13 May 2020 – *This essay is based on a paper I wrote recently as part of my studies for a Doctor of Business Administration (DBA) at Keiser University. I thought readers might like seeing how to properly analyze investment opportunities before making a final decision, so I’ve revised the paper for presentation here.*

In a surprising coincidence, bright and early Monday (3/23/2020) morning I received a call from Saira Morgan of Rustik Haws (RH) publishers wanting to republish a novel (entitled *Red*) that I launched in 2010 with another publisher (iUniverse), which had a disappointing sales history. It seems RH’s editors had reviewed the book, and felt that the problem was not the book’s content, but that it had been badly mispriced at $29.95 in paperback, or $39.95 in hardcover. RH wanted to re-launch a new edition of the book priced more reasonably at $12.99 in paperback. The original publisher had based their price on the book’s large page count (588 pages), and I had uncritically accepted their suggestion. The contract I have with iUniverse stipulates that I own the copyright, and am free to republish the work at will.

SM’s call was a surprising coincidence because that week’s topic for the Financial Theory & Policy course I was taking at the time was the question: “How can you use [mean variance optimization] to ensure that the business organization you are leading will succeed without losing money in some investment activities?” The RH proposal thus presented an opportunity to use the capital asset pricing model (CAPM) to evaluate their offer (Fama, & French, 2004), and write about it on the class forum.

My initial reaction to SM’s call was positive because feedback I’ve received from booksellers was that the price impediment was enough to prevent booksellers from carrying the book at all, thus preventing potential readers from ever sampling its content. Before even starting to evaluate RH’s proposal, however, I wanted to find out who the company was, and whether I wanted to take their offer seriously. I have received offers from other vanity-press publishers that were not at all professional.

Thus, I started evaluating the opportunity by visiting the Rustik Haws website. A cursory inspection showed that it looked quite professional and offered a full suite of the services one would expect from a modern self-publishing house. The biggest concern was that they only started the company in 2014, which is recent in a business where many firms have been around for a century or more.

A visit to the Better Business Bureau (BBB) website showed them to have an A- rating, and the only derogatory comment was about RH’s time in business (Better Business Bureau, 2020). BBB counted as time-in-service only the one year from RH’s move to Tampa, FL in May of 2019. The company did get two derogatory customer reviews, but both were by individuals who never actually worked with them. They’d been put off by RH’s tactic of cold-calling potential customers. I discounted those because how else are you going to drum up business? There were no complaints from actual customers. Altogether, I judged that it was worthwhile to at least evaluate RH’s offer.

The appropriate tool for evaluating a potential investment like this one is the corporate asset pricing model (CAPM). Copeland, Weston, and Shastri (2005) show the inputs for the CAPM to be the risk-free rate of return, the expectation value of the market rate of return, the market variance, and the asset-return’s covariance with the market return, which is called its *beta*. The first four should be available from online sources or my stock broker.

The asset’s expected returns and its beta are another matter, however. I would have to estimate the potential returns based on the deal RH is offering and sales history of other books I’ve written. Luckily, I have quarterly sales history for a how-to book (entitled *How to Set Up Your Motorcycle Workshop*) that I launched in 1995 with another publisher (Whitehorse Press), and which is still selling well in its third edition. I would be able to calculate beta by matching sales figures with contemporary market gyrations. So, I judged that I had identified adequate sources for the information needed to evaluate the RH offer using mean variance optimization (specifically CAPM), and compare it to the RH buy-in price.

## Estimating Beta from Historical Data

It happens that not only did I have the quarterly reports from WP available, I also had complete daily closing prices for the Dow Jones Industrial Average (DJIA) going back to the beginning of the index. I selected from all this information data to form a picture of the first 10 quarters (two-and-a-half years) of the WP-book’s performance using an Excel spreadsheet (summarized as Table 1 below). The first two columns of the spreadsheet include an index (I always include an index as a best practice when composing a spreadsheet), and dates of the closing day of each quarter. The index runs from zero to ten to provide a pre-date-range value to allow taking differences between entries. Note that the first period was dated two weeks before the close of the first quarter because that is when WP closed its books and issued the report for the first-quarter’s performance. It does report a full quarter’s results, though. I chose to start with the initial post-book-launch data as that most likely paints a representative picture of sales for a new-book launch.

The third through fifth columns list DJIA’s closing prices, changes from the previous quarter’s value, and those changes relative to the previous quarter’s closing value (thus, the DJIA rate of change per quarter). Beneath those columns I’ve collected the mean, standard deviation, and variance computed using Excel’s statistical functions. Similarly, I’ve listed the WP data and calculations in columns seven through nine. Column seven lists the WP book’s unit sales. Column eight lists quarterly royalties paid. Column nine converts those royalties into quarterly returns on a hypothetical $1,000 initial investment by WP. I do not have information about what WP’s initial investment actually was, but the amount matches what Rustik Haws was asking, and is fairly typical for the industry. Below the WP performance data is the mean, standard deviation, and variance for the return on investment (ROI) computed by Excel’s statistical functions.

