Random Walk Theory

A random walk, in the version applied to markets by Paul Samuelson, Burton Malkiel, and others, says that the next price change is not forecastable from the previous changes. The price has a drift, a long-run upward tendency in equities from bearing risk, and a shock that is essentially unpredictable. If changes are independent, then support lines, cycles, and candle sequences do not contain the next move. Later work softened the strict version. Returns show some dependence, volatility clusters even when direction does not, and different horizons behave differently. The surviving point is uncomfortable and useful. Most of the bar-to-bar variation you stare at is not a message. A theory that explains all of it is fitting noise.

The practical consequence is a base rate. Before you believe a pattern, ask what a coin-flip path would look like. Random paths produce double tops, head and shoulders, and beautiful trendlines. They produce them often. The pattern is interesting only if, under a rule fixed in advance, the outcome differs from that base rate by enough to pay the costs. Volatility clustering is the exception you can see without fooling yourself: large moves follow large moves more often than a simple story says, which is why ATR changes and why risk cannot be a fixed point stop forever. Directional patterns have a higher bar than volatility patterns, because the random-walk evidence is kinder to "size changes" than to "the next tick is up."

Use the random-walk idea to demand a control. If you trade a breakout, know how often a random entry at the same time of day, with the same stop and target, would have paid. If you cannot beat that, the chart shape is not doing the work. The idea also defends patience. If the edge is small and buried in noise, more trades are not more information. They are more costs. A long-horizon position that collects the drift, the equity risk premium, is a coherent response to a near-random walk. A short-horizon system is coherent only if the measurement says the changes are not random in the specific way you trade. Feeling that they are not is the feeling a random chart also produces.

Treating a random walk as a claim that markets have no trend. Drift plus noise still trends for long stretches. Also treating it as a claim that risk is the same every day. Volatility dependence is one of the best-documented facts in the data. And using the theory as a sneer at all technical work. Some technical rules are just ways of taking known premiums, trend, value, carry, with entries attached. Those can be real and still be consistent with a market that looks nearly random trade by trade.

Strict independence is false in the data. Jumps, overnight effects, expiries, and slow changes in the drift all exist. A random-walk model is a baseline, not a description of a crisis, when liquidity disappears and prices gap through every "independent" increment. The theory will not tell you which of your setups is the exception. You still have to count. And it is silent on the one-period disaster. Even a true random walk with a positive drift ruins the trader who is sized for a different distribution. The lesson is statistical humility plus a hard risk cap, not a shrug.