University Finance: Portfolio Management and Interest Rate Risk

This report examines the effectiveness of hedging interest rate risk using futures portfolios, focusing on the impact of term structure effects. The research aims to determine how a methodology can reduce interest rate risk within a fixed spot portfolio of assets and liabilities. It utilizes a minimum variance hedge, incorporating financial futures into the spot portfolios and evaluates conditions for unique and zero variance hedges. The study highlights the impact of unexpected interest rate fluctuations on market value, using a multivariate model with Taylor Series approximations and portfolio theory. Results reveal greater volatility during the test period, emphasizing the instability generated by rate changes. The report explores the implications of hedging measures in minimizing investment risk and highlights the potential for successful short-term portfolio hedging, while noting limitations in combining short and long positions. The analysis uses data from the U.S. Treasury Bulletin and The Wall Street Journal, applying methodologies such as the covariance matrix and price sensitivity models to derive its conclusions. The study's findings suggest that the net full information strategy is smaller than the price sensitivity strategy and that full information hedging is more pronounced because the price sensitive hedge cannot produce a hedge with short and long positions.

Running head: FINANCE PORTFOLIO MANAGEMENT
Finance Portfolio Management
Name of the Student:
Name of the University:
Authors Note:

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Table of Contents
1. Summary of the paper:...........................................................................................................2
2. Research hypothesis or research purpose:..............................................................................2
3. Data and methodology:..........................................................................................................3
4. Study or test results:...............................................................................................................4
5. Implications of the paper:.......................................................................................................5
Bibliography:..............................................................................................................................6

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1. Summary of the paper:
The aim of the research paper is to detect whether the hedging interest rate risk with
futures portfolio under term structure effects. In addition, the paper adequately develops and
test a methodology for reducing interest rate risk in fixed spot portfolio of assets and
liabilities. The paper utilises the minimum variance hedge by adding relevant portfolio of
financial futures to the spot portfolios. Furthermore, relevant conditions for the existence of
unique and zero variance hedges are mainly evaluated in the article for understanding the
level of risk involved in investments. Moreover, the paper states that the unexpected interest
rate fluctuations have significant impact on the market value of interest rate sensitivity and
bond portfolios.
The results obtained from the paper directly states about the multivariate model that
has been used via, Taylor Series approximations and standard portfolio theory. Therefore, it
has been detected that greater volatility has been detected during the test period in
comparison to the pre-test period by using the covariance matrix for the hedge. Thus, results
of the paper have shown instability that is generated by a scaler multiple of rate changes,
which can have direct impact on the performance of the investment portfolio.
2. Research hypothesis or research purpose:
The main research purpose is to understanding the level of implications of hedging
the interest rate risk with futures portfolio under term structure effects. The paper utilises the
methodology for detecting the levels of reduction that is faced by the interest rate risk in a
fixed spot or portfolio of liabilities and assets. The research also aims in developing a
minimum variance hedge that is constructed by adding a portfolio of financial futures with
the spot portfolio. Thus, the analysis of the relevant theorem is mainly indicated for

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developing and establishing the sufficient conditions that indicted about the existence of
unique and zero variance hedges.
In addition, the measures used in the paper directly states about the hedging approach
that has been used for reducing the interest rate risk by using the price sensitivity models such
as postulated by Kolb and others. However, it has been detected that the cash inflows and
outflows are most efficiently hedged by futures contracts, which have an underlying financial
instruments promising cash flows with equivalent. Therefore, the presence of the overall
financial performance can eventually help in determining the significance of the hedging
measures that can allow the investors to minimise the negative impact of interest rate risk.
3. Data and methodology:
The paper has used adequate level of data and methodology to derive the relevant
results, which can help in understanding the significance of hedging to minimise the risk of
interest rate. The paper has mainly utilised the methodology such as The Minimum Variance
Solution, Using the Term Structure, and Algebraic Properties for deriving the results for the
research. Hence, the analysis might help in determining whether utilising the hedging strategy
of future contracts would help in mitigating the relevant risk involved with the interest risk.
The analysis of the paper has directly portrayed that the data from U.S. Treasury
Bulletin has been used from the data of January 1970 to October 1982, where the closing rate
of last day of the month was taken into considerations, which indicated that the maturity fell
between 1 to 12 months. In addition, the future data was collected from The Wall Street
Journal, where the data stated from last trading day in December 1977 to October 1982. Thus,
the data was recorded at the close of last trading day for each month, as it helped in
synchronising the data with the treasury bill date. The data was mainly collected for using

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relevant methods such as the covariance matrix, unexpected yields, research design, and price
sensitivity models.
Calculation Formula
Unexpected Yields
Price Sensitivity Models
The Minimum Variance
Solution
Using the Term Structure
The above table provides information about the formulas that has been used in the
paper for deriving the relevant results.
4. Study or test results:
The analysis of the paper mainly highlighted several significant points, where it has
been detected that zero variance hedge does not exist for an arbitrarily selected spot portfolio,
where it is detected that the covariance matrix is of full rank. Moreover, the analysis of also
indicates that the portfolio with longer maturities require larger hedge position in the absolute
terms. Thus, it is detected that the net full information strategy is more consistently smaller
than that of price sensitivity strategy. The relevant analysis has mainly indicated that the total
performance of the portfolio that was used in the paper has indicated about the significance of
the hedging measure, which has minimised the level of risk involved in interest rates.
Therefore, it has been detected that the superiority of full information hedging is even more
pronounced, as the price sensitive hedge cannot produce a hedge with short and long

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positions. Thus, it is witnessed that the combination of short an long position would not help
in completely supporting the hedging measure, which might not help in supporting the pure
price sensitivity models.
5. Implications of the paper:
The research paper has certain implications, as it aims in determining the significance
of hedging measures that might help in minimising the level of risk involved in investments.
The hedging measure used in the paper has highlighted the possibility of successful hedging
measures that can be conducted for short term portfolio. However, it is detected that the
combination of short and long position in portfolio does not help in indicating the hedging
platform for he investors. The paper has mainly utilised different sets of the portfolio for
understanding the relevant performance of the portfolio under the hedge models. Thus, it has
been detected that the short term rates tend to fluctuate more, while covariance decreases
over the period of time. Therefore, investors could use the measures highlighted in the paper
to minimise the total risk involved in their investment, which is affected by the interest rate
risk. Consequently, it has been detected that covariance instability is relatively sensitive to
optimal hedging ratios, which indicates that with instability the general scalar of multiple of
rate changes.

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Bibliography:
Hilliard, Jimmy E. "Hedging interest rate risk with futures portfolios under term structure
effects." The Journal of Finance39, no. 5 (1984): 1547-1569.