Amid rising concerns over both US and global economic conditions lately, there are several macroeconomic indicators that investors track in order to make well-informed investment decisions. Understanding the statistical relationships between such economic indicators and S&P 500 performance is essential to make better buying and selling decisions. This article focuses on two economic indicators, the 2yr/10yr Yield Spread and the High-Yield Spread, which are both widely watched barometers for credit conditions. There has been a lot of noise around the flattening spread between the 2yr and 10yr yield lately, as it has induced bearish investors to issue warning signals over both economic conditions and stock market performance. Though on its own it does not spell doom for S&P 500 performance, and investors should incorporate the High-Yield Spread into their analysis to better gauge the relation between economic concerns/credit conditions and equities.

## A reality check on the repercussions of a narrowing 2yr/10yr Spread

In one of my previous research pieces, a negative correlation was found between the 2yr/10yr Spread and S&P 500 performance for both historical periods and the current period, and that equities tend to continue climbing higher even as the spread reaches its trough in negative territory (after inversion). The results from the regression model contradicted bears’ belief that investors should sell out of equities while witnessing flattening/inverting at the 2yr/10yr section of the yield curve.

The reason why a flattening/inverting yield curve is considered a negative sign for the US economy (and consequently stocks) is related to banks’ behaviour. Banks tend to borrow at the front end of the yield curve at short-term yields (2yr) and lend out at longer-term yields (10yr). The positive spread between these two yields are banks’ earnings (Net Interest Income). However, when the spread flattens, banks’ earnings are expected to diminish, while an inverting yield curve is expected to result in losses on lending activity. Hence, it is conceived that a flattening/ inverting yield curve will discourage banks from engaging in lending activity, and that it thereby tightens credit conditions for the economy.

However, there has been a strong negative correlation between the 2yr/10yr Yield Spread and the level of loans made by US commercial banks since the spread peaked on December 31, 2013, with a Pearson’s Correlation of -0.96. The chart below exhibits the divergence between the 2yr/10yr Yield Spread and US commercial banks’ Net Interest Margin (NIM) and the level of credit supplied by banks to the US economy over the same period of time.

*Data Source: Generated using data from Federal Reserve Economic Data (FRED)*

Evidently, the flattening 2yr/10yr Spread since December 2013 has not discouraged US commercial banks from creating more loans to the US economy, as Net Interest Margins have continued to rise due to factors such as historically low deposit betas and the Fed paying Interest On Required Reserves (IORR) and Interest On Excess Reserves (IOER) since the crisis. Hence, this undermines the ability of the 2yr/10yr Spread to reflect economic concerns/worsening credit conditions on its own. Therefore, this variable on its own is not sufficient as a barometer for economic concerns/credit conditions to explain the performance of the S&P 500 in a regression model.

**Adding "High-Yield Spread" to our regression model**

We should add another independent variable to our regression model that is also perceived to be an effective indicator of economic concerns/tightening credit conditions, to better explain the relation between economic concerns/ credit conditions and S&P 500 performance. High-Yield Spread (HYS), which is the Spread between US Treasury yields and Speculative-Grade bond yields, is another important indicator to watch when assessing economic conditions and expecting a recession on the horizon. Using data available from Federal Reserve Economic Data (FRED), High-Yield Spread data has been added to our regression model as an additional independent variable, to assess whether the addition of this indicator better explains the relation between economic concerns/credit conditions and the S&P 500 (as opposed to the 2yr/10yr Yield Spread on its own).

The table below summarizes the statistical results from both our regression models; the first regression model only incorporates the 2yr/10yr Spread as its independent variable, whereas the second model incorporates both the 2yr/10yr Spread and the High-Yield as independent variables, to explain the performance of the S&P 500 since the 2yr/10yr Spread peaked in December 2013.

Statistic | S&P 500 vs. 2yr/10yr Spread | S&P 500 vs. 2yr/10yr Spread & HYS |

Regression Model | S&P 500 = 2,792.62651 - 455.65564 * 2yr/10yr Spread | S&P 500 = 3,340.34229 - 428.20155 * 2yr/10yr Spread - 127.68308 * High Yield Spread |

R-Squared | 0.75631 | 0.94918 |

Adjusted R-Squared | 0.75613 | 0.9491 |

Predicted R-Squared | 0.75571 | 0.94897 |

PRESS | 36,651,914.62 | 7,655,467.04 |

Standard Error of model/estimator | 162.24 | 74.12 |

Standard Error for Intercept | 8.83 | 8.56 |

Standard Error for Coefficient of '2yr/10yr Spread' variable | 6.94 | 3.19 |

Standard Error for Coefficient of 'HYS' variable | - | 1.76 |

MSE | 26322.43 | 5493.62 |

RMSE | 162.24 | 74.12 |

*Note: Results generated using StatPlus*

Our first model had reflected a negative correlation between the 2yr/10yr Spread, in which case contrary to bearish belief, the flattening yield curve does not necessarily translate to a simultaneous downturn in the S&P 500. Though the addition of the High-Yield Spread (HYS) as a second independent variable explains the relationship between tightening credit conditions/rising economic concerns and the S&P 500 better. This variable also holds a negative correlation with the equity index, whereby a widening HYS would cause the S&P 500 to fall. Therefore, the model conveys that a narrowing 2yr/10yr Spread on its own does not push the S&P 500 lower, however when this flattening in the yield curve is accompanied by a widening HYS, it has bearish consequences for the equity index because it acts as a confirmation of rising economic concerns and tightening credit conditions.

