# Questions tagged [statistics]

The study of the collection, organization, analysis, and interpretation of data. Questions may deal with descriptive statistics, probability distributions, random variables, sampling, regression, density estimation, filtering, inference, estimation theory, or computational statistics.

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### What is the proper way to derive risk definitions from utility functions?

In typical mean-variance analysis, the risk-adjusted relative value of an individual asset takes the general form $\frac{\mu}{\sigma^2}$, with further weighting and normalization depending on the ...
• 73
30 views

### Probability distribution function for boundaries on brownian motion

What would be the probability distribution function for brownian motion with 2 boundaries ie a stop loss and take profit. The process is a standard brownian motion. However at values a and b any ...
48 views

### Tiering value in RFQ

I was wondering what are typical strategies employed by market making firms to calculate the tiering value of each client. So when a client create an RFQ, the market maker after calculating the BID/...
51 views

### Robust or Stochastic Optimization Approach for Maximizing Profit with Limited Price Information

I am tackling a linear maximization problem where I need to select the optimal product among several options over a series of weeks, given certain constraints, in order to maximize future profit. The ...
1 vote
75 views

### Learning resources - Any good websites for learning about quantitative finance with a focus on the underlying mathematics? [closed]

Typically when I have ventured into a new subject in my sparetime, I have been able to find an interactive website with reading materials, exercises and the like. To name a few there is https://...
89 views

### Combination of factors

Let's say I have 10 factors and I want to find a combination (basically sum of exposures) of factors (of any length) from this set which has max sharpe. Is there an easy way to find this out rather ...
1 vote
224 views

### How to calculate holding period return of a long-short strategy?

I have daily close prices of two stocks, A and B. Suppose that we long stock A and short stock B. Assume that we do the long-short every day and hold that portfolio for some days. How to calculate ...
• 117
54 views

### Algorithms or references on how to detect and potentially remove jumps in stock returns

Sorry if this has been asked before. Thought this is a standard question but searching on web didn't give me too much useful links. Assuming a series of stock prices, how to detect and potentially ...
• 41
58 views

### Data separation for Time Series Models? (both Statistical and ML)

I had a big question about data slicing for Time-Series model fitting. In university, since I wasn't a stats major, so I didn't do much model fitting for data, other than my ML class, and have ZERO ...
33 views

### A term to compare 2 stocks based on simultaneous trending and ranging characteristics

There a 2 stocks called A and B. We take a look at the daily chart of both stocks over the last 1 year. On 90% of the days A and B both trended or at least one of A or B trended. On 10% of days both ...
146 views

### Оptimal strategy when throwing dice [closed]

Given a dice, you can throw it no more than three times, and you can stop at any time. How should you act so that on average you get as many as possible in the last throw?
1 vote
75 views

### Portfolio risk of correlated assets using Mahalanobis distance

I am trying to understand if there is an agreed methodology to measure the total risk in a portfolio of correlated assets. I am taking a simple model of stock prices following geometric Brownian ...
• 197
73 views

### Backtesting: choosing the "sample split" between in-sample and out-of-sample data

Aims: Given approximately 11 years of historical time-series data, to determine how much of this data should be reserved for in-sample and ...
• 131
132 views

### Test significance for information ratio

Suppose that we have an estimated Information Ratio $IR^*$ calculated from the relative returns between a portfolio and a benchmark. I am looking for a way to quantify the uncertainty of this ...
63 views

### How to construct the probability of default (PD) with not much historical data (<1 year)?

If a financing company has a new funding program, is there a statistical method that can be used to construct a probability of default (PD) for IFRS 9 ECL calculation purposes? Considering that ...
47 views

I am an algorithmic day trader. I am trying to automate certain patterns on the stock markets. Suppose I have a model $M$ (with expected value $E$ and variance $V$) and a wallet with $X$ dollars in it....
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79 views

I have a question regarding hypothesis testing. I used the t-test (2-tailed) for these hypotheses: Whether the (monthly) mean return of company A's stock is different from 0 Whether the (monthly) ...
262 views

### Effect of back-transforming forecasted mean of log returns to get forecasted mean of price

When trying to forecast time series, say forecasting the level of a stock index so we can forecast the future values of an option, it tends to be helpful to analyze the log returns versus the original ...
• 249