13
votes
Do markets really follow a random walk or is this idea outdated?
No, the idea is not outdated. Fama (1970, JF) summarises the early research on stock price behaviour and defines an efficient market as follows:
A market in which prices always ''fully reflect'' ...
6
votes
Do efficient market hypothesis and random walk theory convey the same concept?
They are different concepts, and the relation between them can be described as a conditional: "if EMH holds (all available information about future price movements is already priced into the market), ...
6
votes
Fama: Efficient Capital Markets: A Review of Theory and Empirical Work - are martingales incorrect?
The way I understand it is:
In equation 2 $x_{j, t + 1}$ is defined as the change in of $p_j$ over the period $t$ to $t + 1$. The formula says that the expectation of the change is zero which is the ...
6
votes
Accepted
How to model stock price for a monte carlo simulation with fat tails and asymmetric risk
I did a related project years ago and an example from Matlab's website, Using Extreme Value Theory and Copulas to Evaluate Market Risk, proved particularly helpful as the starting point. At a high ...
5
votes
Random Walk with normal increments and n time periods why is the increment $\sqrt{(t/n)}$?
I don't think I was clear in my comment so I'm putting it in an answer to have more space. The variance of a brownian motion, z, is $t$. (i.e: $E(z^{2}) = t$ ). Notice that
$R_{i}$ really equals $\...
5
votes
Do efficient market hypothesis and random walk theory convey the same concept?
Historically the RWT (Random Walk Theory) came first, as empirical observations by for example M.F.M. Osborne (1959) and others in the 1960s. The EMH came about as a result of theoretical work by ...
5
votes
Accepted
Cannot Understand The Ticket Line Question From Interview Book
If you allow for exchanges between the people in the queue, then there is no problem to be solved. So the implicit assumption must be that people in the queue only deal with the counter.
4
votes
Determining if a time series is random
So there are several issues with your posting that you will need to resolve. The first one is your concept of randomness and distinguishing between a random event and a non-random event. To ...
4
votes
Accepted
some doubts about answers to ticket line question from interview book
The way I understand this approach:
you start at $A = (0, 0)$.
Every time a 5\$ person wants to buy a ticket you move one unit to the right and unit up.
Every time a 10\$ person wants to buy a ticket ...
4
votes
Accepted
Proving Scaled Random Walk Approaches Normal Distribution
$X_j$ can be either 1 or -1 with 50% probability each. So this step is just applying the expectation to both possible cases.
See definition of the Expectation...
\begin{align}
{\mathbb E}\bigl[ X \...
3
votes
Accepted
Why are changes in stock market wealth considered permanent?
I guess the concept you're looking for are martingales. These are stochastic processes which remain on their current level (in expectation!).
Ignoring some technical conditions, a stochastic process $...
3
votes
How to estimate the probability of Clustering illusion in our backtest result?
False positives and false negatives are concepts from Frequentist statistical inference. They depend on people not data mining. Using Keynesian notation, they test $\Pr(X|\theta)$. That is to say, ...
3
votes
Expected number of days inside a corridor
This looks to me like a range accrual. Let $t_1, \ldots, t_n$, where $0 < t_1 < \cdots < t_n$ be business days that are being considered. We compute
\begin{align*}
E\left(\sum_{i=1}^n \pmb{1}...
3
votes
Accepted
Random Walk of N Correlated Assets
The correlation matrix refers to the correlations between the asset returns. In fact, it can be seen as follows. Each asset follows a geometric Brownian motion, i.e.,
$$
\frac{{\rm d}S_t^i}{S_t^i}=\...
3
votes
Generally how to simulate bivariate (or multidimensional) BM sample paths?
For the two-dimensional case, the Cholesky decomposition of the covariance matrix
\begin{equation}
\Sigma = \left( \begin{array}{c c} \sigma_1^2 & \rho \sigma_1 \sigma_2\\ \rho \sigma_1 \sigma_2 &...
