Did you know that you can do a beta hedge of a large portfolio, but it is essential that these are part of the Nifty or at least, large enough. This would also apply more for a portfolio than for individual stocks. As you must be aware, Beta is a measure of systematic risk, which is 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 or the Sensex is always 1. How would Beta hedge work really work?

Here is a portfolio of 5 non-F&O stocks

Serial Number

Stock Name

Stock Beta

Investment Amount

1

Stock A

1.22

Rs.4,50,000

2

Stock B

1.15

Rs.5,50,000

3

Stock C

1.18

Rs.3,50,000

4

Stock D

1.45

Rs.6,00,000

5

Stock E

1.25

Rs.2,80,000

Total Value

Rs.22,30,000

The above portfolio of non-F&O stocks is worth Rs.22.30 lakhs. Each stock has a beta based on past price data. In the above portfolio, all stocks are aggressive stocks with Beta more than 1. That means even the portfolio beta will be more than 1. Let us see how this works out to calculate the portfolio beta.

Calculating the portfolio beta

Stock Name

Stock Value

Stock Weight

Stock Beta

Weighted Beta

Stock A

Rs.4,50,000

20.18%

1.22

0.2462

Stock B

Rs.5,50,000

24.66%

1.15

0.2836

Stock C

Rs.3,50,000

15.70%

1.18

0.1853

Stock D

Rs.6,00,000

26.91%

1.45

0.3902

Stock E

Rs.2,80,000

12.55%

1.25

0.1569

Rs.22,30,000

100.00%

Weighted Beta

1.2622

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 is called the hedge ratio.

How to do Beta hedging with hedge ratio

In the above case the portfolio value is Rs.22.30 lakhs and that the weighted beta of the portfolio is 1.2622. Here is how to do beta hedging!

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)

Since the value of 1 lot of Nifty futures (lot size 75) is Rs.820,950 you need to sell 3.43 lots (28,14,706 / 8,20,950). Since you cannot sell fractional lots, you can sell either 3 or 4 lots of Nifty to hedge your non-F&O portfolio. Again, fractional hedging makes this method also imperfect to an extent.

Did you know that you can do a beta hedge of a large portfolio, but it is essential that these are part of the Nifty or at least, large enough. This would also apply more for a portfolio than for individual stocks. As you must be aware, Beta is a measure of systematic risk, which is 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 or the Sensex is always 1. How would Beta hedge work really work?

Here is a portfolio of 5 non-F&O stocksSerial NumberStock NameStock BetaInvestment Amount1

Stock A

1.22

Rs.4,50,000

2

Stock B

1.15

Rs.5,50,000

3

Stock C

1.18

Rs.3,50,000

4

Stock D

1.45

Rs.6,00,000

5

Stock E

1.25

Rs.2,80,000

Total ValueRs.22,30,000The above portfolio of non-F&O stocks is worth Rs.22.30 lakhs. Each stock has a beta based on past price data. In the above portfolio, all stocks are aggressive stocks with Beta more than 1. That means even the portfolio beta will be more than 1. Let us see how this works out to calculate the portfolio beta.

Calculating the portfolio betaStock NameStock ValueStock WeightStock BetaWeighted BetaStock A

Rs.4,50,000

20.18%

1.22

0.2462

Stock B

Rs.5,50,000

24.66%

1.15

0.2836

Stock C

Rs.3,50,000

15.70%

1.18

0.1853

Stock D

Rs.6,00,000

26.91%

1.45

0.3902

Stock E

Rs.2,80,000

12.55%

1.25

0.1569

Rs.22,30,000100.00%

Weighted Beta1.2622Portfolio 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 is called the hedge ratio.

How to do Beta hedging with hedge ratioIn the above case the portfolio value is Rs.22.30 lakhs and that the weighted beta of the portfolio is 1.2622. Here is how to do beta hedging!

Calculation for beta hedgingValue 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)

Since the value of 1 lot of Nifty futures (lot size 75) is Rs.820,950 you need to sell 3.43 lots (28,14,706 / 8,20,950). Since you cannot sell fractional lots, you can sell either 3 or 4 lots of Nifty to hedge your non-F&O portfolio. Again, fractional hedging makes this method also imperfect to an extent.