Hedging basically means protection. When you buy a stock, there is a risk that the stock price could go down. That will result in losses; either actual or notional. You need to protect yourself from such losses and that is what hedging is all about. Let us look at two of the most common instances of hedging; using futures and using put options. Let us first look at how we hedge using futures. Assume that you purchased 500 shares of Reliance Industries at a price of Rs.1125 in the spot market. If the price goes up to Rs.1170, you can hedge and lock your profits by selling 1 lot (500 shares) of RIL futures at Rs.1170. Thus the profit of Rs.22,500/- {500 x (1170-1125)}, becomes your assured profit. You can also use this logic if RIL price goes down and lock in the loss by selling futures.

Another way of hedging your cash market position is through put options. If you have bought 500 shares of RIL at Rs.1125, then you can hedge by buying an 1120 put option on RIL at Rs.19. Thus your maximum loss will be restricted to Rs.24 (19+5). Even if the RIL stock price goes down to Rs.1000, your loss will still be restricted to Rs.24 per share. These are very useful strategies when you hold a single stock. But, what if you hold a portfolio of stocks? You cannot be hedging stocks one by one. The answer lies in Beta Hedging. Let us look at how to beta hedge. Let us also focus on how to beta hedge a portfolio and the ideal beta hedge strategy to be used.

**Beta hedging the systematic risk of your portfolio**

Any equity investment entails two kinds of risks. Unsystematic risks are unique to stocks and industries and these can be reduced by diversifying your portfolio across dissimilar stocks. But systematic risk stems from factors like inflation, interest rates, geopolitical risk, rupee weakness etc. Here you cannot diversify as it impacts all stocks almost in a systematic manner. That is where beta hedging comes in handy.

Without getting into the nuances of Beta, suffice to say that beta measures how much does a stock fluctuate vis-à-vis the index? If a stock has a beta of 1.3 then it means that a 10% movement in the index will led to a 13% movement in the stock. This applies on the upside and on the downside. Once you know the beta of stocks, you can calculate the beta of the portfolio and use that to hedge your systematic risk. Here is how Beta Hedging works.

**How to Beta Hedge a portfolio of 6 stocks**

A long term investor has a portfolio of 6 stocks as under.

**Sr.No. Stock Name Stock Beta Investment Amount**

1 Bharti Airtel 0.9 Rs.6,50,000

2 Reliance 1.15 Rs.7,50,000

3 Bajaj Finance 1.25 Rs.8,20,000

4 Ultratech 1 Rs.15,00,000

5 Larsen & Toubro 1.25 Rs.7,80,000

6 Kotak Bank 1.3 Rs.1650000

**Total Value Rs.61,50,000**

The investor has a portfolio of 6 stocks worth Rs.61.50 lakhs consisting of 5 stocks in different proportions. Beta has been calculated based on historical price. While Bharti is a defensive stock with a beta of less than 1, Ultratech is a market beta stock. The rest of the stocks are aggressive stocks with a beta of more than 1. With most of the stocks having an aggressive Beta, the overall portfolio beta is also likely to be above 1. Let us now go about calculating the portfolio beta for the investor.

**Using weights to calculate portfolio Beta**

Calculation of portfolio beta is quite simple and it is based on the respective betas based on the stock weightage in the portfolio. Here is how we can go about it.

**Stock Name**

**Stock Value**

**Stock Weight**

**Stock Beta**

**Weighted Beta**

Bharti Airtel

Rs.6,50,000

10.57%

0.90

0.0951

Reliance

Rs.7,50,000

12.20%

1.15

0.1403

Bajaj Finance

Rs.8,20,000

13.33%

1.25

0.1666

Ultratech

Rs.15,00,000

24.39%

1.00

0.2439

Larsen & Toubro

Rs.7,80,000

12.68%

1.25

0.1585

Kotak Bank

16,50,000

26.83%

1.30

0.3488

**Rs.61,50,000**

100.00%

**Weighted Beta**

**1.1532**

Portfolio beta is the weighted average of individual stock betas where the weights based on portfolio value. As the portfolio value changes, the value of the portfolio beta also keeps changing. In this case, the portfolio beta comes to 1.1532 and will classify as an aggressive portfolio. Let us now look at how to use this portfolio for beta hedging the portfolio.

**Using weighted portfolio beta for beta hedging with Nifty futures**

In the above case the portfolio value is Rs.61.50 lakhs and the weighted beta of the portfolio is 1.1532. To perfectly hedge this portfolio we the investor just has to sell Nifty Futures that is equivalent to Beta times portfolio value.

Value of Nifty Futures to be sold = Rs.70,92,180 (61,50,000 x 1.1532)

*Nifty futures are traded based on minimum lots and we need to correspond to that*

The current lot size of Nifty 75 units and the Nifty spot value is 10,690.

That means the value of 1 lot of Nifty futures is Rs.8,01,750/-

*So to perfectly hedge your portfolio you need to sell *

*8.85 lots of Nifty (70,92,180 / 8,01,750)*

Since you cannot sell fractional lots of Nifty, you can round off to 9 lots of Nifty Futures and this will be fairly close to your perfect hedge. Beta hedging is extremely useful in hedging risks of the portfolio. Of course, the assumption here is that unsystematic risks are fully diversified and nullified. If that is not the case, then beta hedging really may not work!

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