<FOOLISH FOUR PORTFOLIO>
RP Variation Math
and why it works
by Ann Coleman
([email protected])
Reston, VA (December 14, 1998) -- Math time. Today we tackle the hows and whys of the RP formula. Just hang in there, math-phobes. I will make this as painless as possible. If you are going to use the RP strategy in your own portfolio, it is important that you understand how and why it works. After that, you can let us do the math for you, and we will never ask you to find a square root again.
The how and the why are actually linked, but I don't think we have done a very good job of explaining that. We have usually described the RP formula as "Yield squared divided by Price." When explaining why the RP works better than the rank-by-yield/rank-by-price methods, we have said that the formula gives more weight to the yield. That's true, but it's not really the best explanation.
There are actually three RP formulas: Yield squared divided by Price, Yield divided by square root of Price, and Dividend squared divided by Price cubed.
Yield x Yield
--------------- = RP
Price
Yield
---------------------- = RP
Square root of Price
Div x Div
----------------------- = RP
Price x Price x Price
Of course, it is obvious to the most casual of observers that these formulas will give different ratios, but those ratios will always rank the stocks in the same order -- of course. (Plup! Sorry for the rude noise, but I just had to get my tongue back out of my cheek.) Since yield is Dividend/price, the first and third formulas are mathematically equivalent, although the third will produce a ratio with fewer leading zeros if you enter the yield as a percentage rather than as a decimal. The middle ratio is the square root of the first -- you did notice that, didn't you?
The point is, no matter which formula you use, the stock rankings will be the same. Because of that, we have usually quoted the easiest formula when explaining things online -- Yield squared divided by Price. This has led to a certain amount of confusion about how the strategy works.
Bob Price and Elan Caspi found the formula by playing with different ratios between dividends and price. Bob's original formula was the third one above -- Dividend squared divided by Price cubed (DsPc or D^2/P^3). Elan's formula was Yield squared divided by Price.
If the fact that these formulas gave great backtested results was the only rationale for the formula, we wouldn't have much confidence in it. Such techniques are often called data mining, meaning you keep looking through a large amount of data until you find something that you like. An example of data mining would be going through the Wall Street Journal stock tables and creating a portfolio from every 100th stock. Now, backtest it -- don't like the results? Try every 101st stock, then every 102nd stock. Eventually, you will find a portfolio that smashes the market.
Say your formula was based on every 167th stock and over the past 20 years it returned an average of 30% a year. (Books have been written on and small, brief fortunes made with such formulas.) Does this mean you should buy every 167th stock in the Wall Street Journal's stock table next year?
I'm not going to dignify that question with an actual answer.
If there is no underlying rationale, then such formulas are useless. They are the financial equivalent of tossing heads 100 times in a row. Sure, it's highly unlikely that anyone would do that, but if you toss a coin long enough, the laws of probability say eventually you will get such a streak. (Better start around the time of the Big Bang.) Does that mean that that you should bet your house that the 101th toss will be a head (or, for that matter, a tail)? Nope. The odds are still 50/50 that the next toss will be either one.
The underlying rationale for the RP formula is this: High yield is positively correlated with better performance. We already know that the 10 highest yielding Dow stocks outperform the Dow. It's been studied, backtested, forward tested, and analyzed to death and the rationale is obvious -- they are bargains. But the 10 highest yielders don't all do equally well. Some are duds, in fact. The question is, how do we refine that group of ten down to just the few best performers?
The Beating the Dow method was to pick the lowest priced of the 10 highest yielders. That worked well. Our various Foolish Four strategies have refined that approach even further by eliminating the lowest priced high yielder because it was too often a stock in real trouble.
Despite their not realizing it at the time, both of the original formulas used a well established predictor of stock price movement: The square root of price. (Remember that the formulas above produce the same rankings.) Academic studies have found that beta is inversely correlated with price but more strongly with the square root of the price (lower price = higher beta).
Beta is a measure of volatility. Volatility just means how rapidly a stock's price moves (up or down). A stock with a high beta tends to move more rapidly and to greater extremes than the market as a whole. For example, if the market goes up 20%, a stock with a beta of 1.5 would be expected to go up 30% (1.5 times as much). If the market goes down 10%, that 1.5 beta stock would be expected to go down 15%. Of course, beta is based on long-term averages, and no stock follows the rules exactly. Still, stocks with higher betas tend to be more lively, and stocks with betas lower than 1 tend to move more sluggishly.
By selecting stocks with high yields, we are selecting stocks whose price movement is more likely to be up. Therefore, by selecting for high beta, the magnitude of the upward movement is increased. That's the secret of the RP's success.
Bear in mind that all of our strategies pick winners and losers. It's a rare year that every single Foolish Four stock goes up. But over the long term, the average performance of stocks identified by this formula has been spectacular: 24.62% per year annualized over the last 25 years.
That's the kind of math everyone likes.
Fool on and prosper!
<% =headlines %>
Get the Fool's new book - The Foolish Four
Current Dow Order | 1998 Dow Returns
12/14/98 Close
Stock Change Last -------------------- UK - 1/2 40.56 IP + 11/16 41.56 MO -1 1/8 51.75 EK -1 1/8 70.88 |
Day Month Year
FOOL-4 -0.90% -5.75% 7.58%
DJIA -1.43% -4.62% 9.96%
S&P 500 -2.17% -1.93% 17.60%
NASDAQ -3.07% 0.89% 25.25%
Rec'd # Security In At Now Change
12/31/97 206 Eastman Ko 60.56 70.88 17.03%
12/31/97 276 Philip Mor 45.25 51.75 14.36%
12/31/97 289 Int'l Pape 43.13 41.56 -3.62%
12/31/97 291 Union Carb 42.94 40.56 -5.53%
Rec'd # Security In At Value Change
12/31/97 206 Eastman Ko 12475.88 14600.25 $2124.38
12/31/97 276 Philip Mor 12489.00 14283.00 $1794.00
12/31/97 289 Int'l Pape 12463.13 12011.56 -$451.56
12/31/97 291 Union Carb 12494.81 11803.69 -$691.13
Dividends Paid YTD $1092.81
TOTAL $53791.31
</FOOLISH FOUR PORTFOLIO> |