## Executive Summary

Traditional market capitalization-weighted indexes are based on the assumption that a company’s current stock market price is the best estimate of value. This notion is supported by the Efficient Market Hypothesis. At Diamond Hill, we reject that assumption. We believe that replacing price with an estimate of intrinsic value is an improvement upon capitalization weighting and results in a better way to achieve broad market exposure. Our methodology, which is consistent with economic theory and supported by empirical evidence, is outlined in this paper. The Diamond Hill Valuation-Weighted 500 index (DHVW Index) calculation of intrinsic value is based on a proprietary, patent-pending investment methodology to estimate the normalized earnings power of each business, the growth in that earnings power over the next five years, the dividends that will be paid to shareholders over the next five years, and a terminal cash flow that accounts for the company’s projected tangible book value and capitalized future earnings. Two key components of the DHVW Index methodology are the separation of tangible book value from the current stock price and the observation that price-to-earnings (P/E) ratios follow a mean-reverting process over time and will revert toward the long-term market P/E.

## Diamond Hill Valuation-Weighted 500 Index Methodology

(DHVW Index)

All companies have what Benjamin Graham referred to as an “intrinsic value”, defined economically as the present value of all future cash flows. At Diamond Hill, we believe that a company’s intrinsic value is independent of its stock market price. We also believe that competitive long-term returns can be achieved by investing in companies when the current market price is at a discount to our estimate of intrinsic value. This principle is at the core of our shared investment philosophy and is evident across all of our investment strategies. In contrast, traditional market capitalization-weighted indexes assume that the current market price is the best estimate of a company’s value. The Diamond Hill Valuation-Weighted 500 index (DHVW Index) employs a distinct discounted cash flow methodology which estimates the intrinsic value of a company and weights index constituents based on these standardized approximations rather than by market-capitalization.

We believe the DHVW Index is a next generation index that applies the principle that valuation is a very important determinant of future investment return. Utilizing several ideas that are consistent with economic theory, and for which empirical evidence exists, DHVW Index is intended to provide superior returns to a comparable traditional market capitalization-weighted index.

**Background**

In the realm of index investing, market capitalization-weighted indexes (referred to here as “traditional” indexes) have maintained a position of dominance over the past four decades. Propelled by the increase in popularity of the Efficient Market Hypothesis and Modern Portfolio Theory, traditional index tracking strategies have grown considerably since they were first introduced in 1976.

From academia, the Efficient Market Hypothesis (EMH) suggests that all relevant information is reflected in current market prices. In an efficient market, price is the best estimate of intrinsic value because investors are assumed to be rational and all available information has already been accounted for in the current price. If true, then investors are better off owning low cost traditional index strategies rather than attempting to generate better than market returns (on a risk-adjusted basis) with high cost active strategies because “actual prices of individual securities already reflect the effects of information based both on events that have already occurred and on events which as of now, the market expects to take place in the future.”^{1}

Traditional market capitalization-weighted index strategies subscribe to the EMH which supports the notion that price equals intrinsic value and that owning a market capitalization-weighted portfolio is optimal. We, however, reject the assumption that investors are rational and that the market is efficient. We believe that a company’s intrinsic value is independent of its stock price and that intrinsic value can be reasonably estimated using a discounted cash flow methodology. Therefore, we believe the best way to weight securities in a broad-market index is based on intrinsic value capitalization.

Some of the oft-cited advantages of traditional index investing include transparency, broad market exposure, and low costs. We believe the DHVW Index retains these benefits, but provides broad market exposure that is valuation-sensitive and consistent with Diamond Hill’s investment philosophy that intrinsic value is independent of stock price.

One of the issues in using price as the sole measure of value is that market capitalization-weighted indexes tend to overweight overvalued securities and underweight undervalued securities. The valuation focus of the DHVW Index acts as a stabilizer at market extremes. When irrational exuberance causes prices to soar too high or fear takes hold and prices decline too much, our focus on intrinsic value (rather than price) will counteract the emotional behavior of investors due to the fact that they are human and not “rational profit maximizers.”^{2}

To that effect, the first step in constructing an index with a focus on intrinsic value designed to improve upon traditional indexes is to determine an appropriate estimate of intrinsic value.

**Estimating Intrinsic Value**

The DHVW Index calculation of intrinsic value is based on a proprietary, patent-pending investment methodology to estimate the normalized earnings power of each business, the growth in that earnings power over the next five years, the dividends that will be paid to shareholders over the next five years, and a terminal cash flow that accounts for the company’s projected tangible book value and capitalized future earnings.

A modified two-stage dividend discount model is then utilized to discount the projected cash flows to the current period. The intrinsic value of a company can be calculated as:

*IV _{0}* = Intrinsic Value per share of Company

_{0}

*D*= Dividend Paid in year

_{t}_{t}

*r*= discount rate

*P*= Estimated price of Company

_{n}_{0}(Terminal Value) in year

_{n}

**Tangible Book Value (TBV)**

A key aspect of the DHVW Index methodology is the separation of tangible book value (TBV) from the current stock price. Traditionally, the most common valuation parameter is the price-to-earnings ratio (P/E), which represents the capitalization of earnings. As earnings are an income statement item, little of a company’s balance sheet is captured in this number. Depreciation and interest expense are typically the only meaningful balance sheet items reflected in the earnings number, however, companies may have significantly different balance sheets not adequately reflected in the traditional P/E ratio. We believe separating the TBV from current price thus allows us to more accurately consider the value of a company’s operations.

