# Recent Articles

## Discretely 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 increases, the annual effective yield also increases because the...

read more## Lognormal 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 natural log of Y (ln Y) is normally distributed. So, we check if the...

read more## Safety-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 safety first ratio (SFRatio). Example An investor has a minimum...

read more## Shortfall 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 perception of risk in that it focusses more on the real economic risk...

read more## Calculating 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) under the standard normal curve corresponding to any Z-score or its...

read more## Standard 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 distributed stock portfolio, the mean could be 10% and the standard...

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