread.
There are a number of economically significant reasons for investigating credit spreads. In the U.S., as the government buys back more government debt and the supply of Treasury bonds decreases, corporate debt will play a more significant role in fixed income portfolio management. In Europe, the emergence of the Euro currency has eliminated various asset classes within European fixed income and this forces portfolio managers to look for other means with which to diversify, namely, in corporate debt. Credit risk is one of the two most important risk factors for fixed income investors (the other is interest rate risk). Given these structural changes in the fixed-income market and the significance of credit spreads as a risk factor for this market, being able to predict the direction of change in credit spreads may enable fixed-income investors (perhaps even equity investors) to achieve a significant alpha on a given trading strategy.
Historical
spreads:
Description of the prediction model and variables used
Methodology
Our
model provides ex ante predictions of spread changes for the following month.
In order to select the appropriate variables for our model, we examined
research on predicting credit spreads and we tried to select variables whose
financial characteristics seemed likely to predict changes in the credit spread. We focused solely on financial variables, excluding economic variables
because we felt these data were less effective in predictions.
Our
sample for this experiment was monthly observations from January 1990 through
December 2000. Our in-sample data
were from January 1990 through December 1999.
We used our model developed from this in-sample data set to forecast
the direction and magnitude of change in credit spreads for the twelve one-month
periods from January 2000 through December 2000. Using the actual data from January 2000 through December 2000 we
were then able to determine our hit rate on predicting direction of change.
After selecting our dependent and independent variables we created several multi-factor regression models. The results of our regression indicated that it we could predict the spread between the AAA and 10-Year T-Bond (R2 = 0.3277) best. This result countered our expectations based on the research we read (see Alessandrini pp. 42,44,45,48). We expected our model to have higher predictive power for the BBB credit spread (R2 = 0.2919) The research suggests that due to the greater volatility in the BBB bonds, there is more room for prediction. The underlying interest rate risk and risk of the underlying firm’s assets explain more of the credit spread for the Baa over the Aaa. Our results differ as we used different attributes to model the AAA credit spread and the BBB credit spread. As such we do not believe our findings counter Alessandrini’s research.
Variables
In
the following, we list the dependent and independent variables we used and
subsequently discuss the economic reason for selection of the variable.
Dependent
variables:
Each of the three following spreads was selected as a proxy for credit risk.
1.
Change in Spread between BBB yield 7-10yr maturities (Merrill
Lynch) and the 10year Treasury Bond yields
2.
Change in Spread between AAA yields 7-10yr maturities (Merrill
Lynch) and the 10year Treasury Bond
yields
3.
Change in 10yr swap spreads
Independent variables:
- Lag
in Change in AAA-10 Yr Treasury credit spread
We would expect a 1 month lag of the change in the credit spread to have some predictive power. We expect on average the yield to decrease after a previous increase, as the spreads on average are mean reverting. By this intuition we expect a negative coefficient. However, we observed that this variable was not statistically significant in predicting the AAA credit spread.
- Lag
in Level of AAA-10 Yr Treasury credit spread
We expect the 1 month lagged level of the spread, assuming mean reversion, to have significant predictive power. If the level is high relative to the mean, we expect the following month on average to see a decrease in the change in the spread. By this intuition we expect a negative coefficient for this factor. We found the lagged level of the AAA credit spread to be statistically significant. Additionally we found this attribute to be statistically significant in predicting the BBB credit spread. The intuition follows here that the spread of the AAA over the 10 Yr Treasury proxies for sentiment of corporate credit risk overall.
- Lag
in Change in BBB-10 Yr Treasury credit spread
We would expect a 1 month lag of the change in the credit spread to have some predictive power. We expect on average the yield to decrease after a previous increase, as the spreads on average are mean reverting. By this intuition we expect a negative coefficient. However, we observed that this variable was not statistically significant in predicting the BBB credit spread. It was significant in predicting the 10 Yr Swap spread.
4. Lag in Level of BBB-10 Yr Treasury credit spreadWe expect the 1 month lagged level of the spread, assuming mean reversion, to have significant predictive power. If the level is high relative to the mean, we expect the following month on average to see a decrease in the change in the spread. By this intuition we expect a negative coefficient for this factor. We found the lagged level of the BBB credit spread not to be statistically significant.
5. Lag in Change in 10 Yr Swap spreadWe would expect a 1 month lag of the change in the credit spread to have some predictive power. We expect on average the yield to decrease after a previous increase, as the spreads on average are mean reverting. By this intuition we expect a negative coefficient. However, we observed that this variable was not statistically significant in predicting the 10Yr Swap spread. It was significant predicting the BBB credit spread.
