The simplest form of hedging your stocks is to sell futures of equivalent amount against your cash market position. So if you have an Rs.10 lakhs long position in equities then you can sell equivalent amount in futures and perfectly hedge your position. But that is perfectly fine if you are hedging just one stock. What if you have a portfolio of stocks? In such cases selling futures against individual stocks may not make sense. The reason is that when you create a portfolio of stocks they automatically reduce the risk because of their correlation with each other. So if you create a portfolio of stocks that are highly correlated with each other then you do not reduce your risk too much. However, if you create a portfolio of stocks that are having a low correlation to each other, your overall risk is automatically reduced.

**Portfolio creation and why only systematic risk is left**

We are aware that there are two kinds of risks in holding stocks. First, is the unsystematic risks that are unique to stocks and industries. These risks can be reduced by creating a portfolio of stocks that are different. The assumption is that any smart portfolio manager is able to reduce the unsystematic risk completely by diversification. That is why we create a portfolio of stocks to reduce the unsystematic risk as much as possible. But then systematic risk cannot be reduced as all the stocks in your portfolio will be hit by systematic factors like inflation, GDP growth, geopolitical risk etc. That is where Beta comes in.

Beta is a measure of systematic risk. It measures the risk that cannot be diversified away. A beta of more than 1 means that it is an aggressive stock and a beta of less than 1 means that it is a defensive stock. The beta of an index like Nifty is always 1. That is why when it comes to portfolios it makes more sense to do beta hedging. But, what is beta hedging? You can actually do beta hedging with futures. You can hedge the systematic risk of your portfolio by beta hedging the portfolio with index futures. Let us understand how to beta hedge a portfolio of stocks.

**Consider a portfolio of 5 stocks that you created**

Serial NumberStock NameStock BetaInvestment Amount1Infosys1.22Rs.4,50,0002Reliance1.15Rs.5,50,0003Axis Bank1.18Rs.3,50,0004BPCL1.45Rs.6,00,0005Larsen & Toubro1.25Rs.2,80,000 Total ValueRs.22,30,000

In the above case, you have created a portfolio worth Rs.22.30 lakhs consisting of 5 stocks in different proportions. Each stock has a beta based on past price data. As we said earlier, the beta of any stock measures its systematic risk. What do you understand when we say that Infosys has a Beta of 1.22. It means that the sensitivity of Infosys to movements in the Nifty is 1.22. That means if the Nifty is up by 1% then Infosys falls by 1.22% and if the Nifty goes down by 1% then the price of Infosys goes down by 1.22%. In our portfolio above, all the stocks are aggressive stocks as they all have a Beta of greater than 1. That means even the portfolio beta will be more than 1 and the portfolio itself will be an aggressive portfolio. Let us see how this works out to calculate the portfolio beta.

**Calculating the portfolio beta**

Stock NameStock ValueStock WeightStock BetaWeighted BetaInfosysRs.4,50,00020.18%1.220.2462RelianceRs.5,50,00024.66%1.150.2836Axis BankRs.3,50,00015.70%1.180.1853BPCLRs.6,00,00026.91%1.450.3902Larsen & ToubroRs.2,80,00012.55%1.250.1569 Rs.22,30,000100.00%Weighted Beta1.2622

How is the portfolio beta calculated? Remember, portfolio beta is nothing but the weighted average of individual stock betas. How do we calculate the weights of various stocks? It represents the relative weight of the stock in the index. In the above example if all the 5 stocks are weighted to the overall portfolio and then the weighted beta is calculated for each stock, then the total portfolio beta comes to 1.2622. This forms the basis of beta hedging. Let us now understand how weighted beta is used for Beta hedging.

**Using weighted portfolio beta for beta hedging**

In the above case we know that the portfolio value is Rs.22.30 lakhs and that the weighted beta of the portfolio is 1.2622. To perfectly hedge this portfolio we need to sell futures equivalent to Beta times portfolio value. Here is how to go about it!

Calculation for beta hedging

Value of the Portfolio – Rs.22,30,000/-

Weighted beta of portfolio – 1.2622

Value of Futures to be shorted – Rs.28,14,706 (22,30,000 x 1.2622)

We know that futures are traded based on minimum lots.

The current lot size of Nifty 75 units and the Nifty spot value is 11,070.

That means the value of 1 lot of Nifty futures is Rs.8,30,250/-

So to perfectly hedge your portfolio you need to sell 3.39 lots of Nifty (28,14,706/8,30,250)

How to sell 3.39 lots of Nifty?

Obviously you cannot sell fractional lots of Nifty so you will have to sell either 3 lots or 4 lots of Nifty depending on your view on the Nifty. You will not be perfectly hedged but this Beta hedging will help you to get as close to a perfect hedge as possible.

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