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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 
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 167 
Part 2 
 Note that the Variable Cells contain the Decision Variables 
 Note where the labels for each Decision Variable are placed in 
the Excel model so that the Decision Variable’s name will appear 
here in Part 2 of the Answer Report as it does 
 Note the type of variable  - Either Continuous or Integer (Integer, 
Binary, or Alldifferent) 
 Note the Before and After values of each Decision Variable 
  
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 168 
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) 
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 169 
Limits Report
The Limits Report is made available when the Solver finds a Globally or 
Locally Optimal solution and no Integer Constraints (Integer, Binary, 
Alldifferent) were used. Part 2 of the Answer Report Shows that the 
variables were Continuous and not Integers. The Simplex LP method 
solves linear problems to globally optimal solutions. 
The 2nd section of the Limits Report just shown indicates that none of 
the Decision Variables have any slack because the upper and lower 
limits of each Decision Variable are the same. 
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