Commercial Real Estate

Beyond the Efficient Frontier: Using a DFA Model to Derive the Cost of Capital CAS Special Interest Seminar The Insurance Market Dallas April 16, 2002 CON N I N G Why Should we care about Cost of Capital? • EVA® • Economic Value Added (Stern Stewart & Co.) • EVA=NOPAT-WACC*Assets • Economic Value added is the Amount of Profit (after-taxes) less the Cost of Capital (weighted average cost of capital times assets) 1 What is “Weighted Average Cost of Capital” • WACC= (COD  Debt + COE  Equity)/Capital • Weighted Average Cost of Capital is the Cost of Debt and the Cost of Equity, weighted by the respective proportions 2 Finance 101 Widget Factory • Widget factory requires: • Equity from investors • Debt from lenders • Weighted Average Cost of Capital is the Cost of Debt (COD) and the Cost of Equity (COE), weighted by the respective proportions • COD - determined easily from actual terms • COE - more troublesome, but can be determined from CAPM, and knowledge of the Widget Factory's beta • (Cost of equity capital = Risk free rate + Stock’s Beta  Market Risk Premium) 3 Finance 101 Insurance Company • Insurance company requires: • Equity from investors • Funds Advanced by policyholders • Weighted Average Cost of Capital is the Cost of Funds Advanced (COFA) and the Cost of Equity (COE), weighted by the respective proportions • COFA - not determined easily • COE - more troublesome, but can be determined from CAPM, and knowledge of the Insurance Company’s beta 4 Goal of this Presentation • Rather than identify COE and COFA separately, calculate overall Cost of Capital • Use a DFA Model to calculate Cost of Capital 5 Cost of Capital • What can I get elsewhere (at similar levels of risk)? • “Opportunity” Cost 6 Properties of the Cost of Capital • Is related to the types of returns available from other financial instruments in the market-place • Increases along with the riskiness of the related strategy - but not a simple measure of dispersion. Investors only rewarded for non-diversifiable risk. • Is related to the length of the project (but this exercise will only examine a one-period result) 7 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 8 Efficient Frontier 15% 12% 9% 6% Economic Value Efficient Frontier 3% 0% 0% 15% Standard Deviation of Economic Value 9 Comparison of Corporate Strategies 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: - Economic Value Added - Cost of capital 1 0 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 1 1 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 1 2 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 deviation of differences - it is the strategy’s basis for the cost of capital 1 3 Identifying a Corporate Strategy’s Basis for the Cost of Capital 1) Generate cumulative returns for each portfolio Cumulative Return Factors Scenario Portfolio A Portfolio B Portfolio C Portfolio D 1 2 3 4 5  s 1.065 1.069 1.031 1.070 1.058 1.059 0.0161 1.112 1.079 1.051 1.059 1.045 1.069 0.0272 1.125 1.051 1.061 1.092 1.101 1.086 0.0301 1.115 1.052 1.095 1.113 1.145 1.104 0.0342 1 4 Identifying a Corporate Strategy’s Basis for the Cost of Capital 2) Model the corporate strategy in the same DFA scenarios Cumulative Return Factors Scenario Portfolio A 1 2 3 4 5 1.065 1.069 1.031 1.070 1.058 Portfolio B Portfolio C Portfolio D 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 1 5 Identifying a Corporate Strategy’s Basis for the Cost of Capital 3) For each portfolio, calculate the initial investment required Cumulative Return Factors Scenario 1 2 3 4 5 Portfolio A 1.065 1.069 1.031 1.070 1.058 Portfolio B 1.112 1.079 1.051 1.059 1.045 1,200,164 Portfolio C 1.125 1.051 1.061 1.092 1.101 1,182,207 Portfolio D 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 Initial 1,211,755 Investment 1 6 Identifying a Corporate Strategy’s Basis for the Cost of Capital 4a) Calculation of Ending Asset Values for Each Portfolio Scenario 1 2 3 4 5 Accumulated Value = Initial Investment * Cumulative Return Factor Portfolio A 1,290,124 1,295,276 1,249,257 1,296,506 1,282,039 Portfolio B 1,335,034 1,295,270 1,261,289 1,271,206 1,254,386 Portfolio C 1,329,848 1,241,921 1,254,034 1,291,127 1,301,221 Portfolio D 1,294,892 1,221,727 1,271,665 1,292,184 1,329,732 Ending Market Surplus 1,487,995 1,232,381 1,138,587 1,279,724 1,271,275 1 7 Identifying a Corporate Strategy’s Basis for the Cost of Capital 4b) The basis for the cost of capital is the portfolio with the lowest standard deviation of differences Difference = Ending Market Surplus – Accumulated Value Scenario 1 2 3 4 5 Portfolio A 197,871 -62,895 -110,670 -16,782 -10,764 118,061 Portfolio B 152,961 -62,889 -122,702 8,518 16,889 103,399 Portfolio C 158,147 -9,540 -115,447 -11,403 -29,946 99,318 Portfolio D 193,103 10,654 -133,078 -12,460 -58,457 121,124 Ending Market Surplus 1,487,995 1,232,381 1,138,587 1,279,724 1,271,275 s 1 8 From: CAS Task Force on Fair Value Liabilities • “An alternative approach to computing the underwriting beta is to regress accounting underwriting returns in a line of business on stock market returns. The method suffers from the weakness that the reported underwriting returns often contain values for the liabilities that have been smoothed over the underwriting cycle, thus depressing their variability.” 1 9 Comparison • CAS Fair Value Approach: • A weighted average of an asset beta and an underwriting beta. • Regression technique applied to empirical underwriting results • Isaac/Babcock Approach • Directly estimate total company Cost of Capital • Regression technique applied to modeled total company results 2 0 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 2 1 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 2 2 Identifying an Optimal Corporate Strategy Ending Market Surplus Strategy X Strategy Y Strategy Z 1,237,995 1,252,381 1,258,587 1,279,724 1,191,275 1,243,992 33,073 A 53,182 1,487,995 1,232,381 1,138,587 1,279,724 1,271,275 1,281,992 128,046 C 60,477 1,337,995 1,082,381 1,458,587 1,399,724 1,191,275 1,293,992 154,545 D 52,067 Scenario 1 2 3 4 5  s Portfolio EVA 2 3 References • Beyond the Frontier: Using a DFA Model to Derive the Cost of Capital by Daniel Isaac FCAS and Nathan Babcock ACAS • http://www.casact.org/coneduc/reinsure/astin/2000/han douts/handouts.htm • EVA http://www.sternstewart.com/evaabout/whatis.sht ml • Underwriting Beta http://www.casact.org/research/tffvl/app02.pdf 2 4 CONNING ASSET MANAGEMENT Beyond the Efficient Frontier: Using a DFA Model to Derive the Cost of Capital April 15-16, 2002 CON N I N G