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DFA Insurance Company Case Study, Part I: - page 13 / 40





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Cash Equivalent returns are the accumulation of 1-month government interest rates over time. Government Bond returns are a function of the applicable interest rate level, the change in the rate and the bond maturity. Corporate and Municipal Bond returns are modeled as a proxy to the US Single A corporate and the insured general obligation municipal bond markets respectively. They are calculated similarly to government bond returns. Corporate yields are modeled at a stochastic spread to government yields and municipal yields are modeled as a stochastic ratio to the government yields. Reported market yields on corporate bonds are adjusted to reflect historical defaults11. Common Stock returns are modeled as a proxy to the S&P 500 index. The returns are composed of capital gains/losses plus dividendsTM.

Table 2 shows the expected annual (arithmetic) and annualized compound (geometric) returns for each of the twelve modeled asset classes.

11This is based on the lO-year cumulative default study for Single A bonds provided by Moodys. A 50% recovery rate on defaults is assumed.

TzBecause we are assuming that long-term mean PIE ratios are equal to initial PIE ratios, valuation changes are not reflected in the risk premium between stocks and bonds. Thus the modeled equity risk premium is less than the historical average (6-7%), but is in-line with the historical average when adjusted for valuation changes.


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