Do you know when to buy and sell? Using the Sine Wave Model

The hardest decision for most equity investors is knowing when to buy or sell a stock. Some investors are trading at a faster pace and are very active in buying and selling. Others regularly buy stocks, but do not know when, if sold. Some investors believe that the answer is "never" to sell, buy and hold basically forever. There is a whole set of philosophy and methods

What is the most meaningful? Is there a correct answer?

To start thinking about this important question, let us create a simple stock price change model.

This is a model:

A simple sine function, it is a simple sine function, wave, the horizontal line through its center. A straight line represents time, while a sine wave represents the price of the stock over time. Prices start at the left end of the timeline, or "time = 0", which may be now. The sine wave begins at the center line, rises for a period of time, equilibrates at the peak, falls for a period of time, downwards through the center line (causing the price to fall below the starting point), again forming a valley, again rising smoothly through the centerline, A peak, and so on.

Anyone familiar with stock price movements knows that prices are volatile. They go up and they come down. They certainly do not have a perfect sine wave shape, but a sine wave picture is a simplified assumption: this is a smooth version of the stock price actually done

For our idealized model, let us cycle Of each peak is 20% above the centerline, and each trough is 20% below the centerline. Thus, there is a 40% difference between the peak price and the lowest price per cycle. This happens to be the difference between a year's high and low prices for many stocks in the real world. So in our model, let each cycle for one year.

Finally, tilt the whole thing up a little so that the centerline, not the level, rises 10% annually. This represents the stock market's average rate of return over the past century.

This is our idealized model. Let's call it Sine's company Sine's stock has behaved like this since the company went public 100 years ago and its behavior would be like this infinitely into the future

We can from this simple model ?? Plenty!

Q: What is the ideal time to buy Sine? At least there are four good answers:

(1) Since we know that the model is tilted upward by 10% per year, simply at time = 0 (when the sine wave is at the centerline) and keep it as long as possible. Or, if you buy Sine's currency for a long time, you can always make a purchase. You do not care where Sine is in its cycle, because you know that over time, you will account for 10% of your average data block every year. You know, because the centerline slopes upward at a 10% slope. This approach has a name: dollar cost averaging. You will buy $ 100 a month for Sine, so you buy it at every point in its cycle, sometimes getting a good price, sometimes not. However, the mixed returns from all of these purchases will match the 10% upward slope of the chart itself. This is a widely recommended method.

(2) But you can do better. Wait a few months, and buy the stock at the exact bottom of its price cycle. This method also has a name: buy on the tilt. This will increase your returns by an astonishing amount because you will get more money from your stock. For example, if Sine's price at time = 0 is $ 100 and you wait nine months until the cycle reaches a low of $ 80, the $ 1000 will get 12½ shares instead of ten. 25% of the same number of shares. You will always benefit from these additional stocks. By the way, that's exactly what investors are aiming for. This is also a widely recommended method, although in the real world it is not possible to know exactly when the exact bottom of the cycle is hit.

(3) Next, let us speculate on your perfect knowledge of Sine's price behavior and know that it will continue to repeat its steady performance year after year, after the cyclical cycle. Then you can improve on # 2 above. Buy at the bottom of a cycle, continue to the top of the cycle, sell it there, take your time six months until the next bottom, repurchase, sell at the next top, and so on. Your return will be astronomical. Let's follow this two-year cycle (and make it simple by ignoring the tilt). Your first purchase will receive 12.5 shares at $ 80 per share, which is the same as # 2 above. At the top of the cycle (six months later), you will sell the shares at a price of $ 112 per share (40% more than you pay), or a total of $ 1,400. Waiting for six months to the next trough, the money will buy you 17.5 shares at the bottom of the cycle. Waiting for more than six months, sales of 17.5 will bring the top of $ 1960. Wait for six months, $ 1960 will buy you 24.5 shares.

In another six months, this cycle will reach another peak, and your stock will rise another 40% to $ 2,744. and many more. In the first 18 months starting at time = 0, you earned 174% ($ 2744 divided by the original $ 1,000), and every year later, it gets better as all compounds. This is to ignore the 10% upward tilt, which will bring more money. In just a few years, your $ 1,000 will become $ 1 million, even if on average, the price of the stock is only 10% higher each year.

(4) In fact, the trend is followed by an additional component that adds more payback. Rather than during the downturn of the cycle, many trend followers simply shift their positions from long-term (holding stocks) to short-term (bets). In this way, when the stock prices fall, they make money. This adds an order of magnitude more to the theoretical payoff of our idealized model.

Okay, that's the model. Now let's inject the reality into the model and see how it affects our real-life decisions.

First, the most obvious is that no one knows the future. In the real world, there is no stock price guarantee that there is a clear trend line up to 10% per year, or any other percentage. No one can believe that this trend will continue. We can only look at what happened in the past, and try to distinguish the future probability of occurrence.

Second, real-world stock prices do not follow a smooth sine wave. Their movements are jagged, subject to abrupt reversal, ambiguous long-term and short-term trends, and certainly not as predictable as our idealized model

However, the model points to a systematic approach Looking for a favorable trading point. The model represents the "buy low, sell high" model.

For sensitive stock investors, the model tells us that value investors have figured out the "buy" side of the equation. Waiting for the valuation is low, low prices, the price at its lowest point in the cycle. This is the best time to buy stocks

How to know when the stock reached a low? You are not, exactly. By sticking to favorable valuations, however, when the price of the stock appears to be lower than the long-term value of the firm, you can approach the buy in the sine valley. Some investors from the recent rise in real prices to confirm the stock has just been lower.

How do you know when the stock arrives? You do not know. But when valuations get higher, when they think the potential value of the price to the company is too high, the stock becomes more likely to peak, and the market will soon "correct" the price of the stock. Sensitive stock investors can do is use tracking to sell stop-loss to protect themselves in the downstream. The stop is set to 15% below the current stock price. Reset once a week, as long as prices continue to rise, continue to rise. If the stock starts to reverse, you can rely on your trailing stop to get you out and too much damage done. In practice, you sometimes find (especially for stocks that are not particularly volatile) that your trailing sells never trigger a sale, and you become a long outstanding stock holder. In other cases, if the stock price continues to fall, your trailing stop will trigger and retain most of the revenue. You will capture and sell the stock near the peak of the cycle