- Lag in Level of 10 Yr Swap spread
We expect the 1 month lagged level of the spread, assuming mean reversion, to have significant predictive power. If the level is high relative to the mean, we expect the following month on average to see a decrease in the change in the spread. By this intuition we expect a negative coefficient for this factor. We found the lagged level of the 10 Yr Swap spread not to be statistically significant for predicting the 10 Yr Swap spread. It was significant predicting the AAA credit spread.
7.
Lag
of the change in S&P 500 P/E – We expect that as stock price valuations
(reflected in the P/E ratio) change positively we would see credit spreads
decrease because we expect that positive changes in valuation indicate a more
secure economic environment. Conversely,
if stock price valuations change negatively, we would expect to see credit
spreads widen as there is a less stable economic environment.
8.
Lag
of the S&P 500 P/E – We expect that as the magnitude of stock price valuations
rise, reflected in higher P/E ratios, credit spreads will narrow.
We feel that increasing equity valuations reflect better economic times.
Better economic times would indicate that credit spreads should narrow
as the risk of default decreases. Again, conversely if the magnitude of the
stock price valuations decrease, we would expect to see credit spreads widen
as there is a less stable economic environment.
9.
Lag
of the change in the VIX – The VIX is computed using the implied volatilities
from 1-month maturity, at-the-money, put and call options on the S&P 100
Index. This measures the general level
of uncertainty in the markets. As the VIX increases, we expect credit spreads
to increase.
10.
Lag
of the change 30-year Treasury Bond future volatility – An increase
in volatility means an increase in uncertainty, hence we expect a positive
correlation with change in credit spreads.
11.
Lag
of the change in the 10 year on/off spread – This measures the liquidity premium
that an on the run (most recently issued) 10 year Treasury bond commands over
an off the run 10 year Treasury bond. We would expect this to be positively correlated as investors flock
to the most liquid security, this reflects uncertainty in the bond market,
meaning larger credit spreads.
12.
Lag
of the change in the yield of 10-year Treasury bonds – As interest
rates rise, we expect credit spreads to rise. An increase in interest rates reflects a higher
cost of capital for the firms, and hence a greater chance of default. This
is consistent with Bevan and Garzarelli’s work “Corporate Bond Spreads and
the Business Cycle: Introducing the GS-SPREAD” March 2000.
13.
Lag
of the BBB yield 7-10yr maturities (Merrill Lynch) and the AAA yields 7-10yr
maturities – We would expect to see that as the spread between the
AAA and the BBB tightens, so would the spreads represented in our dependent
variables. We would also expect to
see them increase at the same time. The
spread between to two corporate bonds may be used as a proxy for default risk.
14. Lag of the change in spread between the 10 year T-bond and 3 Month T-bill – A low spread (flat yield curve) would indicate a tight monetary policy and therefore wider risk premium in the BBB market. A wider spread, or steeper yield curve would imply the opposite. Flat and inverted yield curves have historically been predictors of recessions. (Harvey, 1991) In recessions, spreads increase as companies are more likely to default, i.e. as credit risk increases.
go
to top
Below
is the detail on our models:
AAA
Spread over the 10 Year Treasury
Variables used:
Lag of the spread between AAA and 10 year Treasury (L_LvlSpdAaa10Yr)
Lag of the Swap Spread (L_LvlSwapSprd)
Lag of the change in the S&P500 PE (LCSP500Pe)
Model:
DAAASpread t = 0.103 - 0.511 AAA-10yr T-bond Spread t-1 + 0.477 Swap Spread t-1 - 0.039 DS&P500 P/E t-1
Correlation matrix:
BBB
Spread over the 10 Year Treasury
Variables used:
Lag of the spread between BBB and AAA (L_LvlSpdAaa10Yr)
Lag of the change in Swap Spread (LC10SwapSpd)
Lag in the change of the 10-year Treasury (LC10Ytrsy)
Lag in the change of the S&P500 PE (LCSP500Pe)
Lag of the change in the spread between BBB and AAA (LCSpdBbbAaa)
Model:
DBBBSpread
t = 0.111 – 0.148 D AAA
– 10yr T-bond t-1 + 0.808 D Swap Spread t-1
+ 0.273 D10yr
T-bond t-1 - 0.049 DS&P500
P/E t-1 + 0.614 DBBB - AAAt-1
Correlation matrix:
Swap
Spread over the 10 Year Treasury
Variables used:
Lag of the S&P500 PE (L_LvlSP500Pe)
Lag of the Swap Spread (L_LvlSwapSprd)
Lag of the change in the S&P500 PE (LCSP500Pe)
Lag of the change in the spread between BBB and 10 year Treasury (LCSpdBbb10Yr)
Model:
D SwapSpread t = - 0.016 + 0.002 S&P500 PE t-1 - 0.055 Swap Spread t-1 – 0.004 D S&P500 P/E t-1 + 0.032 D BBB – 10-yr T-bond t-1
Correlation matrix:
Interpretation of the models
Our best model for the AAA spread over the ten year treasury has an adjusted R^2 of 32.74%, and an out-of-sample directional hit rate of 58.33%. The variables for this model were all significant, with T-Statistics between 2.7 and 5.8.