The new multiple linear regression model exhibits a notable improvement in data fit and other statistical characteristics. Firstly, it has a higher R-Squared of 0.94918, compared to our first model which held an R-Squared of 0.75631. Nevertheless, this comparison on its own is not sufficient to conclude that this new model fits the data better than the old model, because statistically, adding more variables to a model will automatically increase the R-Squared, as two variables will explain the data better than one variable on its own. Regardless, in order to adjust for the difference in the number of predictors between the two models, we should use the Adjusted R-Squared metric instead. The Adjusted R-Squared for our new model is also about 0.9491, which is higher than the 0.75613 level of our first model. The higher Adjusted R-Squared for our new model reflects that the additional variable meaningfully enhances the regression model, and that the higher R-squared wasn’t by chance.

Furthermore, the Predicted R-Squared for our new model is also notably higher at 0.94897, compared to our first model’s 0.75571. This implies that the multiple linear regression model holds better predictive capability than the model with the 2yr/10yr Spread as a single independent variable. However, simply relying on the Predicted R-squared value to determine the model’s effectiveness for extrapolation is not prudent. The Prediction Error Sum Of Squares (PRESS) is another metric used to assess the predictive capabilities of our model. It is calculated by leaving out one observation turn by turn, forming a new model (excluding each observation) each time, and then using that new model to try and predict the outcome using the left-out observation. The errors, which are the differences between the predicted results and actual results, for each observation are squared and summed together to produce the PRESS value. The lower the PRESS value, the better the predictive capability of our model. From our statistical summary table, we find that the PRESS value for our new model (7,655,467.04417) is considerably lower than that of our first model (36,651,914.62208). Hence, this confirms the improved predictive capability of our new model following the addition of "HYS" as an independent variable. What does this mean for investors? When trying to gauge the potential performance of the S&P 500 amid rising economic concerns, investors should take the High-Yield Spread into consideration as well to make more accurate predictions.

The new model also offered smaller Standard Error "S" values. The Standard Error for our first model was 162.24, whereas the addition of the "HYS" variable has dropped the "S" value to 74.12. This implies that predictions made for the S&P 500 level using this new model are found in a narrower range, with one standard deviation away from the average outcome implying +/-74.12 points from the average predicted level for the S&P 500. Moreover, the results summary table also shows how the individual Standard Errors for the intercept/ variable coefficients for our new model are much smaller than those of our first model, indicating that not only has the addition of the "HYS" variable improved the overall accuracy of the model, but it has also narrowed the margin of error for the intercept and coefficient of the "2yr/10yr Spread" variable. This further supports the importance of incorporating the High-Yield Spread when examining the impact of rising economic concerns/tightening credit conditions on the S&P 500.

**Assessing the significance of our new model/ individual variables**

The table below lists the results for the F-Tests and T-Tests conducted on our two regression models, using a confidence interval of 99%, implying a significance level of 1% (0.01).

*Note: Results generated using StatPlus*

The F-Test is commonly used to assess the significance of regression models/estimators; more specifically, it tells us whether our independent variables (2yr/10yr Spread and HYS) are jointly significant in explaining the behavior of the dependent variable, in this case the S&P 500. Let us assess the results from the F-test summarized in the results table above. The higher the F-value, the more significance our model holds. The F-value of our new model (12,961.21) is much higher than that of our first model (4,310.81), which is a positive sign. However, we must take this a step further and assess the significance of our new F-value itself. The F-Test conducts a null-hypothesis test, where the null-hypothesis is that the data does not fit our new model any better than an intercept-only model (a model without independent variables), which we seek to reject. Note that the p-value represents the probability of obtaining the F-value that we have, and hence, the lower this p-value, the lower the chance of this F-value occurring, and therefore, the more significance this F-value holds in reflecting the significance of our overall model. A p-value below the significance level allows us to reject the null-hypothesis.

In this case, we conducted our tests using a significance level of 1% (0.01). Given that the p-value from the F-Test for our new model is 0 (which is lower than 0.01), we can reject the null hypothesis. While the p-value from the F-Test for our first model was also 0, we can still conclude that our new model holds more significance than our first model, due to the higher F-value.

