The simplest form of the random walk is a function that has an equal probability of being +1 or -1. The expected outcome of this function is zero and the standard deviation is the square root of the number of periods.
A simple random walk in one dimension has two important properties. The first property is that it is recurrent. Over time, it crosses zero infinitely often. The second property is that it is unbounded - it can exceed any positive or negative threshold.
Our stock markets can be considered to be nearly normal (or Gaussian) random walks with a positive drift. This means that the stock market changes by an amount drawn from a normal distribution.
The implication is thus, once you deduct the equity premium and the risk free rate, the stock markets returns are supposed to be random a mean value of 0%. This is the efficient markets hypothesis - it posits that future prices must follow a random walk.
There is too much unnecessary debate on the efficient market hypothesis.
I think the way forward for a good quantitative investor is that, eventually, all factors of outperformance will disappear once it becomes well known enough for people to follow it. The January Anomaly is almost non-existent these days. The Grossman and Stiglitz paradox says that if too many people believe in the EMH, they will stop analyzing, and this make markets more inefficient. If too few people believe in EMH, they will put in more work on analysis, making markets more efficient.
One consistent trope promoted by many other folks in this industry is the idea that dividend growth is something that is worth investing in. This has caused some retail investors to ask me whether it is possible to construct a backtest using dividends growth as a factor. So recently, I had some time to refine my models and I tried to use this factor to see if it truly outperforms as claimed by many gurus.
If we had bought an equally weighted REIT portfolio for the past 10 years, returns would have been 21.25% with a semivariance of 9.64% ( What to do ? Times were good ! ). If you had bought half of the REIT universe that grew dividends by the most throughout over the past 5 years, your returns would be below the average at 18.25% with a semivariance of 13.41%.
(Test was done on Bloomberg on 26 March 2019.)
Buying REITs for dividends growth for the last 10 years would have resulted in underperformance.
To rub salt in the wound, the investors would also have to stomach more volatility at the same time.
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