The following real estate analogy illustrates such a difference: two houses can be identical in all respects except for location (perhaps one rural, one urban; one on a large piece of land, the other on a small lot; etc.). The primary explanation for a difference in market value, or current price, of these two identical houses is simply their location, or the value of the land on which the house sits. In this analogy, TBV is similar to the land value. By separating this summary of the balance sheet from the stock price, we believe we can more accurately value the income statement.

To isolate the operational earnings component of a company, we use a price in our price-to-earnings ratio that is adjusted for TBV. The adjusted price is calculated by subtracting current TBV (TBV_{0}) from the current price. In conjunction with the TBV adjustment, we use the earnings metric net operating profit after taxes (rather than the traditional earnings per share), which is discussed below. So a traditional P/E ratio of 15x now might be an adjusted price-to-net operating profit after taxes ratio of 10x for the same company. A subtle but important idea is that the stock price is still part of the calculated ratio, meaning it has some valuable information regarding investor’s opinions of growth prospects and risk.

**Net Operating Profit After Taxes (NOPAT)**

Separating TBV from the current stock price used in the calculation of the P/E ratio necessitates an additional adjustment. The earnings number must be adjusted by removing any balance sheet items such as depreciation or interest, which results in the income statement item called net operating profit after taxes (NOPAT). Removing the balance sheet items from the estimate of earnings avoids double counting the impact of a company’s capital structure.

We can now consider both the cyclicality and the growth rate of NOPAT. With regards to cyclicality: the smoothing technique of a regression line coupled with rolling periods (rather than fixed calendar periods) results in a current “Normalized NOPAT” (NOPAT_{0}). It is this number to which we apply a growth rate estimate to arrive at an estimate of year 5 NOPAT (NOPAT_{5}).

Dividends are calculated assuming the current dividend payout ratio remains unchanged for the next five years. The dividends, calculated as projected year t NOPAT (NOPAT_{t}) times the payout ratio, are cash flows to be discounted to the present. Year 5 TBV (TBV_{5}) can also be calculated in a straightforward manner. Current TBV (TBV_{0}) plus the sum of retained NOPAT over the 5 year period results in TBV_{5}.

An additional, and critical, idea underpinning the methodology is that P/E ratios follow a mean-reverting process over time and will revert toward the long-term market P/E.^{3} We account for this phenomena when deriving the Year 5 adjusted P/E ratio (P/E_{5}). Finally, we can solve for year 5 terminal value (P_{5}) using Adjusted P/E_{5}, NOPAT_{5}, and TBV_{5}. The estimate of P_{5} is then discounted to the present.

**Discount Rate**

The last variable to be addressed is the discount rate. The idea of a quality adjustment, similar to bond pricing, where yields are a function of the bond rating (AAA, BB, etc.)^{4}, is applied to create company specific risk-adjusted discount rates.

_{d}= r

_{f}+β

_{q}(R

_{m}-r

_{f})

*r _{d}* = discount rate

*r _{f}* = risk-free rate

*β _{q}* = Beta adjusted for quality of company

*R _{m}* = normalized market return

Discount rates in the DHVW Index methodology are a function of a risk-free rate, a general equity risk premium, and a qualitative differentiator between companies. The quality differentiator, or quality beta in the equation above, drives the individual discount rates used in discounting cash flows.

**Weighting**

The Diamond Hill Valuation-Weighted 500 index uses the methodology described above to estimate the intrinsic value of the largest 700 U.S. companies by market capitalization. The largest 500 companies by intrinsic value capitalization (estimated intrinsic value X number of shares outstanding) are selected for inclusion in the index. These 500 companies are then weighted based in intrinsic value capitalization within the index.

**Conclusion**

The DHVW Index methodology represents a rigorous technique to derive the intrinsic value of a company. We believe eliminating the impact of a company’s capital structure on its earnings by adjusting for tangible book value allows us to isolate the effect of a company’s operations when valuing the company. Additionally, the methodology accounts for observed mean-reversion in individual company valuation multiples and systematically risk adjusts the discount rates used to discount estimated future cash flows. We believe that the DHVW Index methodology, which relies on economic theory and sophisticated techniques, is an improvement upon traditional market capitalization-weighted approach to gain broad market exposure.

^{1} Fama, Eugene F. “Random Walks in Stock-Market Prices,” *Financial Analysts Journal*, Vol. 21, No. 5 (September/October 1965): 55-59.

^{2} For more on this topic, please see the Diamond Hill paper “Why Does ‘Closet Indexing’ Exist?” by Thomas P. Schindler, CFA & William P. Zox, CFA, J.D., LL.M. published in Spring 2001.

^{3} Beaver, William and Dale Morse, “What Determines Price-Earnings Ratios?,” *Financial Analysts Journal*, Vol. 34, No. 4: 61-64.

^{4} Investment Grade is a Bond Quality Rating of AAA, AA, A or BBB. Security quality ratings are derived from underlying portfolio securities as rated by Standard & Poor’s. For securities that are not rated by Standard & Poor’s, but are rated by Moody’s, the Moody’s rating will be used. Diamond Hill does not calculate a rating for securities that are not rated by Standard & Poor’s or Moody’s. The Standard & Poor’s and Moody’s ratings represent an opinion only, not a recommendation to buy or sell. Unrated securities by both Standard & Poor’s and Moody’s will show in the “NR” category.

*Originally published on March 17, 2015*

The views expressed are those of the author as of March 17, 2015, are subject to change, and may differ from the views of other members of the firm or the firm as a whole. These opinions are not intended to be a forecast of future events, a guarantee of future results, or investment advice.

An investment cannot be made directly in an index.