Yield Curve and Relationship Between Interest Rates and Inflation

This report analyzes the yield curve of treasury bonds and the relationship between interest rates and inflation in the United States. It examines the different types of bonds, their yields, and prices, and discusses the factors that influence the yield curve. The report also includes a regression analysis of the relationship between interest rates and inflation.

FINANCIAL MARKET AND INSTITUTIONS
YIELD CURVE AND RELATIONSHIP BETWEEN INTEREST RATES AND INFLATION
1. Introduction
The report is an analysis of interest rate market of United States of America for purpose of
determining the yield curve of treasury bonds and relationship between interest rates and
inflation.
Bond is one of the major source of finance for government, institutions and private player. There
are various types of bonds like zero coupon bonds, plain bonds, inflation protected bonds etc
ranging from 30 days to 100 years or more depending on needs of finance. The US treasury too
issue bonds of various days with different coupon rate depending on tenure of bond. Some of the
key terms which are generally used in the bond market have been defined here-in-below:
(a) Face Value: It is the nominal amount of the bond that shall be available at maturing or the
amount printed on the face of the bond;
(b) Coupon: It is the interest rate that shall be available on the face value of the bond yearly,
quarterly, semi-annually depending on the nature of the bond and the covenant mentioned
on the prospectus;
(c) Yield: Bond Yield is the actual rate of return realised by the investor on the bond over a
period of time generally an year. It is a function of the price of the bond and the coupon rate
over a period;
(d) Price of bond: It is the market value of the bond and is determined by the market forces of
demand and supply and other factors.
(e) Tenure of bond : It is the time period of the bond for which the bond matures generally an
year or more depending on the covenant of the bond.
2. Analysis of Information of US Treasury Bonds
For the purpose of analysis the yield curve of treasury bonds the following bonds have been
considered for analysis:
(a) 3 Months Treasury Bonds;
(b) 6 Months Treasury Bonds;
(c) 12 Months Treasury Bonds;
(d) 24 Months Treasury Bonds;
(e) 60 Months Treasury Bonds; (Bloomberg)
(f) 120 Months Treasury Bonds;
(g) 360 Months Treasury Bonds;
The details of the yield, coupon and price of the bond has been presented here-in-below along
with the graph presenting the relationship between tenure of the bond and the yield to maturity:

U.S.Treasury Bonds
Sl No Particular ( Months) Price Coupon Yield
1 3 2.33 0 2.37%
2 6 2.43 0 2.49%
3 12 2.5 0 2.58%
4 24 100.46 2.75 2.56%
5 60 101.36 2.88 2.58%
6 120 103.33 3.13 2.74%
7 360 107.5 3.38 2.99%
(Bloomberg)
On perusal of the above, it may be inferred the following:
(a) Yield Curve is upward sloping;
(b) Long term bond shall have higher yield in comparison to short term bond;
(c) There exists a strong relationship between tenure and yield of the bond and they are directly
proportional to each other;
The reason and rationale for the aforesaid observations have been detailed here-in-below:
(a) Expectation of market of higher interest rate in long run compared to short run;
(b) Increased risk over increased period on account of market volatility;
(c) To boost consumption, investment and economic growth in the economy;
(d) Limitation of arbitrage opportunities;
(e) Account for liquidity premium as the bond are going to mature after a long tenure and are
not immediately maturing ; (Sontakke)
(f) Impact of taxes on the longer period of time and market uncertainty;

Further, the yield that should be primarily focussed on is the yield on 90 day treasury and the
yield on 30 years treasury which is 2.37% and 2.99% respectively and depicts a positive
relationship between tenure and the yield of the bond. Thus, the same depicts a healthy market
perception over a long term.
Further, the difference in the yield curve of the 90 day treasury and the yield on 30 years treasury
can be explained better by the following reasons:
(a) Expectation of market of higher interest rate in long run compared to short run;
(b) Increased risk over increased period on account of market volatility;
(c) To boost consumption, investment and economic growth in the economy;
(d) Limitation of arbitrage opportunities;
(e) Account for liquidity premium as the bond are going to mature after a long tenure and are
not immediately maturing ;
(f) Impact of taxes on the longer period of time and market uncertainty;
The theory that best explains the present situation shall be Liquidity Premium or liquidity
preference theory whereby certain investors prefer holding short-term security as they provide
liquidity and demand premium for long term investment and thus the curve slope upward with
the passage of time. Thus, on the basis of above theory return for 90 day treasury security shall
be higher than 30 day security as 30 day provides higher liquidity compared to 90 days security.
Thus, liquidity premium or liquidity preference theory accounts for lower return of 2.37% in 90
day treasury security and 2.99% return on a 30 year security and liquidity premium is the
difference between the two return keeping other factors constant.
3. Analysis of Information of Three month US Treasury Bonds
The last 10 month yield on three month US treasury bond has been presented here-in-below:
observation date TB3MS
2018-01-01 1.41
2018-02-01 1.57
2018-03-01 1.70
2018-04-01 1.76
2018-05-01 1.86
2018-06-01 1.90
2018-07-01 1.96
2018-08-01 2.03
2018-09-01 2.13
2018-10-01 2.25
Further, the graph of the above data has been presented here-in-below:

On perusal of the above data and graph, it can be inferred that the curve is upward sloping and
there has been hike in short term interest rates very steeply over the tenure of 10 months on
account of the following reasons:
(a) Direct intervention by Federal Reserve of USA;
(b) Recovery of US economy;
(c) Impact of inflation and real interest rate; (The Financila Times ttd)
(d) Demand and supply and strong optimism regarding the US economy;
(e) Expectation of higher interest rates.

