# Is Magic Formula Really Profitable?

I have invested in stocks since 2006 and have been since searching for the holy grail of investing which could give me outstanding market-beating results with lower risk than the market portfolio offers. When I read about quantitative value investment strategies a few years ago, I was sold. All the blog posts, books and research papers showed massive results. But still I did not start to follow these types of strategies. Why? Because I think that no one should invest in any kind of black box system until he/she has verified himself/herself that it actually works and understands the underlying reason for the alpha. It is quite hard and expensive to get hands-on historical fundamental data so that is why I did not have the chance of testing quantitative value strategies. Until now. With a lot of work I was able to code my own simulator which I used to simulate all kinds of investment strategies. As I had access to both 25 years worth of historical fundamentals and price data, my simulator has been running full-time during these couple of last months when I was giving a ride for all those value strategies out there. Low P/E, P/B, P/S, Graham Net-Nets, Piotroski, Magic Formula etc. were tested. In this article, I will be presenting the results for the possibly magical Magic Formula value strategy which is originally based on Warren Buffet’s ideas of buying cheaply wonderful companies. Hopefully you will find the results interesting, so keep on reading.

As mentioned earlier, the simulation is done with my own Java-based simulator. The reason for this was simple. I wanted a free, open-source white-box system. I can easily add any kind of features, test any kind of investment strategies with any kind of data and import or export the data however I wish, for free. In addition, as the simulator is my own, I fully understand its limitations, how it works and can be 99% sure that the results are really valid. Otherwise, this would not have been possible.

Ok, I think I have had enough of chit-chat and can continue with the actual Magic Formula results. The rules are very simple, calculate the Return on Equity and earnings yield for every stock included in the simulation and rate them based on points. For instance, if stock A has the highest RoE of all stocks in the simulation and the 10th highest earnings yield, it will be given 11 points. After all points are assigned, the simulator will choose a maximum of 50 stocks with the lowest points and invest 2% of entire capital to each of those stocks. The portfolio was rebalanced on the beginning of April and October each year and last year’s fundamental data was used in order to avoid look-ahead bias. The simulation interval was from 1988 to mid-2014 for U.S. listed stocks. The normal way of calculating RoE would be to use net income but in this simulation I used owner earnings which is a term introduced byWarren Buffett (Trades, Portfolio). Owner earnings is simply cash flow from operating activities subtracted by capital expenditures. So, RoE was calculated by dividing owner earnings by total equity. Earnings yield was calculated by dividing the market cap by owner earnings. The bigger the values, the better it was. Dow Jones Industrial Average will be used as the benchmark index which delivered 8.63% during the simulation interval. Dividends were included in the portfolio results but not in the benchmark returns. The equity curve for the Magic Formula strategy can be found below.

The strategy delivered 22.63% per annum and outperformed 79% of the time the benchmark, which is really astounding. I think we can quite fairly say, that Magic Formula really is magical in terms of returns and my results seem to be aligned with all other researches out there. But wait a minute! When I am buying a stock I always have to pay something to my broker. Let’s now assume that I have to pay 0.1% with a minimum of 7$ to my broker from each transaction. In addition the spread will be 0.1% because I have to use market orders to get my transaction quickly through during rebalancing. This shouldn’t lower the results much, I guess. The equity curve after all transaction costs and spread can be found below.

It still looks very impressing as the return was 21.68% per annum. Hmmm, what about the government? I think they want their share as well in the form of capital taxes. Let’s assume next that the tax on capital gains is 30% and it needs to be paid at mid-July. The equity curve after transaction costs, spread and taxes can be found below.

Wow, government took away nearly 2/3rd’s of the entire end net-worth and the return per annum dropped from 21.68% to 15.88%. The Magic Formula is still outperforming the benchmark roughly 68% of the time which is still good enough. I hope there are no more other factors, limiting the returns. Let us recap, we have included the broker fees, spread and taxes. What else? Ah, what about the survivorship bias? Let’s next run the same simulation with de-listed stocks as well. The equity curve for Magic Formula after transaction costs, spread, taxes and with de-listed stocks included can be found below.

That didn’t seem to lower the results much as the strategy is still returning 15.55% per annum. However, one must note that in this case the results would actually be annually 0.7%-1.4% (guesstimate) higher as I did not have access to dividend data for delisted stocks. So, in that sense including delisted stocks actually increased the results slightly. Are there still any other limiting factors to consider? Unfortunately, there is one more. We simply can not assume that we could buy low liquidity stocks without affecting their prices. As slippage is impossible to simulate, the simulator excludes all stocks which do not have enough trading volume. If 5% of stock’s yesterday’s trading volume was lower than the amount of capital planned to be used for buying it, the stock was not bought. The equity curve after transaction fees, spread, taxes, with de-listed stocks and liquidity check is shown below.

Once again, the results dropped substantially from 15.55% to 11.81% per annum. This might be because the smallest stocks seem to produce most of the alpha and as bigger the portfolio gets, the larger the trading volume for any given stock has to be so that we would not affect the share price. If we would include the dividends after taxes from delisted stocks as well, the actual annual return would be somewhere in the ballpark of 12.6%-13.4%.

The first result with a 22.63% per annum seemed to be roughly aligned with all the other researches about Magic Formula. However, I’m not quite sure what expenses and limitations are actually taken into consideration in them. I’m quite confident that taxes are excluded in every single research I have read and if you still recall, taxes took away roughly 2/3rd’s of the ending net-worth. Broker fees and spread is one thing which might be missing from most of the researches as well, but I could be wrong as well. However, this factor decreased the returns “only” by 1% per annum so it should not affect the results much. Survivorship bias affected the results in a positive way which was a clear surprise. The biggest limiting factor along with taxes was liquidity. In some of the previous researches I have read, stocks which have the lowest 40% market cap were excluded but I don’t honestly think this is correct. This kind of an approach might still exclude stocks which have enough volume or include stocks which clearly might not have enough volume. The liquidity factor really starts to affect after the portfolio has grown substantially. This is why I would assume that the longer the time frame for testing Magic Formula, the lower the results would be because the biggest gains would be made while the portfolio is still small in size and as the portfolio grows, the smaller stocks would have to be excluded which are the ones producing the most of the gains. Still, even though accounting all the limiting factor, Magic Formula proved to be a viable, robust and alpha-producing strategy. It seems to beat the index by 58% of the time with a slightly higher volatility even though dividends for delisted stocks were excluded. Now, a careful reader might ask that what about the dividends for the benchmark which were excluded? If we assume a 2% per annum dividend yield for the benchmark, it would have returned 10.4% per annum. After taxes this would equate to roughly 8.9% per annum so we could conclude on a very high level that dividends and taxes roughly balance each other out and Magic Formula still beats it quite substantially. The next question is that can anyone disregard the Magic Formula results? For instance, if compared to my own personal investment strategy, Magic Formula crushed it by a country-mile so in that sense the only viable option for me would be to switch everything to Magic Formula. However, some psychological factors seem to prohibit me from doing this. How about you?

The entire report can be read from here: http://s000.tinyupload.com/?file_id=01483729989677288575