3
votes
Accepted
The right choice when the price of a stock follows a random walk
It makes no difference. Starting with a capital of 1, let $X_i$ be the multiplying factor for the $i$th day, so $X_i\in\{1+r,1-r\}$ with each possibility having probability 1/2. The expected capital ...
3
votes
Simulating artificial asset prices: Random walk vs Brownian motion?
Echoing some of the comments to the OP above, the only real difference between random walks and Brownian motions is a question of time frequency. IE a Brownian motion is just an aggregation of a (...
2
votes
Counting random paths
As I mentioned above, I am not sure what the variable $r$ is. If we ignore that, or assume the questioner wanted to say its the risk free interest rate, then it has no effect on the number of paths.
...
2
votes
Accepted
random walk with drift and absorption barrier
Firstly, this is very normal fare for Stochastics which studies properties of such processes. So if you're not finding anything, look up any stochastics textbook.
One thing that is not clear from ...
2
votes
How to create a volatile market, by combining less volatile markets?
Let $X_1$ and $X_2$ be your two assets and $C$ your financial product. For now we only assume products which are a linear combination of $X_1$ and $X_2$ with no shorting allowed, hence:
$$\begin{align}...
2
votes
How to create a volatile market, by combining less volatile markets?
Throw in correlation as the additional variable.
Similarly, volofvol could be another candidate to play with.
A spread option could have a larger volatility than either of the two underliers.
2
votes
How does the efficient market hypothesis fit with the rapid changes in prices?
It depends on which form of EMH you're considering as to provide a rationale.
Strong-form EMH could or would assert there's private information potentially changing hands that agents are acting on ...
2
votes
Rare Events in Normal Multivariate distributions
If you’re comfortable making the assumption of multivariate normality (I’m not sure that you are), then this seems like a perfect place to use Mahalanobis distance.
One of the first facts that ...
2
votes
Forget Kelly, forget fractional sizing. Where is the general theory?
I've recently had to do quite a bit of work on position sizing.
Leonard C MacLean, Edward O Thorp, and William T Ziemba have written an incredible amount of literature on this. The following text ...
2
votes
Accepted
Variance of Random Walk with Drift
Setup
Let
$$Z_n\equiv \prod\limits_{i=1}^n(1+x_i)$$
where each $x_i$ is iid normally distributed as $x_i\sim \mathrm{N}\left(\tilde{\mu},\sigma\right)$. For simplicity, and with some abuse of ...
1
vote
Accepted
Accumulation Rate of Variance in Random Walk
If we denote the random walk with $(X_k)_{k \in \mathbb{N}}$ than for all $k$ the random variable $\Delta X_k := X_{k} - X_{k-1}$ has mean zero and variance one:
\begin{align}
\mathbb{E}[\Delta X_k] = ...
1
vote
How to estimate the probability of Clustering illusion in our backtest result?
I think what you have in mind is similar to the Cowles Test, described by Alfred Cowles in his 1933 paper Can Stock Market Forecasters Forecast? (link)
Cowles wanted to evaluate the trading ...
1
vote
If price is a random walk, is ok to use the binomial distribution to estimate a trading strategy?
It is a good idea to make an assumption of "no informational content" on prices to have a reference level for this $H_0$ hypothesis.
The best is probably to make Monte-Carlo simulations, i.e. to ...
1
vote
Accepted
How does the efficient market hypothesis fit with the rapid changes in prices?
You‘re right. The "true price" should only jump when news arrives but in practice, market participants need time to arrive at a new equilibrium, i.e. the market needs some time until it is clear how ...
Only top scored, non community-wiki answers of a minimum length are eligible
Related Tags
random-walk × 78stochastic-processes × 16
time-series × 9
brownian-motion × 9
monte-carlo × 8
probability × 8
programming × 5
martingale × 5
market-efficiency × 5
equities × 4
volatility × 3
finance × 3
quant-trading-strategies × 3
statistics × 3
correlation × 3
simulations × 3
itos-lemma × 3
random-variables × 3
option-pricing × 2
finance-mathematics × 2
mathematics × 2
binomial-tree × 2
econometrics × 2
quants × 2
normal-distribution × 2