The purpose of this article is to make the reader familiar with the analysis methods necessary to compare a traditional investment fund that accrues realized income to its net asset value (NAV) with an investment fund that does not accrue realized income to its NAV. We will discuss how readers can calculate the dividend premium in any index fund and how you can create a side by side comparison by indexing an investment fund and its underlying index to a common number to recreate how an investment fund’s NAV would perform without realized income included in its price.

We will refer to this article in many of our blogs as a means to explain how we conducted the analysis that we are referring to in the blog. As you can see, the explanation of our analysis methods is comprehensive and would clutter up our blogs if we incorporated it into the text of each of our blogs. The text below was extracted from an extensive research paper that we wrote describing all of the flaws of the last holder of record payment system. We are happy to provide this research paper, and our supporting math, to anyone interested in learning more above our product and how it will transform the way markets work. If you are interested in our paper please reach out to us using the contact form on our homepage and provide us the email address that we can send the paper.

**Data and Methods**

Historical data was downloaded from Yahoo Finance for the S&P 500 Index as well as FXAIX, which is Fidelity’s S&P 500 Index mutual fund. The data was collected from 12/14/2018 through 10-4-2019. The data series begins on an ex-dividend date of FXAIX and ends on an ex-dividend date. The management fee for FXAIX is .015% annually, so the drag on the price series of FXAIX is not material. Additionally, the majority of this analysis was conducted on a recent quarter of data for FXAIX beginning on 7-5-2019, ending 10-4-2019. The management fee drag on this quarter of data would be approximately .003% – which again is not material given the results.

We are not singling out FXAIX for any reason other than it is a popular index fund. Any income-producing S&P 500 index fund would have similiar results, so these results are not unique to FXAIX.

**Defining and Calculating the Dividend Premium**

For the purpose of our blogs, the “dividend premium” shall be defined as the amount of realized income collected from the investment fund’s underlying holdings, for a given payment period, in the form of dividends or interest. This income is accrued or added to the net asset value (NAV) of the investment fund when received. Investment funds account for the income that an investment fund collects as an asset, with no offsetting liability payable. It should be noted that Federal Securities Laws mandate that an investment fund is prohibited from earning income. Therefore, the securities laws require that “realized income” collected by an investment fund be paid to its shareholders such that the investment fund makes no profit.

The act of accounting for dividends and interest received as an asset, with no offsetting liability/declaration payable to recognize that these funds must be paid out in periodic dividend payments, per the investment funds prospectus, causes the value of the investment fund to become inflated relative to its underlying assets. As a result, the percent change of an investment fund will exceed the percent change of its underlying index for a given dividend payment period. Then, on the ex-dividend day, the investment fund finally recognizes all of the dividends received as a liability of the fund, resulting in a reduction of the NAV by an amount equal to the dividend per share that will be payable to the last shareholders of record.

The dividend premium is, therefore, equal to the percentage per-share value of all realized income collected by the investment fund divided by the investment funds NAV. For example, if an investment fund has a current price of $100 per share, and the fund will pay a $1.00 per share dividend to the investors of record the following day, the dividend premium is 1% or ($1.00 / $100 = 1%.) This is because the dividends received by the fund are equal to $1.00 per share of the total price of the investment fund

The dividend premium can, therefore, be calculated by comparing the percent change of the investment fund to the percent change of the investment fund’s underlying index, calculated by anchoring the percent change calculation to the value of the price series beginning on an ex-dividend day. Then, you subtract the percent change values of the investment fund from the percent change values of the investment fund’s index. This process flushes out the income collected by the investment fund, as a percentage of the fund’s share price. People believe that the percent change of an investment fund and the percent change in the underlying index should be equal since the investment fund is constructed in a manner that is supposed to replicate the precise movements of its index, but this is not the case. Even though their values are derived from the same components in the same amounts (i.e., the fund’s underlying investments/holdings must equal that of its index), the percent change of the investment fund is nearly always higher than the percent change in the index. This process contributes to the investment fund having an increased tracking error. Therefore, the percent change of a traditional investment fund will drift away from its underlying index.

The chart above titled “FXAIX Dividend Premium” was generated by using the methods previously explained. As you can see, we begin the calculations on 7-5-2019, which is an ex-dividend day for FXAIX, and we end the calculations on the following ex-dividend day 10-4-2019. On 7-5-2019 all the dividends collected from the previous payment period were paid. This process of paying out the dividends collected from the prior payment period resets the investment fund’s value to equal the value of the underlying investment fund holdings. Then, almost immediately, the investment fund begins receiving income in the form of dividends from its underlying holdings. When the fund books this income as an asset, with no offsetting liability payable, the fund’s value begins to exceed that of its index. So, the fund’s NAV is equal to the value of the underlying securities plus any dividends received to date. This realized income will build throughout the payment period until the following ex-dividend day on 10-4-2019 when the investment fund will finally book a liability that is equal to the sum of all the realized income that the fund has collected. This process drops the investment fund’s NAV, resetting the value of the fund to be identical with its index, which represents the fund’s fair value.

**Indexing of Price Series for Comparison Purposes**

To examine the effect of accumulating dividends and income received by an investment fund to its NAV, we must have a way to understand the performance of the investment fund if it did not accumulate realized income to its NAV. Since an index fund is structured to precisely replicate the returns of its index, we will use the price series of the investment fund’s index, in our case the S&P 500 price index, to represent the returns that the investment fund would generate if the investment fund changed its accounting treatment such that realized income of the investment fund used double-entry GAAP accounting principles to book realized income as an asset, with an offsetting liability payable or dividend declaration which effectively removes the income from the NAV of the investment fund. Again, the returns of an investment fund and its underlying index should be identical since they are comprised of the same assets in exact proportions. Therefore, in order to understand the performance of an investment fund that does not accrue income to its NAV, we can simply use the performance of the investment fund’s underlying index, as the index does not include accrued income in its price and its underlying securities are a replica of the securities that are contained in the traditional investment fund. Then, we add back the dividends paid by each fund at the end of the payment period to arrive at each fund’s total return. It is important to remember that FairShares pays dividneds differently. We pay ALL investors, not just the last holders of record.

To deal with the fact that the S&P 500 and FXAIX have two different values, we must index each price series to a certain common number. For the purpose of our calculations, we will index both the S&P 500 Index and FXAIX to a starting NAV of $100 per share. From that starting NAV, the prices will be adjusted up and down based on the percent change of both FXAIX and the S&P 500. This process creates an apples-to-apples comparison of the changes in the NAV of each type of investment fund. Now that each fund is indexed to a common number, we can begin our analysis using the actual data of each price series to determine the number of shares purchased, investment returns, taxes owed and yield.

It may be difficult to see, but indexing each price series to $100 per share, and then introducing the percentage change price series for FXAIX and the S&P 500 Index (or FairShares 500) creates a chart like the one below. Can you see how FXAIX begins to drift above the FairShares 500? That is because of the dividend premium. Now you can see that you are overpaying when you buy a traditional index fund.

Below is an example of the indexing math that allows a comparison of each fund type. We start with a NAV of $100.00 and then adjust that value by the percentage change of each price series.

## Author

#### Jeremy Roseberry

CEO