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Construct A Sound Portfolio

Assign correct weights to each asset in your portfolio by studying the correlation between them…

One of the keys to portfolio construction is an understanding of correlation, its implications and consequences. But few investors bother to do this. Any portfolio consists, by definition, of many different assets.

Most people focus on the performance of individual assets in isolation. But it is crucial to learn how they interact together because that tells you what your ratio of exposure ought to be, and what your net return will be.

If two assets move in the same direction, should you hold both, and if so, in what proportion? If two assets move in the opposite directions, what do you do? If two assets move randomly with respect to each other, what do you do?

These questions are difficult enough to answer for just two assets. They are way more difficult with a realistic portfolio, which may contain dozens or hundreds of assets. In the broadest terms, any investor wants two non-correlated assets that both give positive long-term returns. That way, some of your money is always working for you. But in practice, there are many levels and grades of correlation. Cross correlations and portfolio optimisation can hence be a nightmare.

One way to do this is to simplify the process as much as possible by clubbing assets together. This is where indices are useful. An index clubs multiple assets together so that we can treat them as a single “pooled” asset.

Equity mutual funds are benchmarked to indices, or in the case of ETFs (exchange traded funds) and index funds, they mirror indices exactly. If you build a portfolio of funds that track different indices, you can hold very wide exposure in hundreds of underlying stocks across multiple sectors, while only needing to track the relationship between a few assets.

Tools of the trade
So, how do the major equity indices interact with each other? To understand this, we can use basic tools such as the correlation and beta to map and compare their changes in value. One visual way of understanding this is to map changes in one asset versus changes in another on a simple x-y graph. If the relationship is close to linear, the two assets are highly correlated. The slope of the line (positive or negative, and value) gives us more information.
Correlation is expressed as a number ranging between -1 and +1. Perfect correlation — two assets moving together every time — is +1; perfect reverse correlation of two assets always moving in opposite directions is -1. If the absolute value is close to zero, there is little or no correlation. As a rough rule of thumb, a value of =+/-0.65 is significant correlation, or reverse correlation, depending on the sign.
Beta is the coefficient of correlation and it measures the relative volatility of changes. A positive beta means the assets are positively correlated. But the degree of movement, the volatility, could be very different. A value of beta = 1 means that the second asset moves exactly as much as the benchmark. A beta greater than 1 means that it moves more, but in the same direction. Low beta assets are defensive with respect to the benchmark. A negative beta signals inverse correlation.
Let’s say we look at the three most liquid indices in the Indian equity markets. This would be in order, the Nifty, the Bank Nifty and the CNX-IT. All three generate respectable futures volumes, the Nifty has huge option volumes, and the Bank Nifty has acceptable option volumes. This means that portfolios based on these indices can be hedged or traded in both directions. An investor could easily hold ETFs or index funds tracking those three indices (or, they could hold speciality funds for IT and financials and widely-diversified funds benchmarked to the Nifty). They can also be long or short in the derivatives markets.
We can also consider the Junior Nifty, CNX500, and sector indices like the CNX-Infra and CNX-Realty. These cannot be directly hedged or traded in the derivatives markets. But they can be indirectly hedged by benchmarking to the Nifty. Certainly, if you have serious exposure to mid-caps, real estate, etc., you should track these relationships.

Relationship between indices
How correlated are the three major indices? Since January 2010, the Bank Nifty is highly correlated to the Nifty with a value of 0.88. The CNX-IT is also significantly correlated to the Nifty with a value of 0.7 but the relationship is less strong. The Bank Nifty is not very significantly correlated to the CNXIT with a value of just 0.5.
The Bank Nifty has a beta of 1.2 with respect to the Nifty while the CNX-IT has a beta of 0.85 with respect to the Nifty. This means the Bank Nifty is more volatile than the broad market while the CNX-IT is less volatile. These relationships change over time and so they need to be updated.
As an investor, we can use this information quite effectively. While retaining core holdings that benchmark to the three indices, we can juggle portfolio weights accordingly. During a bull market, one way to aggressively seek short-term gains is to be overweight on the financial index. If the Nifty is gaining, the Bank Nifty will gain more.
Of course, this method leaves you more exposed if there’s a sudden downturn. During a bear market, on the other hand, the CNX-IT will lose less ground than the Nifty or the Bank Nifty, so it’s the best defensive asset of the three.
The relatively low correlation between the CNX-IT and the Bank Nifty makes them desirable assets to hold in combination since the low correlation should reduce overall risk. But ideally we should look for two assets that have even lower correlation, or negative correlation, to reduce the volatility of returns even further.
If you wish to hedge a long portfolio during a bear market, you would normally short the Nifty, using either long puts or short calls or selling the Nifty future. You can also short the Bank Nifty using either futures or long puts on the logic that, given high correlation and high beta, the Bank Nifty will lose more ground than the Nifty. So it may be a more efficient hedge than the Nifty.

Paired trading strategies
If you are prepared to trade, there are far more possibilities using correlations-betas between indices. Paired long-short trades of futures should reduce volatility of return, while still yielding positive returns. For example, take the Nifty-Bank Nifty combination (one long future, one short future) with the Bank Nifty held in the direction you favour. If you are right in your bias, the Bank Nifty (where you make money) will outperform the Nifty (where you lose money) and thus give a positive return. If you are wrong, the Nifty will make enough profits to help you cut losses.
A similar paired position is possible using the Nifty-CNX-IT as a long-short combo with the Nifty held in the direction you expect and the CNX-IT providing the stability. This is less aggressive due to the lower CNX-IT beta and it may suit a conservative trader.
Of course, one can’t look at equities in isolation. Any well-rounded investment strategy should include other assets such as debt, commodities and real estate in various proportions. So the same principles of correlation and beta can also be applied to analyse overall net worth and for the purpose of broader asset allocation.
Consider your equity portfolio as a single asset —think of it as a personalised index that exactly reflects the weight of individual holdings. Then see how it interacts with debt holdings, which can also be clubbed together similarly. Running a correlation study on these can yield very useful insights that will help you allocate weights.