Factors:
Lag Level of AAA credit spread: If we assume that a change in the credit spread is mean reverting, then the level of the credit spread provides information about the direction of the change in credit spread. If the level is high relative to the mean, then we would expect on average a decrease in the change in the spread. The negative coefficient of this variable confirms our expectations.
Lag Level of the 10 Yr Swap Spread: If we assume that the Swap Spread is a proxy for investor sentiment on the direction of interest rates, then we expect a positive coefficient for this attribute. If the swap spread level is high, then the floating rate is expected to increase in the future. This occurs when long term interest rates are expected to increase.
Lag Change in the SP 500 PE: The most basic relationship between stocks and bonds is categorized as inverse. People flock to equities when returns are high. Thus we expect an inverse relation between this variable and the AAA credit spread. The negative coefficient confirms this. Again according to our research, a proxy for the riskiness of the firm was found to be a significant predictor of credit spreads.
For our trading strategy we used the model to predict credit spreads was the BBB spread over the 10-year Treasury. This model had an in-sample hit rate of 69.75% and an out of sample hit rate of 66.67%. The R^2 for this model was pretty high at 29.19%. Additionally, all of the coefficients were statistically significant with all of the T-Statistics in excess of 1.85. We used this model for our trading strategy.
Factors:
Lag Level of AAA credit spread: If we assume that a change in the credit spread is mean reverting, then the level of the credit spread provides information about the direction of the change in credit spread. If the level is high relative to the mean, then we would expect on average a decrease in the change in the spread. The negative coefficient of this variable confirms our expectations. We theorize that the AAA lagged level proxies for investor sentiment of over corporate credit risk.
Lag Change of the 10 Yr Swap Spread: If we assume that the Swap Spread is a proxy for investor sentiment on the direction of interest rates, then we expect a positive coefficient for this attribute. If the swap spread level is high, then the floating rate is expected to increase in the future. This occurs when long term interest rates are expected to increase. Unlike the AAA credit spread, the BBB credit spread was related to the change in the swap spread and not the level. This may indicate that the Swap spread predictive power is related to the default risk.
Lag Change in the SP 500 PE: The most basic relationship between stocks and bonds is categorized as inverse. People flock to equities when returns are high. Thus we expect an inverse relation between this variable and the AAA credit spread. The negative coefficient confirms this. Again according to our research, a proxy for the riskiness of the firm was found to be a significant predictor of credit spreads.
Lag Change in the 10 Yr Teasury: Changes in the 10 Yr Treasury were found in our research to have a high degree of predictive power with regard to predicting credit spreads, but significantly in predicting higher risk bonds. Again this follows the intuition that as long term interest rates rise, the ability of BBB rated firms to service their debt becomes more risky. Investors then demand higher premium for these bonds. As expected a positive coefficient was observed for this variable.
Lag Change in the BBB over AAA spread: This variable proxies for the default risk. Our research indicated that as the default rates rise, the riskiness of the debt of lower rated firms increases. Investors demand a higher premium for this debt. As such we expect a positive relationship between this variable and the credit spread. The positive coefficient confirmed this expectation.
Our best model for the 10 year swap spread had the lowest adjusted R^2 among the three dependent variables. It was 6.5% with two of its four independent variable showing coefficients below a T-Statistic of 2. The out of sample hit rate for this model was 52.94%.
Factors:
Lag Level of AAA credit spread: If we assume that a change in the credit spread is mean reverting, then the level of the credit spread provides information about the direction of the change in credit spread. If the level is high relative to the mean, then we would expect on average a decrease in the change in the spread. The negative coefficient of this variable confirms our expectations. We theorize that the AAA lagged level proxies for investor sentiment of over corporate credit risk.
