# Measuring Investment Risk – Calculating Returns

In addition to Computational Investing, I’ve also signed up for the Introduction to Computational Finance class through Coursera – it’s a similar topic, but a different point of view.  Instead of assuming you want to be a hedge fund manager, it goes into calculating returns, risk of an investment, and building a portfolio.  This is more “normal” stuff that any investor should know – but it has a very mathematical bent (several proofs, etc).  The class is self-paced through November, so it’s not too late to join if you’re interested.

The first two weeks are on calculating simple, annual effective rate, and continuously compounded returns and the probability background needed to complete the class.  One of the closing topics of week two was measuring investment risk.  It’s generally accepted that standard deviation (σ) is an easy to calculate measure of risk.  This tells you how far values deviate from the expected result – the mean (μ) – or the simple/continuous rate of return, so you know how “wild” the investment can be.  A larger standard deviation implies a larger risk to the investment.  In investing, a larger mean (or expected return value) also tends to imply a larger standard deviation because people expect to take more risk for a larger return. We haven’t gotten to actually calculating the standard deviation yet – although I think I know how.

## Calculating Returns

The first value to calculate is a return over a time period.
$latex R$: Return
$latex P_{t}$: Price at time $latex t$
$latex P_{t-1}$: Price at time $latex t-1$
$latex R = \frac{P_{t}-P_{t-1}}{P_{t-1}}$
$latex R$ can be any time period, but we’ve been using monthly for the most part in class.

## Calculating Portfolio Returns

Not only do we need to worry about the returns for a single investment, but we also need to calculate the return for our entire portfolio for it to be useful. The return for a portfolio is pretty easy, it’s a weighted average based on the initial total investment. If asset A has a return of 5%, and asset B has a return of 3%, and we spend $3000 on asset A, and$7000 on asset B, the portfolio rate of return is:
$latex R_{p,t} = .30*R_{A} + .70*R_{B} = .30*0.05 + .70*0.03 = 0.036$
or 3.6%

Disclaimer: I’m writing these posts as a way to solidify my understanding of class materials, they may not be completely correct – and I welcome any corrections.

## 2 thoughts on “Measuring Investment Risk – Calculating Returns”

1. cashrebel

That sounds like a fascinating course to take through Coursera. I signed up for a class there last year but never followed through. Learning the math behind investing will no doubt make you a smarter investor.

1. Mom Post author

It has been really enjoyable so far, anyway. I’m really learning a lot. I love having the opportunity to take university level classes for free.