Optimized Yield Curve Matching - PowerPoint PPT Presentation

1 / 24
About This Presentation
Title:

Optimized Yield Curve Matching

Description:

Subtle implicit weighting. Questionable: Not enough emphasis on short term ... Implicit Weighting. Apply weight = 1 for each observation. Simple Short-Term Weighting ... – PowerPoint PPT presentation

Number of Views:32
Avg rating:3.0/5.0
Slides: 25
Provided by: markdav
Category:

less

Transcript and Presenter's Notes

Title: Optimized Yield Curve Matching


1
Optimized Yield Curve Matching
  • Mark Davenport
  • 3 December 2007

2
Outline
  • Motivation
  • Financial Background
  • Black Box Optimizer
  • Alternative Objective Functions
  • Simulations
  • Results
  • Conclusion

3
Motivation
  • Employee pension benefits provide flows of income
    to retired or disable employees
  • Pension funds provide the necessary cash flows to
    cover these pension obligations
  • The goal of managing these funds is to ensure
    sufficient cash flows
  • The focus of this project will be how to best
    manage the risks associated with attaining this
    goal

4
Financial Background
  • Price-yield relationship of a bond
  • Shifts in the yield curve cause PV of bond to
    change
  • Duration
  • Measure of sensitivity of the price of a bond to
    changes in interest rate
  • Portfolio Immunization
  • Practice of minimizing amount of interest rate
    risk to a portfolio
  • This project explores a duration matching strategy

5
Black Box Optimizer
  • Optimization routine using Excel Solver
  • Allocates plan across grouping of assets
  • Initial point
  • Random proportion of plan size assigned to each
    bond
  • Total amount allocated equals plan size
  • Test of assumption
  • 6 Yield Curves, 3 random starting points
  • Average difference between points
  • 28,969 trivial considering over 1 billion
    plan size

6
Optimization Routine
C difference in contribution to duration T
total plan size B amount invested D
duration w maximum relative duration v, u
minimum amount invested
7
Alternative Objective Functions
  • Twofold Process
  • Five objective function structures
  • Four weighting strategies
  • Total of 20 objective functions tested
  • Benchmark Objective Function
  • NISAs Current Strategy
  • Subtle implicit weighting
  • Questionable
  • Not enough emphasis on short term
  • Single year diluted across entire investment
    horizon

8
Alternative Objective Functions
9
Weighting Schemes
  • Implicit Weighting
  • Apply weight 1 for each observation
  • Simple Short-Term Weighting
  • Apply weight 1-
  • Power Weighting
  • Apply power of six to first ten years, power of
    four to the next twenty years, power of two for
    the remaining
  • Simple Weight-to-End
  • Apply weight

10
Simulation
  • As input, used single upward sloping yield curve
  • Created portfolio for each objective function

11
Volatility
  • Three volatility environments
  • Moderate
  • Extreme
  • NISA

12
Moderate Volatility
  • Two shift scenarios
  • Short-Term Long-Term
  • For each, 3 types of shifts
  • 100 basis point shift
  • 200 basis point shift
  • 50 basis point bend

13
Extreme Volatility
  • Examined Short-Term, Long-Term, and Constant
    volatility scenarios

14
NISA Volatility
  • Generated in-house at NISA
  • Assuming to be closest proxy for true Yield Curve
    volatility
  • Used as benchmark for my volatility

15
Determining Results
  • Results based off of 50,000 simulated yield curve
    shifts observed for each objective function
  • Difference in PV of assets and liabilities
    recorded
  • Standard deviation of differences determined the
    tracking error for each environment
  • Reported as raw number and in of liability

16
Results Objective Functions
  • Best for Short-Term Volatility in all
    environments
  • Least Squares Method
  • Two-Period Lagged Method (only power-weighted and
    simple weight-to-end strategies)
  • Best for Constant and Long-Term Extreme
    Volatility
  • Five Period Lagged Method
  • Change in Summation Method

17
Results Weighting Strategies
  • No impact on Least Squares Method
  • Short-Term Weighting Strategy in general
  • Encouraging results for power weighted benchmark
    and two-period lagged methods
  • In general, best for extreme short-term and
    extreme constant volatility

18
Results Weighting Strategies
  • Long-Term Weighting
  • Not a well designed test because cash flows
    resulting past 40 year mark are essentially zero
  • However, still positive results
  • Simple weight-to-end best for moderate long-term
    volatility, also for moderate short-term
    volatility
  • Oddly, generated better results as compared to
    short-term weighting strategy

19
Discussion
  • Least Squares and Two-Period Lagged (power
    weighted and simple weight-to-end) Methods

20
Discussion
  • Five-Period Lagged and Change in Summation Methods

21
Discussion Which is best?
  • Different yield curve environments require
    different objectives
  • Similarly, different money managing styles
    require different objectives
  • Reallocate once a day? Month? Decade?
  • Best objective?
  • Moderate short term volatility most realistic
  • Least Squares or Two-Period Lagged

22
Extensions
  • Interface Excel and Matlab
  • Take advantage of strength of Matlabs NLP
    capability
  • Introduce knowledge of convexity of assets and
    liability
  • Explore stronger short term weighting strategies
  • Introduce more asset classes into the problem
  • Become more interesting
  • Eliminate skewing effect of large 30 year cash
    flow
  • Explore different inputs

23
Accomplishments
  • Optimizer can identify global minimum
  • Simulated results determined better optimization
    routine
  • Given the constraints of the problem
  • Demonstrated importance of design in solving this
    problem
  • Knowledge of external factors

24
Questions?
Write a Comment
User Comments (0)
About PowerShow.com