The technique of portfolio selection proposed by Harry Markowitz provided a good recipe for minimizing risk. But good recipes are sometimes tougher to follow. The hardest part of Markowitz’s formula involved putting all the basic ingredients together. Let’s try to understand some of the basic difficulties associated with the Markowitz model and how the work of William Sharpe helped in improving it.

**Johnny:**Last week you had explained how we can select a diversified portfolio by using the technique proposed by Harry Markowitz. But tell me, Jinny, how far can a common investor use this technique for investments?

**Jinny:**Well, the technique of portfolio selection proposed by Harry Markowitz in 1952 was based on a remarkable insight—for every level of return, there is one investment that is available at the lowest possible risk, and for every level of risk there is one investment that offers the highest return. The aim of portfolio selection is to minimize risk while maximizing return. But the real challenge was how this unique idea of portfolio selection could be put to actual use. The technique of portfolio selection as originally proposed by Markowitz remained ignored for many years both by professional fund managers and common investors, mainly because it was really hard to derive the main inputs of the model.

Last week I had explained how the three inputs of Markowitz’s model—expected return, volatility of return and correlation of return between different assets—help us in portfolio selection. By doing some number crunching, you can find out the expected return and volatility of return for different securities, but Markowitz’s model also expects you to calculate the correlation of return for different pairs of securities, which is a tough job. Even the fastest computer available during the 1960s required hours for the calculations necessary and the cost of using such a facility was really prohibitive. But the model started arousing some curiosity after another academician, William Sharpe, suggested some changes.

Illustration: Jayachandran / Mint

**Johnny:**What changes?

**Jinny:**Sharpe recognized that finding out how the return from asset A is correlated with that from asset B, or return from asset C is correlated with that from asset B, is a tiring job. You can go on counting the stars but will never be able to find their exact number. Sharpe suggested that instead of using the correlation of return of different pairs of individual assets, we can use the correlation of return of different assets with a common index for the whole market. So, if I is the index for the market, you need to find out how asset A is correlated with I or asset B is correlated with I and so on. In all cases, I remains common. If A is positively correlated with I, then its return would rise or fall in tandem with the rise or fall of I, and if A is negatively correlated, then its return would move in the opposite direction of rise or fall of I.

This greatly reduced the number of calculations required for Markowitz’s original model and with the advent of faster computers, things became merrier for professional fund managers and institutional investors who relied on the application of this model for making allocations for different assets. But common investors, who are not very computer savvy, have to mainly rely on the services of investment advisers to utilize this model for selecting a well-diversified portfolio.

Markowitz and Sharpe together received the Nobel Prize in 1990 for their work on portfolio selection. But even now the basic idea behind the Modern Portfolio Theory (MPT) receives brickbats from critics.

**Johnny:**All that glitters is not gold. What do critics of MPT have to say?

**Jinny:**Well, many critics believe this theory oversimplifies risk by assuming that risks can be quantified in terms of numbers by measuring the standard deviation or volatility of return. Critics argue that it is wrong to treat risk and volatility of return as synonymous. Critics believe that we still don’t know what exactly risk is. Standard deviations or volatilities of return are just like the footprints of some dreaded beast which no one has seen. By no means can the footprints represent the whole picture. Further, critics believe that risks in the future may arise from totally unexpected events. No one knows where the unknown beast may leave his footprints tomorrow. So the use of past data for calculating future risk is like trying to make a new car by using old parts.

No matter how much we may try, all our future risk assessments will remain imperfect. When forced with unknown situations, all measurements of risk may just wither. Critics believe that sometimes intuition can be a better guide for avoiding risk than our mathematical risk models.

**Johnny:**Thanks for explaining, Jinny. I will keep all this in mind while thinking about risk and return in future.

**Who:**William Sharpe, an academician, suggested some changes to simplify the Markowitz’s formula of portfolio selection.

**Why:**Changes were necessary because it was difficult ot calculate the inputs required for Markowitz’s model.

**How:**Sharpe suggested the use of correlation of individual assets with a common index.

*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*