Capital Markets Assumptions

1 Capital Markets Assumptions 2021. 2021. Capital Markets Assumptions I. Overview The reasoning behind this methodology is to use the Capital Markets Assumptions are the expected direction and strength of relationships across various returns1, standard deviations, and correlation estimates asset classes for the common time periods to infer that represent the long-term risk/return forecasts for what these relationships would have been for the various asset classes. We use these values to score time periods, where one of the asset classes does not portfolio risk, assist advisors in portfolio construction, have data.

2 In the original methodology all the available construct our own asset allocation models and assets are used to construct these cross-asset create Monte Carlo simulation inputs for portfolio relationships. We have improved this methodology wealth forecasts. by utilizing stepwise-fit multivariate linear regression framework (see Glossary of Terms) to guide us in Our approach to estimating Capital Markets estimating these cross-asset relationships. Assumptions and constructing asset allocation models is based on the following general Assumptions : STEP 2. Theoretical Model: Reverse Optimization To obtain the long-term expected return estimates T he global Capital Markets are largely efficient in as implied by the CAPM, we use the reverse the long run, where the efficiency of the Markets is optimization approach proposed by William Sharpe measured by the Capital Asset Pricing Model (CAPM) (1974).

3 While this approach is based on the same (see Glossary of Terms). theoretical principles as the CAPM, it allows us to avoid While the global Capital Markets are efficient in the estimating the risk premium on the market portfolio. long run, there might exist identifiable shorter-term Estimating the risk premium on the market portfolio inefficiencies in the Capital Markets . can be a challenging task due to the dependence of Risk premia are time-varying. this estimate on the data period used. Instead, the reverse optimization calls for using (A) the observed Our Capital market Assumptions construction process market portfolio, (B) market risk aversion coefficient, is based on using statistically advanced techniques and (C) the standard deviations and correlations to combine information coming from three sources: (estimated in Step 1), to obtain the estimates of the theory, researcher views ( , forecasts by recognized expected returns.)

4 These expected returns, when economic analysts or our own views into future returns used in conjunction with the standard deviation and of equity and fixed income asset classes), and historical covariance estimates, then imply the observed market data. The process consists of the steps that are portfolios as the efficient market portfolio under the detailed in the next section. CAMP theory. To estimate the observed market portfolio we II. Process estimate the market capitalizations of all the non- overlapping indexes commonly used in constructing STEP 1: Estimating Standard Deviations and long-only strategic portfolios (see Figure 1).

5 For Correlations example, to estimate the market capitalization of We employ a method created by Robert Stambaugh2 domestic equity we look at the market capitalization (1997) to calculate standard deviations and of russell 's Top 200 Value/Growth, russell correlations that are forward looking, in that they MidCap Value/Growth, and russell 2000 Value/. account for estimation risk (See the Glossary of Growth indexes . Terms). In addition, this estimation method eliminates the need to look at only the common data periods The risk aversion coefficient can be thought of as a when estimating the standard deviations and magnitude of the trade-off between expected return correlations a common, but a very restrictive way and variance (Sharpe, 1974).

6 Instead of trying to estimate to guarantee that correlation matrixes are positive this value, we will set this parameter to a value that makes definite3 and allows for the usage of all the available the rate of return on domestic equity (proxied by russell data deemed appropriate for a particular asset class. 3000 Index) implied by the reverse optimization equal to the forecast that we make in Step 3. 1. The expected returns are given in nominal arithmetic mean terms, although as we note later the translation between nominal vs real and arithmetic vs geometric mean returns is straightforward.

7 2. Robert Stambaugh is a professor of finance at The University of Pennsylvania Wharton School. 3. See the Glossary of Terms. Also, note that positive definiteness of correlation matrixes is essential when this correlation matrix is used in optimization or simulation. Note that a correlation matrix that is obtained from individual pairwise correlations cannot be guaranteed to be positive definite. 2. 2021. Capital Markets Assumptions Thus, the reverse optimization framework can be empirically and also intuitively is the rate of real GDP. thought as a way of obtaining the correct relative growth per capita, which under positive population expected return relationships among various assets, growth scenario is usually substantially lower than the while the methodology in Steps 3 and 4 ( , obtaining of headline real GDP growth rate.)

8 Since after the World Researcher Views) guides us in setting the levels of these War II, the real GDP growth has been almost 3 percent, forecasted expected returns. while the real GDP growth per capita has been only slightly above 2 percent. In fact, there have never been STEP 3. Researcher Views: equity prolonged periods with above 2 percent real GDP. We forecast the return for the russell 3000 Index per Capital growth rates outside of the 1990s, when it (which proxies for the entire domestic equity asset averaged 12 percent. class) and use this estimate as an anchor for the expected return levels for the other asset classes Arnott (2011) notes that while the aggregate real in Step 2.

9 Earnings track the real GDP growth well, the real earnings per share grow at a rate that is significantly Any equity return (both realized and expected) can slower than the aggregate real earnings, mainly due be broken down into parts that are attributable to to a dilution effect. That is, a large part of aggregate dividend yield and Capital gains. Capital gains can be earnings growth happens due to growth in new further broken down into a portion that is attributable business, which is not reflected in the existing stock to the growth in earnings per share and a portion that market indexes .

10 Is attributable to growth in P/E ratios. These are exact algebraic relationships, and if viewed independently Forecasting the Change in P/E. of each other do not provide any additional insight for If the P/E's are mean reverting, then today's P/E's carry purposes of forecasting. However, if we assume that information either about future growth of earnings per pricing multiples ( , P/E's) are mean-reverting (or at share or future returns, or both (Campbell and Shiller, least are not likely to stray orders of magnitude outside 1988). In addition, as shown in Campbell and Shiller historical norms), then, as shown in a seminal paper by (1998), current P/E's have a strong negative correlation Campbell and Shiller (1988), present dividend ratios with future returns, while at the same time they have have to forecast either future increases in earnings per practically no correlation with the future earnings per share or decreases in future returns.