How is financial risk measured ? First approach - standard deviation

All you wanted to know. How is risk measured in Finance ? Is there a detailed theoretical and conceptual understanding of risk ? How is risk measured in a portfolio ? Is it different from risk of an individual stock ? We know that returns are dependent on risk levels in your portfolio, but how much risk ? Let's try and answer some of these questions, and more.

Risk is one word no one wants to be associated with. Especially when you are investing your hard earned money. But all investments, irrespective of what they are, have some risk.

If you ask any layman, in general, how much risk would he like in his portfolio, then the answer would be - "None ! I don't want any risk at all ! " Forget laymen, most financial experts also would give you the same answer.

And for us, investment experts too, the answer is a bit difficult to give. Some would say - "Little risk", some other will say "Moderate risk". Some will try to quantify it in some reference numbers, but most will have generic answers - "I can take high risk" or "I want low risk". What exactly is this risk in financial theory and how is it measured ?

Risk Paradigms in finance theory

While there are many ways in which risk can be quantified or measured, in general there are three different types of methods that are used to measure risk.

1. Based on statistical methods, such as standard deviation, variance, range etc.

2. Based on some form of probabilistic theory, with assigned probability of losing some capital, e.g. Value at Risk (Var).

3. Based on comparatives with other assets, e.g beta.
   

While there are many different ways in which risk can be measured, for retail investors, in general, there are two most important risk measure. These are - Standard deviation (SD) and Beta. Let's look at both these terms in more details.

Standard Deviation

This is a statistical method, rooted very deep in finance and statistical theory. Most people regard SD as one of the best measures of risk, comparable to the returns and most amenable to calculations including advance mathematical calculations like calculus or discrete maths. Anyway, forget those jargons, SD is a simple concept and very easy to understand.

Let's consider the data of returns below. We see two stocks, stock 1 and stock 2, and their 5 year returns from 2017 to 2021.

Stock returns example

Also note that stock 1 has given same return of 8% in each year from 2017 to 2021, and its compounded annual growth rate, CAGR is 8%. Stock 2 on the other hand, has also given exact same CAGR of 8%, however there are years of negative returns, followed by years of higher, positive returns. As a rational investor, given only the information as above, which stock should you buy ? And why ?

I would buy stock 1, given that its expected return is 8%, and its almost certain to get that 8% returns (Important note : past performance does not guarantee future performance, but here it looks like stock 1 is very stable. In absence of all other information, let's assume past trends will follow). Stock 2 also has expected return of 8% over a 5 year period, however it's not sure. It can be negative, or positive over the years, as we can see from the data above.

So returns that vary too much are more risky. In other words, variability of returns can be taken as proxy for its risk. So just by looking at the data above, we know that stock 2 is more risky as compared to stock 1, simply because there is high volatility in stock 2. But not all return patterns will be as simple as the above one. Consider the following

Stock returns example

Both the stock in this data have expected average return of 8%, but it's not possible now to find which one of these stocks is more risky. Why ? Because both have volatility in returns. Both have negative and positive returns.

What is Standard deviation ?

Here is where statistics that comes to our rescue. If both have average return of 8%, we can find how much is each return away from this 8% average return. And then sum it over, average out these distances. Here is the formula used for calculating standard deviation

Where ∑ is 'sum of' , x is a particular return value in the data set, μ is the mean of the data set, and N is the number of data points in the population.

For the two sets data from two different stocks, here is calculation of standard deviation

Now this is making more sense. SD of stock 2 is 14.21% while SD of stock1 is 20.20%. Clearly, as indicated by standard deviation, stock 1 is more volatile, hence more risky. While expected returns are same at 8%, a rational investor should invest in stock 2 because it's less riskier.

SD has a nice symbol, and almost always used to denote standard deviation. This is σ (sigma).

One last topic on standard deviation, σ, before we end this article. We will discuss another measure of risk, β (Beta ) in next article.

So, how do you compare two investment options ? Which one is better of the two below ?

Option 2 has higher expected return, Re at 15%, but also has higher expected risk, σ. Option 2 has lower risk and lower returns too. In general, this goes well with risk- return tradeoff. Higher return means you have to assume higher risk.

However, if the investor is indifferent at the level of risk, which investment is better ? This comparison is done using Sharpe ratio. You will find most websites, fund houses and investment companies publish sharpe ratios prominently to allow investors to make quick comparisons. Here is the formula used for Shape ratio

Here is calculations for our two options given above.

Now you can see, that sharpe ratio of option 2 is more (0.42) than that of option 1 (0.35). In that sense, option 2 is better risk adjusted return as compared to option 1, even though on standalone risk basis, option 2 has higher risk (24%) as compared to option 1 (20%)

Final words

We saw one of the most used measure of investment risk here. It is extensively used measure for investment risk management. We also saw three investment risk types, and discussed one of them (Standard deviation) in detail here. The other risk type, Beta, will be topic of our next blog soon. One important point to keep in mind is that standard deviation of assets, and hence the risk, keeps changing. Investment risk monitoring strategies must be employed to ensure your risk does not go too far ahead of your expectations.

How much risk can you take ? You should look at investment risk profile calculators. Or some other risk profiling questioners.