The results from the T-Tests also reveal insights about the effectiveness of our regression models. While the F-Test assesses whether our independent variables are jointly significant to explain the dependent variable, the T-Test assesses the individual significance of our independent variables. In terms of interpreting the results from the T-Test, the larger the T-statistics for our variable coefficients (whether positive or negative), the more significance they hold within the model. The table earlier exhibits how the T-statistics for each of our variable coefficients are larger in the new model compared to our first model (in both positive and negative directions), implying that our variables in the new model hold enhanced statistical significance. However, just like in the F-Test, we must assess the significance of our T-statistics themselves using our p-values for each variable coefficient. Again, the lower the lower the p-values, the lower the chances of obtaining the T-statistics we have, and hence, the more confidence we can hold in the significance of our T-statistics and independent variables. The T-Test was also conducted using a significance level of 1% (0.01), and thus, given that the p-value for each variable coefficient was 0 (as shown in the table earlier), the lower p-values allow us to reject the null-hypotheses. Therefore, these favorable results, using 99% confidence intervals, allow us to infer that our variables in the multiple linear regression model hold more statistical significance than our first model. Therefore, there is significant statistical evidence that including the High-Yield Spread into S&P 500 analysis amid rising economic concerns allows for more accurate examination. Thus, going forward, as investors brace for slowing economic conditions in 2019/2020 and prepare for the potential return of financial market volatility amid rising economic concerns, one should not solely track the 2yr/10yr Spread but should combine this indicator with the High-Yield Spread to better gauge potential future performance of the S&P 500.

## Limitations

While our new model certainly does convey statistical strengths, it is essential to also address its limitations. The Durbin-Watson (DW) metric is a measure that assesses the autocorrelation present between our error terms, values for which range from 0 to 4. A value between 0 and 2 reflects positive autocorrelation, while a reading between 2 and 4 reflects negative autocorrelation. The ideal reading is "2", which would represent no autocorrelation and would support our assumption that the residual errors are statistically independent from each other. For our multiple linear regression model, we have a DW of 0.0758 (rounded). While this is better than our first model’s reading of 0.0224 (rounded), it is certainly a very worrisome reading given that it reflects strong autocorrelation between our residual errors.

The "Residuals vs. Fitted Plots" chart below further confirms this pattern in our residual errors.

*Note: Generated using StatPlus*

Ideally, we would want to see our results randomly scattered around the chart. However, we can actually see some trends forming in the scatter diagram, implying that our errors are not completely statistically independent.

A common reason behind low DW readings and patterns forming in the "Residuals vs. Fitted Plots" is specification bias. This occurs when we do not have enough predictor variables in our model to explain variations in the dependent variable. Not surprisingly, the "2yr/10yr Spread" and "High-Yield Spread" as independent variables are not sufficient to entirely explain the performance of the S&P 500, and more variables would be needed for this purpose to overcome the specification bias problem.

Nevertheless, our main goal from this research was not to formulate a model that perfectly explains the performance of the S&P 500, but our main focus was to enhance our approach to assessing the relationship between economic indicators (suggesting tightening credit conditions) and the equity index. Amid the market concern surrounding the flattening at the 2yr/10yr section of the yield curve, investors would be mistaken to sell out of the S&P 500 based solely on this single development. Our research through multiple linear regression modeling has found significant statistical evidence supporting the notion that investors should only turn bearish on the equity index if the narrowing 2yr/10yr Spread is accompanied by a widening High-Yield Spread, as this would confirm the heightened economic concerns amid tightening credit conditions.

## Bottom Line

We have found that contrary to market belief, a flattening 2yr/10yr Spread has not suppressed commercial banks’ Net Interest Margins and lending activity, which undermines the rationale behind the narrowing 2yr/10yr Spread reflecting dire economic conditions/ tightening credit conditions on its own.

Adding the High-Yield Spread (HYS) to our regression model has resulted in a significant improvement in explaining the performance of the S&P 500 in reaction to elevated economic concerns/tightening credit conditions. Our new multiple linear regression model has a much higher "Adjusted R-Squared" of 0.9491, a lower Standard Error of 74.12, and more significant coefficient variables to better manifest the relation between elevated economic concerns/tighter credit conditions and the S&P 500.

While our two independent variables are certainly not sufficient to entirely explain the performance of the equity index (given our low DW reading and patterns in "Residuals vs. Fitted Plots"), the research does reveal that investors solely relying on the 2yr/10yr Spread for bearish economic/equity market signals are making a mistake, and that there is significant statistical evidence to support the strategy that one should only turn bearish on stocks when the narrowing 2yr/10yr Spread is accompanied by a widening High-Yield Spread.

Therefore, ensure to assess the flattening 2yr/10yr Spread in combination with movements in the High-Yield Spread to make more well-informed investment decisions.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.