Lag Change in the SP 500 PE and Lag Level in the SP 500 PE: The most basic relationship between stocks and bonds is categorized as inverse. People flock to equities when returns are high. The significance of the Lag change in the SP500 PE was very minimal but it added to the overall R-squared of our model. The lagged level of the SP 500 PE was significant with an positive relationship to the swap spread. We do not believe these variable are good predictors from an intuitive perspective.
Lag Level of the 10 Yr Swap Spread: If we assume that the Swap Spread mean reverting then we expect an inverse relationship between this variable and the swap spread. This was confirmed by the negative coefficient of the variable.
Trading Strategy
Our trading strategy was to go long in the BBB corporate bond and go short an equal amount in the 10 year Treasury bond when our model predicted that credit spreads were going to tighten. We took the opposite position when our model predicted that credit spreads were going to widen. The intuition behind this trading strategy is that as the spreads tighten indicating better economic times investors would be more likely to buy corporate bonds because the risk was declining. Using Bond pricing theory provides a simple illustration:
1. BBB Yield increases. 10 Yr Treasury Yield remains the same.
The BBB price theoretically will decrease. Therefore we make money by holding a short position in the BBB bond index.
2. 10 Yr Yield increases. BBB Treasury Yield remains the same
The 10 Yr price theoretically will increase. Therefore we make money by holding a long position in the 10 Yr bond index.
Results of our trading strategy:
Interpretation of results:
From the results above one can clearly see that we did not achieve a significant alpha. Over the 9 year in-sample period our return for this total time period was in excess of the benchmark 30-day EuroDollar rate by only 10.73 percentage points representing a 1.01 percentage point annualized alpha. Our methodology for calculating the return on our trading strategy is based on calculating the theoretical price from the yield. We then calculated the monthly return on each asset. From these monthly returns we calculated the returns on our spread position. This theoretical calculation is may not be reflective of actual potential return from this trading strategy.
From our results we concluded that the strategy of using credit risk prediction to implement a strategy of buying and shorting the BBB and 10 year Treasury bond spread produces an alpha that is significant in the context of returns on fixed income. Additionally, the position can be levered up, further increasing returns.
Conclusions/Future paths of study
We found that we were able to predict the change in the credit spread with some degree of success, and our trading strategy produces a significant alpha. We further believe that predicting the change in the credit spread offers valuable economic information. Some of our research indicated that changes in credit spreads are useful for predicting changes in the business cycle. For example, when the business cycle is anticipated to downturn in the near future, it has been observed that the credit spread of the Baa over the 10 Year Treasury widens, due to the increased riskiness of firms rated a Baa. Intuitively this makes sense. If the economy has a downturn, firms with a lower rating are at a greater risk of defaulting. The Baa rated firm’s ability to meet its debt schedule becomes more uncertain. Investor’s thus demand a higher premium over the 10 Yr Treasury. Therefore in further work we would seek to implement a trading strategy that capitalizes on this predictive power. Such a model, for example, might seek to pick cyclical stocks in an asset class such as consumer cyclical stocks.
Bibliography
Alessandrini, Fabio, “Credit Risk, Interest Rate Risk, and the Business Cycle” The Journal of Fixed Income, September 1999.
Bevan and Garzarelli, “Corporate Bond Spreads and the Business Cycle: Introducing the GS-SPREAD” The Journal of Fixed Income, March 2000.
Clare, Ioannides, and Skinner, “Hedging Corporate Bonds with Stock Index Futures: A Word of Caution” The Journal of Fixed Income, September 2000
DeRosa-Farag, Blau, Matousek, and Chandra, “Default Rates in the High-Yield Market” The Journal of Fixed Income, June 1999.
Erb, Harvey, and Viskanta, “National Risk in Global Fixed-Income Allocation” The Journal of Fixed Income, September 1994.
Garman, Christopher, “Pricing European High-Yield New Issues” The Journal of Fixed Income, March 2000.
Harvey, Campbell “The Term Structure and World Economic Growth” The Journal of Fixed Income, June 1991.
Okashima and Fridson, “Downgrade/Upgrade Ratio Leads Default Rate” The Journal of Fixed Income, September 2000.
Pendergast, Joseph R, “Predicting the Ten-Year LIBOR Swap Spread: The Role and Limitations of Rich/Cheap Analysis” The Journal of Fixed Income, December 2000.
Rodrigues de Almedia, Duarte, and Fernandes, “Credit Spread Arbitrage in Emerging Eurobond Markets” The Journal of Fixed Income, December 2000.