Stock Price Movement Using a Binomial Tree
The future price movement of a stock can be approximated using a binomial tree. Let’s say the current stock price is S. The price of the stock can either move up or move down. We will refer to the up...
View ArticleTracking Error and Tracking Risk
Tracking error is a measure of how closely a portfolio follows its benchmark. A tracking error of zero means that the portfolio exactly follows its benchmark. The benchmark could be an index such as...
View ArticleContinuous Uniform Distribution
We know that a discrete uniform random variable is a discrete random variable for which the probability of each outcome is the same. We also know that a random variable is continuous if it can take an...
View ArticleNormal Distribution
The normal distribution is the well-known bell-shaped curve depicted below. The bell-shaped curve comes from a statistical tendency for outcomes to cluster symmetrically around the mean (or average)....
View ArticleUnivariate Vs. Multivariate Distribution
A univariate distribution refers to the distribution of a single random variable. Note that the above characteristics we saw of a normal distribution are for the distribution of one normal random...
View ArticleConfidence Intervals for a Normal Distribution
A confidence interval is an interval in which we expect the actual outcome to fall with a given probability (confidence). Consider the following statement: In a normal distribution, 68% of the values...
View ArticleStandard Normal Distribution
A normal distribution can be described using just two parameters, namely (μ), mean and variance (σ2). In a normal distribution, these two variables could take any value. For example, for a normally...
View ArticleCalculating Probabilities Using Standard Normal Distribution
Once we have the z-scores, we can use the standard normal table to calculate the probabilities. The standard normal table shows the area (as a proportion, which can be translated into a percentage)...
View ArticleShortfall Risk
Shortfall risk refers to the probability that a portfolio will not exceed the minimum return level (target return; benchmark return). Shortfall-risk is more consistent with the investors’ intuitive...
View ArticleSafety-first Ratio
Roy’s Safety first criterion states that the optimal portfolio minimizes the probability that portfolio return, RP, falls below RL. According to this criteria, we select the portfolio with the highest...
View ArticleLognormal Distribution and Stock Prices
The concept of lognormal distribution is very closely related to the concept of normal distribution. Let’s say we have a random variable Y. This variable Y will have a lognormal distribution if the...
View ArticleDiscretely Compounded Rate of Return
A discretely compounded rate of return is simply a compounded rate of return with a discrete compounding frequency such as daily, monthly, quarterly, or semi-annually. As the frequency of compounding...
View ArticleContinuously Compounded Rate of Return
In contrast to discrete compounding, continuous compounding means that the returns are compounded continuously. The frequency of compounding is so large that it reaches infinity. These are also called...
View ArticleSampling and Estimation
In the real world, it is often not possible to collect data about an entire population to conduct a statistical analysis. For example, to make conclusions about the saving habits of families in a city,...
View ArticleSimple Random Sampling and Sampling Distribution
Simple Random Sampling Simple random sampling is a type of sampling method, in which each element of the population has an equal chance of being selected in the sample. A simple random sample can be...
View ArticleSampling Error
Sampling error is the difference between the sample statistics (such as sample mean) and the corresponding population parameter (such as population mean). Sampling error occurs due to the random...
View ArticleStratified Random Sampling
Stratified random sampling is a sampling method that goes one step further than simple random sampling. It can be used in situations where the population can be separated naturally into sub-groups or...
View ArticleTime Series and Cross Sectional Data
In investment analysis, we observe two types of data, namely, time-series data and cross-sectional data. Time-series data refers to observations made over a period of time at regular intervals. For...
View ArticleCentral Limit Theorem
The Central Limit Theorem is a fundamental theorem of probability and describes the characteristics of the population of the means. According the Central Limit Theorem, for simple random samples from...
View ArticleStandard Error of the Sample Mean
The standard error of the sample mean is calculated using the following formula. Note that the larger the sample size, the smaller will be the standard deviation. Let’s say the monthly average savings...
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