Random Walk Theory: What It Is, How It Works, and an Example.

#### What is random walk without drift?

A random walk without drift is a term used in finance to describe the motion of a security's price over time that is not influenced by any external factors. The security's price is said to be "random" because it is not influenced by any external factors, and it is said to have "no drift" because there is no overall direction or trend in the security's price movements.

### How are risk and return related?

Risk and return are inversely related, meaning that as one increases, the other decreases. This relationship is represented by the risk-return tradeoff. The risk-return tradeoff is the idea that investors must accept more risk if they want to earn a higher return. This is because higher-risk investments are more likely to produce higher returns. However, there is no guarantee that this will always be the case.

##### What is the best strategy according to the random walk theory?

There is no definitive answer to this question as it depends on a number of factors, including the time frame being considered, the level of risk tolerance, and the specific market conditions. However, in general, the random walk theory suggests that it is best to buy when prices are low and sell when prices are high. This simple strategy can be difficult to implement in practice, however, as it can be difficult to accurately predict when prices will rise or fall. What is the distribution of a random walk? The distribution of a random walk is the probability distribution of the position of the random walker at each step. It is given by the convolution of the distributions of the individual steps.

How do you model a random walk? First, you need to decide on the parameters of your random walk. This includes the starting point, the step size, and the number of steps. For example, you could start at 0, take steps of 1 or -1 with equal probability, and take 10 steps.

Once you have decided on the parameters, you can generate a random walk by taking a random step at each step. For example, if you start at 0 and take 10 steps, you could end up at either 10 or -10, with equal probability.

You can also simulate a random walk using a computer program. This can be useful for investigating the properties of random walks and for testing trading strategies that rely on random walks.