XXXII International ASTIN Colloquium Beyond the Frontier:

XXXII nd International ASTIN Colloquium

Beyond the Frontier:

Using a DFA Model to Derive the Cost of Capital

Daniel Isaac, FCAS

Nathan Babcock, ACAS

Swiss Re Investors Beyond the Frontier: Using a DFA Model to

Derive the Cost of Capital Z

Comparison of Corporate Strategies

• Recent papers: use a DFA model to compare strategies

• DFA model’s focus: to find the Efficient Frontier of corporate strategies

• Efficient Frontier

– Subset of strategies that maximize reward for each level of risk

– A company will improve its results by moving towards the Frontier



2

Question:

How should management choose among strategies that are points on the “corporate strategy” Efficient Frontier?

Answer:

Determine two additional strategy-specific measurements from existing DFA results:

- Cost of capital

- Economic Value Added



3

Properties of the Cost of Capital

• Increases along with the riskiness of the related strategy

• Is related to the types of returns available from other financial instruments

• Is related to the length of the project



4

Cost of Capital

• Definition: portfolio on the “asset-only” Efficient Frontier with the smallest value of s [ (strategy results) - (portfolio results) ]

• Variance of the cost of capital is referred to as the systemic, or non-diversifiable, risk



5

Economic Value Added (EVA) for a Strategy

• Definition: strategy’s return in excess of the return that would have been generated by the strategy’s cost of capital

• Variance of the EVA is referred to as diversifiable, or non-systemic, risk

• Variance of the EVA is independent of the returns on all other securities in the marketplace



6

Identifying a Corporate Strategy’s Basis for the Cost of Capital

1) Run the DFA model to generate cumulative returns for each portfolio on the “asset-only” Efficient Frontier

2) Model the corporate strategy in the same DFA scenarios

3) For each portfolio, calculate the initial investment required to minimize the std. dev. of the differences between a) ending portfolio value and b) ending market surplus

4) Select the portfolio with the lowest standard devation of differences - it is the strategy’s basis for the cost of capital



7

1) Generate cumulative returns for each portfolio

Cumulative Return Factors

Scenario Portfolio A Portfolio B Portfolio C Portfolio D

1 1.065

1.112

1.125

1.115

2

3

1.069

1.031

1.079

1.051

1.051

1.061

1.052

1.095

4

5

1.070

1.058

1.059

1.045

1.092

1.101

1.113

1.145

 1.059

1.069

1.086

1.104

s

0.0161

0.0272

0.0301

0.0342



8

2) Model the corporate strategy in the same DFA scenarios



3

4

1

2

5

1.065

1.069

1.031

1.070

1.058

1.112

1.079

1.051

1.059

1.045

1.125

1.051

1.061

1.092

1.101

1.115

1.052

1.095

1.113

1.145

Ending

Market

Surplus

1,487,995

1,232,381

1,138,587

1,279,724

1,271,275



9

3) For each portfolio, calculate the initial investment required



3

4

1

2

5

Initial

Investment

1.065

1.069

1.031

1.070

1.058

1,211,755

1.112

1.079

1.051

1.059

1.045

1,200,164

1.125

1.051

1.061

1.092

1.101

1,182,207

1.115

1.052

1.095

1.113

1.145

1,161,338

Ending

Market

Surplus

1,487,995

1,232,381

1,138,587

1,279,724

1,271,275



10

4a) Calculation of Ending Asset Values for Each Portfolio

Accumulated Value

= Initial Investment * Cumulative Return Factor

Ending

Market

Surplus

Scenario Portfolio A Portfolio B Portfolio C Portfolio D

1 1,290,124 1,335,034 1,329,848 1,294,892 1,487,995

2

3

1,295,276 1,295,270 1,241,921 1,221,727 1,232,381

1,249,257 1,261,289 1,254,034 1,271,665 1,138,587

4

5

1,296,506

1,282,039

1,271,206

1,254,386

1,291,127

1,301,221

1,292,184

1,329,732

1,279,724

1,271,275



11

4b) The basis for the cost of capital is the portfolio with the lowest standard deviation of differences

Difference

= Ending Market Surplus – Accumulated Value

Ending

Market

Surplus


1 197,871 152,961 158,147 193,103 1,487,995

2

3

4

-62,895

-110,670

-16,782

-62,889

-122,702

8,518

-9,540

-115,447

-11,403

10,654 1,232,381

-133,078 1,138,587

-12,460 1,279,724

5 -10,764 16,889 -29,946 -58,457 1,271,275 s

118,061 103,399 99,318 121,124



12

Preference of Market-Based Values over Accounting Values

• Comparison of strategy’s returns with portfolio benchmarks’ market returns

• Allows comparison of different companies

• Eliminates the advantage of changing the valuation of certain assets and/or liabilities



13

Market Surplus - Difficulty due to the Existence of a Net

Operating Loss (NOL) Carryforward

• An NOL carryforward has value to the company

– will reduce future taxes

– will increase future returns

• An NOL has restricted usage

– cannot be sold to another company

– even if entire company is purchased, only 10% is available each year

• The value of an NOL is a function of

– the age and size of the NOL

– expected future profits



14

Identifying an Optimal Corporate Strategy

• For each strategy under consideration:

– Run the strategy through the DFA model

– Identify the benchmark that best matches the strategy’s results

(i.e., the strategy’s basis for the cost of capital)

– Calculate the cumulative EVA (compared to the benchmark)

• Select the strategy with the largest cumulative EVA



15

Swiss Re Investors

Scenario

1

2

3

4

5

 s

Portfolio

EVA

Identifying an Optimal Corporate Strategy

Ending Market Surplus

Strategy X Strategy Y Strategy Z

1,237,995 1,487,995 1,337,995

1,252,381

1,258,587

1,232,381

1,138,587

1,082,381

1,458,587

1,279,724

1,191,275

1,243,992

33,073

1,279,724

1,271,275

1,281,992

128,046

1,399,724

1,191,275

1,293,992

154,545

A

53,182

C

60,477

D

52,067

Beyond the Frontier: Using a DFA Model to


16

XXXII International ASTIN Colloquium Beyond the Frontier:

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