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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 160
Part 3
Note how each Constraint is labeled in the Excel model in order
for the Constraint’s name to appear here in Part 3 of the Answer
Report as it does
Note which Constraints are binding (had their limits hit) and which
aren’t.
Note how much slack is still available in any Constraint that has
not had its limit hit.
Note any Integer Constraints (Integer, Binary, Alldifferent)
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 161
Bond Portfolio Optimization Example
Optimizing the Allocation of Bonds in a Portfolio
To Maximize Return
One basic use of the Solver is to correctly divide a bond portfolio among
bonds of different yield, maturity, and risk or in order to maximize yield or
minimize risk.
The Problem
Correctly divide a bond portfolio among 4 bonds of varying yields
and maturities in order to achieve an overall bond portfolio with an
average maturity of 5.5 years while maximizing overall yield.
Specific information about each bond is as follows:
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 162
Problem Solving Steps
Step 1 – Determine the Objective
In this case, the Objective is to create a portfolio that maximizes the
overall portfolio yield while having a specific average maturity. The
Objective is the overall yield of the entire portfolio. The cell that
calculates this overall yield is the Objective Cell.
Step 2 – Determine the Decision Variables
We are trying to determine what percentage of the overall portfolio to
allocate to each bond in order to maximize the total yield while
maintaining an average maturity of 5.5 years. The Decision Variables
are the percentages of the overall portfolio that are allocated to bond
type.
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 163
Step 3 – Build the Excel Equations That Combine
the Objective With All Decision Variables
The yellow Objective cell G8 displays the overall portfolio yield and will
be maximized. The green Decision Variable cells (E3 to E6) display the
percentages of the overall portfolio to achieve the objective while
creating a portfolio with an average maturity of 5.5 years. The light blue
Constraint cell in the model (F8) establishes the average bond maturity
and is controlled by the light blue user input in cell B12 in the following
diagram:
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 164
Step 4 – List all Constraints
Step 5 – Test the Excel spreadsheet
Test the Excel spreadsheet completely before adding information to the
Solver dialogue box. Make sure that any changes to green Decision
Variables produce the correct results in the yellow Objective cell.
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 165
Step 6 – Insert All Data into the Solver Dialogue
Box
Input the Objective cell, Decision Variable cell, and all Constraints into
the Solver dialogue box as follows:
All equations on the Excel spreadsheet are linear (1
st
order) so we can
use the Simplex LP (Linear Programming) method for this optimization
problem.
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 166
Step 3 shows the completed problem with Decision Variables that have
been optimized by the Solver to maximize the Objective while staying
within the problem’s Constraints.
Answer Report
Part 1
Note:
The Solver Result
How long Solver took to solve the problem
The Solver Engine that was used and the Solver Options settings
Where the Objective Cell was labeled in the Excel model for its
name to appear as it does in Part 1 of the Answer Report