I was unhappy with the results returned by Excel’s covariance function, so I added column six that manually computes the covariance between the DJIA fluctuations and those of the ROI. The columnar portion computes the product of quarterly changes in the DJIA and those of the ROI. Cells below the column sum the quarterly contributions from column nine, then divides that sum by a count of the values in the sum to average the covariance values. Finally, I added a cell below that computes the investment’s beta by dividing by the variance Excel computed for the DJIA fluctuations.

The estimated beta has a magnitude of slightly over 0.6 and moves opposite the market fluctuations (shown by its having a negative sign). These data will inform the CAPM calculation of an expected return on the contract proposed by Rustik Haws (Ross, 1976).

## Expected Value of Rustik Haws Proposal

To be an attractive proposition, the Rustik Haws proposal would have to provide an expected quarterly return greater than that projected by the CAPM (Fama, & French, 2004), which reads:

*E*_{i}* = R*_{f}* + **β*(*E*_{m}* – R*_{f}),

where *E*_{i} is the expected return required for the investment, *R*_{f} is the return on a risk-free asset (e.g., a three-month Treasury Bill), *β* is the covariance of royalties from the sale of the WP book with the market chosen for comparison (the DJIA), *E*_{m} is the expected market return.

The quarterly returns from the DJIA give *E*_{m} = 0.0489 ≈ 0.05 (the average relative return per quarter), and *β* = -0.06172 ≈ -0.06. I’ll take the risk-free rate to be the Federal Reserve’s target rate. Right now, the Fed has decided to set its target interest rate anomalously low (approximately zero) in response to stress on the economy from the COVID-19 pandemic, but it is reasonable to expect that to rise back to the pre-pandemic rate of 2% per annum (0.02/4 = 0.005 per quarter), which can be used for the risk-free rate, *R*_{f}. Plugging these values into the CAPM equation gives a required quarterly return of 0.0473, or 4.7%. That return on a $1,000 investment means the quarterly royalty projection should be >$47.30.

Not surprisingly, Rustik Haws has not projected quarterly sales for the re-launched book, but the assumption for this analysis is that unit sales might be similar to those of the WP book, which appear in Table 1. Rustik Haws’ per-copy cost structure provides $12.99 (retail price) – $3.89 (bookseller’s commission) – $5.83 (printing cost) = $3.27. The average quarterly sales for the WP book was 211 during that first 10 quarters. That makes the expectation value of royalties equal to $3.27 x 211 = $689.97. This is over 14 times the $47.30 required by CAPM, and argues strongly in favor of accepting the offer.

## Best Competing Use of Funds

Completing the analysis requires using the CAPM to compare the RH opportunity to the best alternative use of the funds. That happens to be expanding my portfolio of stocks. To do that, requires estimating the expected return on the stock market going forward, and the beta of the portfolio.

The stock market is currently in the recovery phase after a serious disruption by the COVID-19 pandemic. So far, the recovery appears to be more-or-less L-shaped. That is, after a 34% initial drop (23 March), there was an immediate recovery to somewhere around 17% down, followed by a movement around that 17% down value with no clear direction. I interpret the 34% initial drop to be an overcorrection that was reversed by the rise back to 17% down. That I consider the true level based on the market’s expectation of future returns. The flatness of the current movement of both the DJIA and S&P 500 indices signals uncertainty as to whether there will be a second peak in COVID-19 cases.

Historically, after a financial crisis markets recover to their previous-high level after about a year (which would be near the end of 1Q 2021). So, guesstimating a typical recovery scenario without a double-dip, we can expect a 17% recovery from the current level in very roughly one year, which gives a compound quarterly growth rate of 4.9% on the $1,000 investment, or only $49.26. This still argues in favor of taking the RH opportunity.

In actual fact, experience shows that it takes roughly a year to bring a new edition of a book to launch. Thus, the returns for both the relaunched book and recovering stock market should commence more-or-less at the same time. At that point, experience indicates the market should have settled on the long-term compound annual growth rate, which is 7% (corrected for inflation) for the S&P 500 (Moneychimp, 2020). This translates into $70.00 for the projected $1,000 investment, which is still only one tenth of the expected $689.97 quarterly return on the RH investment. Thus, working with RH to relaunch *Red* appears to be by far the best use of funds.

## References

Better Business Bureau (2020) *Rustik Haws LLC.* [Web site] Clearwater, FL: Better Business Bureau. Retrieved from https://www.bbb.org/us/fl/tampa/profile/digital-marketing/rustik-haws-llc-0653-90353994

Copeland, T. E., Weston, J. F., & Shastri, K. (2005). *Financial Theory and Corporate Policy*. Boston, MA: Pearson.

Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model: Theory and Evidence. *Journal of Economic Perspectives*, *18*(3), 25–46.

Moneychimp. (2020). Compound annual growth rate (annualized return). http://www.moneychimp.com/features/market_cagr.htm

Ross, S. A. (1976). The arbitrage theory of capital asset pricing. *Journal of Economic Theory*, *13*, 341-360.