Revisiting the sum-of-parts approach to Capital Market Assumptions

When it comes to forming Capital Market Assumptions (CMAs) for equity markets, it is very common to see institutions, consultants, and other providers use a variant of the same approach. They express expected returns as the sum of a dividend yield, a cash flow growth component, and a repricing or 'multiple expansion' term. The framework goes by different names — the Grinold-Kroner model, the supply-side model (Ibbotson and Chen (2003)), or the "sum-of-the-parts" method (Ferreira and Santa-Clara (2011)). While implementations can differ a little, they more or less use the same underlying structure.

This approach is a simple way to tackle the difficult task of constructing expected returns. But the sum-of-parts decomposition can also be misleading, since it abstracts from common underlying drivers to expected return components. In this article, we integrate discounted cash flow logic into the sum-of-parts framework, and explain how this avoids inconsistencies in building expected return estimates.

Somewhat unusually for our Insights articles, we resort to a small amount of math and keep the discussion at a more conceptual level. While on the abstract side, these ideas provide robust foundations for our CMAs, scenarios, and other asset allocation tools that tackle real-world problems.

Recap: the 'sum-of-parts' return decomposition

While the sum-of-parts approach is widely used and familiar to many, we quickly recap where it comes from using the minimal possible steps and notation. The starting point is the fact that the total return on an equity index over one period equals the dividend yield plus capital appreciation:^[1]

Under the sum-of-parts approach, a very simple manipulation splits the capital appreciation term into growth in price-earnings ratios and earnings growth. This is achieved by multiplying and dividing top and bottom by earnings at time t+1 and t:

With a bit of rearranging and taking expectations, we can arrive at an expression that captures the essence of sum-of-parts models, where expected returns combine dividend yield, growth, and multiple expansion components:

From this point, building expected returns involves estimating these components and summing them together.

Integrating discounted cash flows

The simple exercise above can miss a lot of intuition and underlying mechanics. It’s easy to forget that the manipulation of return definitions is just a way to extract a number for capital appreciation to add to dividend yield. It is completely mechanical: if earnings grow by some amount and the P/E ratio changes by another amount, then the price can simply be backed out as approximately the sum of these changes. The decomposition does not tell you why earnings grow, or multiples change, and how to ensure these changes are consistent with each other.

One way to introduce consistency is to integrate discounted cash flow thinking into building expected returns. We can think of price as the present value of all future cash flows (we equate these to earnings to keep things simple):

Going back to the definition of returns, a DCF framework gives an immediate way of understanding capital appreciation. If prices will be higher relative to today, it will result from higher expectations of future cash flows or lower discount rates. Using the DCF framework, we can also see how the earnings growth and multiple expansion components can be related. Dividing both sides of the $P_t$ expression by current earnings $E_t$ shows the P/E ratio is fully determined by the path of expected future earnings growth and discount rates:

Price-earnings ratios and earnings growth components from the sum-of-parts expected return expression are therefore intertwined and should not be adjusted independently of one another.

By integrating discounted cash flows into return definitions, we have a collection of relationships between prices, earnings, and expectations, that help us understand how these sum-of-parts components are related. When using the sum-of-parts method today, an analyst might set the earnings growth term to be relatively high, for example driven by the belief there will be AI-related productivity gains. Another typical assumption is to set the multiple expansion term in a backward-looking way: for example near zero or possibly negative today given that multiples are relatively stretched.

DCF logic disciplines these assumptions. Strong earnings growth can likely lead to higher prices, but in the DCF framework, what matters is how this growth comes in relative to what was already expected. If earnings growth is indeed strong relative to expectations, this likely has implications for expected growth priced into equities tomorrow, which the expression above tells us will drive price-earnings ratios. If strong earnings growth is expected to continue in the future, a flat PE ratio implies that the higher growth outlook is exactly offset by an increase in discount rates. This is what would need to happen for the valuation multiple to remain unchanged in the face of better fundamentals.

We might also think about the consistency between earnings growth and the dividend yield component of returns. If an analyst projects strong earnings growth, what does this mean for the path for dividends (per share, which also includes net issuance effects)? A reasonable assumption may be to treat these variables as positively correlated (subject to payout ratio behaviour).

From theory to practice

Some CMA providers might argue that it is a pragmatic choice to focus on forecasting earnings growth while assuming that markets will assign the same multiple to these earnings as they do today. While this approach might be thought of as taking an 'agnostic' view on pricing, it can quickly introduce inconsistencies among underlying relationships that are difficult to reconcile with expected return narratives.

It is rare to see the full implications unpacked from a DCF point of view, which is our preferred approach. This consistency pays off beyond the conceptual coherence too. We embed a macro present-value framework in our expected return, risk, and scenario modelling, which results in expected returns that can be defined across horizons, with better predictive performance. This approach also provides a more intuitive and consistent understanding of risk and scenarios. We will return to more concrete examples that embed DCF thinking into expected returns and scenarios in the next Insights articles.