Modeling -Ten Year Treasury Yield

Assignment 3 (Modeling - 10Y Treasury Yield)

Oct 24, 2017

Regression Model for US 10-year Treasury Yield

1.Introduction

Treasury notes are government bonds issued by the U.S. Treasury department with maturities between one and ten years. They are usually considered “risk free”, because they are backed by the U.S. Government. Investors who are risk-avoiding or with a negative view of future market are likely to buy Treasury notes, in exchange of a lower rate of return, compared to other financial instruments like stocks or high yield bonds. A 10-year Treasury note is a bond with maturity of 10 years, paying a fixed coupon every six month and returning face value at maturity.

‘10-Year Treasury Yield’ refers to the annualized rate of return on the investment of a 10-year treasury note. In this model we will try to understand whether and how 10-year treasury yield is affected by other factors according to historical data, and test model fitness by regression statistics.

2.Modeling Analysis

2.1 Selection of original explanatory variables

When looking at the factors that may contribute to the trend of 10-year Treasury yield, we primarily considered it as an average expectation of US long-term interest rate, so we considered stability of domestic and international environment and market volatility into X variables. Also, as a long-term financial instrument, the expectation of yield is intuitively impacted by yield of its alternatives. Then we selected typical indexes of each field and ran the original regression.

• Yield of Alternatives

For alternatives, we mainly considered stocks, corporate bonds and mortgages. In compability, corporate bonds and mortgages-backed securities make more sense than stocks as stock tends to be relatively short-term investment and also it interprets a lot about market volatility which may later cause notable correlation. We also chose corporate bond yield over mortgage rates basically due to the fact that the financial crisis in 2008 was generated by the bubble of subprime mortgages, which means mortgage rates covering this period would be inefficient and might cause heteroscedasticity.

• Stability of Domestic Environment

Initially we used unemployment rate for social stability. In addition, price level can illustrate overall inflation which means economic stability. Upon initial discussion, we chose CPI instead of GDP for the following reasons: 1. They are basically the same thing when illustrating overall inflation; 2. Monthly GDP is unavailable and thus transferring it from quarterly data will result in slight amount of inaccuracy.

• Stability of International Environment

Here we considered oil price - DCOILWTICO, which interprets global stability of politics and economy; also the relative power of U.S. - US Dollar Index (DXY) in the international society.

• Market Volatility

Based on model simplicity and the rule of variable independence, we used VIX to represent market volatility.

2.2 Data Generation

We collected monthly data from January 1990 to June 2017 with 330 months in total. We chose this time period as it contains the most available recent data series for all the variables above. For data only available in daily frequency (10-year treasury yield, VIX & mortgage rate) we took monthly average in the regression model. All data samples were sourced from St. Louis Fed website and Bloomberg.

2.3 Objective

Multiple regression was conducted to understand by which variables of the above can the US 10-year treasury yield be explained best and to look at the overall fitness of this financial model.

3. Regression

3.1

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The Adjusted R2 seemed good which meant that the regression covered most of the contributing factors, though Residual Sum of Square is rather high indicating a low efficiency. The coefficient of US Corporate Total Return is considerably small, combined with a high correlation with CPI, so we made an attempt to replace US Corporate Total Return with mortgage rate (15-Year Fixed Rate Mortgage Average). In addition, the P-value of DXY also drew our attention, indicating it did not significantly imply 10-year Treasury yield. So we removed DXY and ran the second regression as displayed below. The change worked as it surprisingly increased R2 and decreased Residual Sum of Square.

3.2

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Then we noticed that the P-value of CPI and the correlation coefficient between CPI and 15-Year Fixed Rate Mortgage Average were both notably large, along with a P-value of intercept at 0.92. So we removed CPI from the model, in the assumption that mortgage rate also accounts for inflation, causing a variable correlation.

3.3[pic 5]

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In the third regression things worked pretty well: all the P-values were much smaller than 0.05 and all the correlation coefficients decreased without sacrificing R2 and Residual Sum of Square. In summary, we finally came to the regression formula as: