Portfolio hedging is a form of insurance to protect your portfolio from a deep draw-down in the event of a steep market fall. With equities hitting all time highs in this bullish market and demanding sky high valuations there is a sense of caution that we are veering into a bubble territory.

## Nifty Market - High Valuations?

Price to earnings (P/E) ratio is a widely used valuation metric by the investors. A lower PE ratio means the stocks are cheaper and higher PE ratio means stocks are expensive. Here, we will take a look at the PE ratio of Nifty index to get a general sense of market valuations. Nifty PE ratio is obtained by dividing the total market cap of Nifty by weighted average earnings of stocks comprising the Nifty 50 index.

Here is the 20-day moving average (20DMA) chart of historical PE of Nifty.

The current 20DMA PE ratio of 27 was last observed on two occasions - during the bullish markets of dot-com bubble year of 2000 and prior to sub-prime crisis of 2008. On both these occasions, market has corrected steeply by eroding the market value by more than 50 percent in the following months.

Some say, this time its different. It may be true or may be not, we don't know for sure. History is known to repeat itself more often than not and equity markets are no different. Instead of guessing and double guessing whether market will correct or not, its better to prepare for such an eventuality if it were to happen in coming months if not tomorrow.

That's where portfolio hedging comes into picture. There are a variety of equity portfolios focusing on different themes - multi-cap, sector specific, momentum, value, growth, blue-chip etc. In this article, we will discuss portfolio hedging and cover topics on when to hedge your portfolio, how to hedge your portfolio, and which kind of portfolios can be hedged and which portfolios cannot be.

## When to Hedge Portfolio

Hedge your portfolio if you meet the below criteria

- When you have a reasonable belief that market is going to correct steeply over a specific period of time either due to an event risk or high valuations or some other reason. The time period for your belief to play out can be 2 weeks, 1 month, 2months, 6 months or 3 years.
- If the portfolio worth is greater than 3 lakhs.
- If there are reasons not to exit & re-enter the portfolio either for tax purpose, dividends or fear of timing the re-entry (or fear of missing out).
- When you are willing to pay the risk amount of at least 1% of your portfolio value to hedge.
- If you have a portfolio that is not mid-cap/small-cap stocks heavy. I will explain the reason later in the article.
- And finally, you should have a good understanding of options.

If you have met the above criteria, then you can be certain that your portfolio needs hedging. Otherwise, explore other possibilities which I will list later in this article to control the risk to your portfolio .

## How to Hedge your Portfolio

The most simple form of hedging a portfolio is to buy an option to protect from the downside risk. But it is important to understand what kind of options and how many options need to be bought for hedging.

An ideal hedging option has two components - efficiency and cost-effectiveness. A hedge is efficient when it provides a one to one protection. A 10% draw-down in your portfolio should be compensated by an equivalent gain in your put option thus offsetting the draw-down. A hedge is cost-effective if it provides downside protection to your portfolio at reasonable cost without eating into you returns.

### Portfolio Beta Calculation

The first step in finding an efficient and cost-effective hedge is to find the beta of your portfolio. *Beta* is a measure of the volatility, or risk, of a stock or a portfolio in comparison to the market index benchmark. A stock with a beta of greater than one is more volatile than the index benchmark and a stock with beta of less than one is less volatile than the index benchmark.

In the case of NSE stocks, a broad based index like Nifty 500 is an ideal benchmark for large set of portfolios. But unfortunately, there is no derivative instrument available for trading Nifty 500 index leaving us with no choice but to use Nifty as our benchmark. Nifty has a variety of derivative instruments that can be used for hedging and we will use put option as out hedging tool.

In our case, we want a portfolio whose beta is close to one which can be hedged with an index put option. that provides downside protection. A portfolio beta of one means it moves in the same direction of index benchmark but also move by the same amount as the index. And therefore easy to have a one to one correlation and hedging.

Beta of a portfolio is computed in 4 steps

- Calculate the beta of the individual stocks in your portfolio
- Calculate the allocation percentage (weightage) of each stock in the portfolio
- Multiply beta of stock with their weightage to get the weighted beta.
- Finally, summing up all the individual weighted betas will give you the final
*portfolio beta*

#### Beta of the Stock

Beta of a stock can be simply calculated by taking the co-variance of the daily fractional returns of stock and index over last one year which is divided by the variance of the daily fractional returns of index over last one year. The period of calculation can be different but 1 year is most commonly used.

Here is a link to the page where it shows how to calculate the beta of the stock in an excel sheet.

Weighted Beta of the Stocks

Calculate the allocation percentage (weightage) of individual stock by dividing the individual stock allocation in rupees over the total portfolio value in rupees. Then multiply the stock weightage with the stock beta to get the weighted beta of the stock

#### Portfolio Beta

Sum up all the weighted beta of stocks in the portfolio to get the portfolio beta.

Here is a sample calculation of portfolio beta in Excel sheet. Link to the Excel file here.

In the next step, we will use the portfolio beta to choose the right hedge.

### Choosing the Hedge

In order to choose proper hedge, we need to know how much of the portfolio needs to be hedged. To know the amount of the portfolio need to be hedged, we multiply the portfolio value with the portfolio beta.

In the case of above sample portfolio,

- portfolio value of 4,15,000 with portfolio beta of 1.11 to get the value of 4,60,650, the amount that needs to be hedged.

To get the amount of Nifty that needs to hedge the portfolio, we get the notional value of Nifty index by multiplying the current price of Nifty with its lot size and then divide the portfolio value with notional value of Nifty.

At current price of 11070 & the lot size of 75,

- The notional value of Nifty is 8,30,520 (11070 x 75).
- The number of lots Nifty needed to hedge our sample portfolio will be 0.55 (4,60,650/8,30,520 ).

Since we cannot buy/sell fractional lots of Nifty futures, we can instead buy Nifty put options as hedge. A one lot Nifty futures contract has a delta of 1 and and therefore a 0.55 lot of Nifty will have a delta of 0.55. And this will be the delta of the put options that we need to buy to hedge the sample portfolio. In general, put options have a negative delta value implying that they have negative correlation to Nifty's underlying movement. But, from here on we will consider delta of put options in absolute terms without assigning the negative value.

*Delta* is an option greek that represents rate of change of the price of the option with respect to its underlying security's price. A put option with a delta of 0.55 will move up by 55 paisa for every 1 rupee down-move in the underlying Nifty's price. For example, if Nifty corrects by 100 points, then the put option of 0.55 delta will go up by 4120 bucks (0.55 x 100 x 75) at expiry. But if the correction if steeper and the option becomes in the money, the delta of the option becomes 1 and the value of options changes by 1 buck for every rupee move in Nifty.

### Hedged vs Unhedged Portfolio

Here is the rough estimate pay-off chart of an Unhedged and Hedged sample portfolio with 0.55 delta put option of strike 11,200 of February 2018 expiry (current month expiry).

Here are the different scenarios of how hedged vs hedged portfolio behaves with respect to the Nifty index benchmark

Nifty % Change | Nifty Value | Portfolio % Change | 11200 Put Option Value | Portfolio Value | Hedged Portfolio Value | Hedged Portfolio % Change |
---|---|---|---|---|---|---|

+5% | 11622 | 5.55% | 0 | 438043 | 417869 | 0.69% |

0 | 11069 | 0% | 9825 | 415000 | 404635 | -2.45% |

-5% | 10516 | -5.55% | 31151 | 391960 | 423111 | +1.95% |

-10% | 9962 | -12.4% | 72663 | 368923 | 441594 | +6.4% |

-15% | 9409 | -16.65% | 114176 | 345894 | 460070 | +10.86% |

### Hedging Cost

The amount payed for the hedge (Nifty 11200 put Feb2018 expiry) is 20,000 (option price of 268 * lot size of 75) which is around 4.8% of the total portfolio value. The put options gives protection only up to Feb 22nd 2018. But this is not a cost-effective hedge as it costs 4.8% of portfolio value for just 24 days of protection.

Currently, the expensive premium of options is mainly due to very high implied volatility (IV) of options in the run-up to the 2018 budget. A cost-effective hedge, ideally, should not cost more than 2-3% of portfolio for a year worth of protection. In general, an hedge should be bought under normal market conditions when IV (VIX) of the Nifty is at low or average levels of 12-13.

The stronger the hedge you want, the costlier it will be. If the investor doesn't mind a 5-10% correction in the market, he can reduce the cost of hedge by buying a cheaper far out of the money put option which gives protection to the portfolio only if the market crashes beyond 5-10%.

For example, if we want to hedge the sample portfolio only after 5% fall in market, we buy a put option 5% away from the current Nifty price of 11069. A 10500 put option of Feb 2018 expiry costs around 3700. This is 0.9% of the portfolio value and 1/5th of the 0.55 delta 11200 strike put option.

Here is the pay-off of the hedged sample portfolio with a 10500 put option.

So, depending on the conviction of the investor of a market crash over short-term, medium-term or long-term, he has option of choosing the right put option as an hedge for the portfolio protection.

## Who cannot Hedge the portfolio

Earlier in the article, I talked about not hedging your portfolio if its too mid-cap or small-cap heavy.

The main reasons for this are

- Mid-cap & Small-cap stocks have high beta due to their high volatile nature and therefore not reliable beyond a point. This will lead to incorrect portfolio beta calculation which may result in not selecting a proper hedging and loosing the returns for no reason.
- Even if we consider that portfolio beta is accurate, the portfolio beta is very high, usually above 1.4. A high beta of portfolio means a higher cost of hedging, thus making it inefficient.

Momentum based portfolios, sector specific portfolios, mid/small/micro-cap heavy portfolios etc are all good examples of portfolios where hedging is not recommended.

Investors with smaller portfolio size of less than 3 lakh shouldn't bother about hedging. Hedging costs will make it inefficient for smaller portfolios.

## Alternatives to Hedging

If investor still doesn't like the cost of hedging, the alternative is to exit the portfolio gradually.

One can exit portfolio

- By partial bookings of the profits by selling the a percentage of portfolio when the markets are showing signs of exhaustion
- When the portfolio hits a predetermined portfolio level stop loss is hit
- When index benchmark reaches a predetermined range
- By using a trailing stop loss based on Average True Range (ATR)

## Conclusion

In this article, we have discussed about the need to hedge depending up on the investor's conviction of a market correction over a time period. Then we learned how to hedge the portfolio using index put options and how to choose the hedge using portfolio beta and Nifty index delta. And finally, we discussed about who cannot hedge their portfolios and which portfolios shouldn't be hedged.

## Portfolio Hedging App

Using the techniques applied to calculate stock beta, portfolio beta, Nifty delta and how to choose the hedge, I've made a Portfolio Hedging App which automates all this workflow and presents you the options to choose the right hedge according to your requirements by simply uploading your portfolio to the app.

Try this sample portfolio, upload it to the app and check it for yourself.

Here is a video on how to use the app

[…] Link to article describing all the calculations used in this app. […]

Thanks for sharing this knowledge. I have one question.

What would be the delta of a portfolio worth 18lacs, with median 1.18?

Kindly reply. TIA

At current price of Nifty at 11040, the delta should be 2.56 if your portfolio beta is 1.18 & portfolio value is 18L

Thanks for replying Sir. Now as the delta is 2.56, how to choose the right PUT for this. TIA.

Your articles are in depth and easy to understand. Can you suggest few good books to read. Thanks