Investment Management with Python and Machine learning Specialization lecture Notes Part-I

I recently started learning about the Portfolio Management course on Coursera through the EDHEC Risk Management course. This is a brilliant course for someone who would like investment management roles requiring programming skills. So in this series of writings, I am documenting my learnings from the course. In this blog post, I will cover the first two weeks of Course 1.

WEEK 1

• In this week, we covered topics on annualized return, volatility, Sharpe ratio, VaR (Value at Risk)
• Return is the difference in portfolio value from time t to time t+1 divided by the portfolio value at time t. So this would (V_{t+1}-V_t)/V_t. We don’t consider the average return of a portfolio over a time period because the results might be skewed. If a portfolio gave sub-optimal results for the most part of the time and outstanding results for some part, it may have a higher average return, but it is not a preferable portfolio, so it may be a misleading KPI.
• Also, dividends are included as part of the portfolio value to calculate the return, ((V_{t+1}+D_t)-V_t)/V_t
• Suppose a portfolio gives a return of 10% in the first year and 3% in the second year. So compounding works in the following way if you invest $1 in the portfolio, after one year you will have 1 + 0.1*1 dollars, so 1.1. Again this is used as principal for the next year, hence 1.1 + 0.03*1.1. This is equal to 1.067. So your initial $1 dollar is now 1.067, with a return of 0.067, hence return is 6.7%.
• So return is just the cumulative product (1+return) till the end. The return can be positive or negative. And the end can be monthly, quarterly, or yearly. Let’s say we have return for each month, then (1+return_each_month)¹². If you subtract the principal amount 1 from it, you will get the annualized return.
• Now, for annualized volatility, we measure the standard deviation of the returns. Standard deviation is the measure of the distance of an observation from its mean weighted by the number of data points. But we subtract 1 from the data points to reduce bias. Explanation video
• We know that the variance (square of standard deviation) of independent random variables can be added. So suppose we have the standard deviation of portfolio value for each month. To find the yearly variance, we will just add the variance of the series…