You may have heard about a statistician who had his head in an oven and his feet in a refrigerator but on average he felt just fine. That’s right. Things on the average sometimes may look very comfortable. But what looks comfortable may actually be deceptive. Think of this. If two investments are giving an annual return of 10% on average, then what does that mean? Can you conclude that both investments are equally good? Maybe? Or maybe not?

**Johnny:**Hi, Jinny! Last week you had promised you would talk about the work of Harry Markowitz.

**Jinny:**Yes. Last week I had explained how the risk-return trade-off works in general; now we can talk about the work of Harry Markowitz in detail.

Illustration by Jayachandran / Mint

*The Journal of Finance*. This important work hardly aroused any interest for many years after its publication, but with the passage of time, it became the raw material for what became popular as Modern Portfolio Theory. Markowitz believed that merely looking at the average return of an investment may not be enough.

What we also need to look at is “variance of return” for different investments, which tells us how much the actual return has fluctuated over the period. High variance of return or high volatility means the actual returns over the period may have fluctuated wildly.

Speculators no doubt like such opportunities where the upside is high, but for common investors such wild fluctuations or variance of return represents what we call risk.

So, Markowitz was the one who suggested that it is possible to understand what exactly risk is. But more than this, it was Markowitz who showed how to think about risk in terms of numbers. By using past data, it is possible to know in terms of numbers how much the variance of return is for any particular investment.

**Johnny:**What a relief it is to know that we can actually quantify risk in terms of numbers. Once we know where the risk is, we can choose what suits our appetite.

**Jinny:**I think you should not immediately jump to any conclusion. First, listen to the whole prescription. Quantifying risk by calculating “standard deviation” or variance of return is just one step. Markowitz suggested that for actually choosing a diversified portfolio you also need to calculate the “covariance of return” for different investments.

Now you may be wondering what this covariance of return is. Covariance of return is also known as correlation of return for different assets. Those who are good at crunching numbers already know what correlation means. But for the benefit of many like you who believe that numbers are our worst enemies I will briefly explain what it is.

Correlation of return for different assets is expressed as a number lying between +1 and -1. There could be three different scenarios: the correlation could be positive, negative or zero. If the correlation of return for two assets is positive, then the returns from the two assets are likely to move in tandem, that is, if the return from one asset is rising, the return from the other asset would also rise, and if the return from one asset is falling, the return from the other asset would also fall.

Assets having a negative correlation show just the opposite relationship. When the return from one asset is rising, the return from the other asset falls. Assets having zero correlation do not show any relationship. The rise or fall of return from one asset has no effect on the rise or fall of return from the other asset.

**Johnny:**What role does correlation of return from different assets play in the selection of the right portfolio?

**Jinny:**Well, once you know the correlation, you can use it for diversifying your portfolio. We can summarize the whole process suggested by Markowitz in three steps.

First, you need to find out the expected return from different investments over a period.

Second, you need to find out how much the return from each investment has varied from the average over the period. In other words, you need to find out the standard deviation of return from each investment.

Third, you need to find out the correlation of return for different investments, that is, how returns from different assets have moved in comparison with each other. Once you are through with all these calculations, you can use Markowitz’s prescription for selecting your portfolio—choose the investment that enjoys high expected return with low standard deviation and also low correlation with other assets in your portfolio.

The basic idea is that, overall, a portfolio of uncorrelated assets faces less risk than a portfolio of correlated assets. I hope you now understand why it is so.

**Johnny:**Jinny, I was just wondering whether it is actually worth taking the trouble to find out the standard deviations and correlations of so many different assets.

**Jinny:**Well, we will probe this issue next week.

**What:**Harry Markowitz laid the foundation of risk-return trade-off in his doctoral thesis Portfolio Selection.

**How:**The process of portfolio selection suggested by Markowitz involved comparison of expected returns, standard deviation of returns, and correlation of returns from different assets.

**Why:**Choosing uncorrelated assets helps in diversifying the portfolio and hence minimizing risk.

*Shailaja and Manoj K. Singh have important day jobs with an important bank. But Jinny and Johnny have plenty of time for your suggestions and ideas for their weekly chat. You can write to both of them at realsimple@livemint.com*