4. Regression Analysis
Regression Analysis has been conducted on the basis of data for 3 month treasury yield for period
ranging from 01-11-2013 to 01-10-2018 and the data for Producer price index for the similar period
which is a representative of inflation. Further, monthly data has been considered for analysis. On the
basis of above, the following regression equation has been obtained:
Change in Interest Rate (Dependent Variable)= 0.1593- (-18.37)* Change in Producer Price Index
On the basis of above equation, it can be stated that the change in producer index is positive
correlated as the positive change in producer price index shall result in positive change in Interest
rate. Thus, change in inflation is positively correlated with change in interest rate of treasury bill for
3 months.
Thus, the above equation represents a positive relationship between variables i.e. interest rate and
inflation.
Further a change of 1% in the inflation rate shall result in change of 34% in the interest rate as
computed based on the computation detailed here-in-below:
Monthly Date TB3MS Change Producer Price Index Change
2013-11-01 0.07 201.2
2013-12-01 0.07 0% 202 0%
2014-01-01 0.04 -43% 203.8 1%
2014-02-01 0.05 25% 205.7 1%
2014-03-01 0.05 0% 207 1%
2014-04-01 0.03 -40% 208.3 1%
2014-05-01 0.03 0% 208 0%
2014-06-01 0.04 33% 208.3 0%
2014-07-01 0.03 -25% 208 0%
2014-08-01 0.03 0% 207 0%
2014-09-01 0.02 -33% 206.4 0%
2014-10-01 0.02 0% 203.4 -1%
2014-11-01 0.02 0% 200.9 -1%
2014-12-01 0.03 50% 197 -2%
2015-01-01 0.03 0% 192 -3%
2015-02-01 0.02 -33% 191.1 0%
2015-03-01 0.03 50% 191.5 0%
2015-04-01 0.02 -33% 190.9 0%
2015-05-01 0.02 0% 193.4 1%
2015-06-01 0.02 0% 194.8 1%
2015-07-01 0.03 50% 193.9 0%
2015-08-01 0.07 133% 191.9 -1%
2015-09-01 0.02 -71% 189.1 -1%
2015-10-01 0.02 0% 187.5 -1%
2015-11-01 0.12 500% 185.7 -1%
2015-12-01 0.23 92% 183.5 -1%
2016-01-01 0.26 13% 182.6 0%

Monthly Date TB3MS Change Producer Price Index Change
2016-02-01 0.31 19% 181.3 -1%
2016-03-01 0.29 -6% 182.1 0%
2016-04-01 0.23 -21% 183.2 1%
2016-05-01 0.27 17% 185.3 1%
2016-06-01 0.27 0% 187.6 1%
2016-07-01 0.30 11% 187.7 0%
2016-08-01 0.30 0% 186.6 -1%
2016-09-01 0.29 -3% 186.9 0%
2016-10-01 0.33 14% 186.7 0%
2016-11-01 0.45 36% 186.3 0%
2016-12-01 0.51 13% 188.2 1%
2017-01-01 0.51 0% 190.7 1%
2017-02-01 0.52 2% 191.6 0%
2017-03-01 0.74 42% 191.5 0%
2017-04-01 0.80 8% 193 1%
2017-05-01 0.89 11% 192.8 0%
2017-06-01 0.98 10% 193.6 0%
2017-07-01 1.07 9% 193.5 0%
2017-08-01 1.01 -6% 193.8 0%
2017-09-01 1.03 2% 194.8 1%
2017-10-01 1.07 4% 194.9 0%
2017-11-01 1.23 15% 195.9 1%
2017-12-01 1.32 7% 196.3 0%
2018-01-01 1.41 7% 197.9 1%
2018-02-01 1.57 11% 199.3 1%
2018-03-01 1.70 8% 199.3 0%
2018-04-01 1.76 4% 200.3 1%
2018-05-01 1.86 6% 203.2 1%
2018-06-01 1.90 2% 204.2 0%
2018-07-01 1.96 3% 204.3 0%
2018-08-01 2.03 4% 203 -1%
2018-09-01 2.13 5% 203.2 0%
2018-10-01 2.25 6% 204.3 1%

SUMMARY
OUTPUT
Regression Statistics
Multiple R
0.2138
58
R Square
0.0457
35
Adjusted R
Square
0.0289
94
Standard
Error
0.6967
05
Observations 59
ANOVA
df SS MS F
Significa
nce F
Regression 1 1.326035
1.326
035
2.731
851
0.10386
3537
Residual 57 27.66768
0.485
398
Total 58 28.99371
Coeffici
ents
Standard
Error t Stat
P-
value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept
0.1593
38 0.090762
1.755
572
0.084
534
-
0.02240
8437
0.3410
8525
-
0.02240
8437
0.34108
525
X Variable 1
-
18.367
2 11.11255
-
1.652
83
0.103
864
-
40.6196
6353
3.8853
2775
-
40.6196
6353
3.88532
7754
Conclusion
Thus, on the basis of above discussion it may be concluded that the Interest rate fluctuation of
treasury bills of 3 months has a direct relationship with change in rate of inflation over the covered
period. In addition to above, the interest rate of treasury bills of 3 months has seen a drastic
increase over the years on account of growth in US economy.

References:
Bloomberg. United States Rates & Bonds. 2018. 26 December 2018
<https://www.bloomberg.com/markets/rates-bonds/government-bonds/us>.
Mayur Sontakke, FRM. Key takeaways: Why is the yield curve normally upward-sloping? 1 May 2014.
26 December 2018 <https://marketrealist.com/2014/05/key-takeaways-yield-curve-
normally-upward-sloping>.
The Financila Times ttd. Leverage our market expertise. . 2018. 26 December 2018
<https://www.ft.com/content/870ff6b8-c721-11e8-ba8f-ee390057b8c9>.