Portfolio Hedging using Index Options Explained

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Contents

Portfolio Hedging using Index Options

An alternative to selling index futures to hedge a portfolio is to sell index calls while simultaneously buying an equal number of index puts. Doing so will lock in the value of the portfolio to guard against any adverse market movements. This strategy is also known as a protective index collar.

The idea behind the index collar is to finance the purchase of the protective index puts using the premium collected from selling the index calls. However, as a result of selling the index calls, in the event that the fund manager’s expectation of a falling market is wrong, his portfolio will not benefit from the rising market.

Implementation

To hedge a portfolio with index options, we need to first select an index with a high correlation to the portfolio we wish to protect. For instance, if the portfolio consist of mainly technology stocks, the Nasdaq Composite Index might be a good fit and if the portfolio is made up of mainly blue chip companies, then the Dow Jones Industrial Index could be used.

After determining the index to use, we calculate how many put and call contracts to buy and sell to fully hedge the portfolio using the following formula.

No. Index Options Required = Value of Holding / (Index Level x Contract Multiplier)

Example

A fund manager oversees a well diversified portfolio consisting of fifty large cap U.S. stocks with a combined value of $10,000,000 in October. Worried by news about surging oil prices, the fund manager decides to hedge his holding by purchasing slightly out-of-the-money S&P 500 index puts while selling an equal number of slightly out-of-the-money S&P 500 index calls expiring in two months’ time. The current level of the S&P 500 is 1500 and the DEC 1475 SPX put contract costs $20 each while the DEC 1525 SPX call contract is quoted at $25 each.

The SPX options has a contract multiplier of $100, and so the number of contracts needed to fully protect his holding is: $10000000/(1500 x $100) = 66.67 or 67 contracts. A total of 67 put options need to be purchased and 67 call options need to be written.

  • Total cost of the put options is: 67 x $20 x $100 = $134,000.
  • Total premium collected for selling the call options is: 67 x $25 x $100 = $167,000.
  • Net premium received is: $167,000 – $134,000 = $33,000.
S&P 500 Index Call Option Value Put Option Value Net Premium Received Unhedged Portfolio Hedged Portfolio
1200 $0 $1,842,500 $33,000 $8,000,000 $9,875,000
1300 $0 $1,172,500 $33,000 $8,666,666 $9,872,166
1400 $0 $502,500 $33,000 $9,333,333 $9,868,833
1500 $0 $0 $33,000 $10,000,000 $10,033,000
1600 -$502,500 $0 $33,000 $10,666,666 $10,197,166
1700 -$1,172,500 $0 $33,000 $11,333,333 $10,193,833

As can be seen from the table above, should the market retreat, as represented by the declining S&P 500 index, the value of the put options rise and almost fully offset the losses taken by the portfolio. Conversely, should the market appreciate, the rise in his holding’s value is capped by the rise in the value of the call options sold short. Hence, once the index collar in entered, the fund manager has effectively locked in the value of his portfolio.

Note: The example does not include transaction costs in the calculations and also assumes full correlation (beta of 1.0) between the portfolio and the S&P 500 index.

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Writing Puts to Purchase Stocks

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Effect of Dividends on Option Pricing

Cash dividends issued by stocks have big impact on their option prices. This is because the underlying stock price is expected to drop by the dividend amount on the ex-dividend date. [Read on. ]

Bull Call Spread: An Alternative to the Covered Call

As an alternative to writing covered calls, one can enter a bull call spread for a similar profit potential but with significantly less capital requirement. In place of holding the underlying stock in the covered call strategy, the alternative. [Read on. ]

Dividend Capture using Covered Calls

Some stocks pay generous dividends every quarter. You qualify for the dividend if you are holding on the shares before the ex-dividend date. [Read on. ]

Leverage using Calls, Not Margin Calls

To achieve higher returns in the stock market, besides doing more homework on the companies you wish to buy, it is often necessary to take on higher risk. A most common way to do that is to buy stocks on margin. [Read on. ]

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Day trading options can be a successful, profitable strategy but there are a couple of things you need to know before you use start using options for day trading. [Read on. ]

What is the Put Call Ratio and How to Use It

Learn about the put call ratio, the way it is derived and how it can be used as a contrarian indicator. [Read on. ]

Understanding Put-Call Parity

Put-call parity is an important principle in options pricing first identified by Hans Stoll in his paper, The Relation Between Put and Call Prices, in 1969. It states that the premium of a call option implies a certain fair price for the corresponding put option having the same strike price and expiration date, and vice versa. [Read on. ]

Understanding the Greeks

In options trading, you may notice the use of certain greek alphabets like delta or gamma when describing risks associated with various positions. They are known as “the greeks”. [Read on. ]

Valuing Common Stock using Discounted Cash Flow Analysis

Since the value of stock options depends on the price of the underlying stock, it is useful to calculate the fair value of the stock by using a technique known as discounted cash flow. [Read on. ]

Portfolio Hedging using VIX Calls

When the VIX is low, the negative correlation of the highly volatile VIX to the S&P 500 index makes it possible to use VIX options as a hedge to protect a portfolio against a market crash.

To implement such a hedge, the investor buys near-term slightly out-of-the-money VIX calls while simultaneously, to reduce the total cost of the hedge, sells slightly out-of-the-money VIX puts of the same expiration month. This strategy is also known as the reverse collar.

The idea behind this strategy is that, in the event of a stock market decline, it is very likely that the VIX will spike high enough so that the VIX call options gain sufficient value to offset the losses in the portfolio.

Implementation

To hedge a portfolio with VIX options, the portfolio must be highly correlated to the S&P 500 index with a beta close to 1.0.

The tricky part is in determining how many VIX calls we need to purchase to protect the portfolio. A simplified example is provided below to show how it is done.

Example

A fund manager oversees a well diversified portfolio consisting of thirty large cap U.S. stocks. For the past two months, the market has been climbing steadily with the S&P 500 index climbing from 1273 in mid-March to 1426 in mid-May. At the same time, the VIX has been drifting downwards gradually, hitting a five month low of 16.30 on 17th May. The fund manager thinks that the market is getting too complacent and a correction is imminent. He decides to hedge his holdings by purchasing slightly out-of-the-money VIX calls expiring in one month’s time. Simultaneously, he sells an equal number of out-of-the-money puts to reduce the cost of implementing the hedge.

  • For simplicity’s sake, let’s assume the value of his holdings is $1,000,000.
  • The S&P 500 Index stood at 1423.
  • The VIX is at 16.30.
  • June VIX calls, with a strike price of $19, are priced at $0.40 each.
  • June VIX puts, with a strike price of $12.50, are priced at $0.25 each.
So, how many VIX calls does the fund manager need to buy to provide the necessary protection?

According to the CBOE Website, on average, the VIX rise 16.8% on days when the S&P 500 index drops 3% or more. This means that if the SPX move down by 10%, the VIX can potentially shoot up by 56%. To play it safe, the fund manager assumes that the VIX will rise by only 40% when the SPX drops by 10%. This means that, in theory, the VIX should rise from 16.3 to 22.8 if the S&P 500 drops 10% from the current level of 1423 to 1280.

  • When the VIX is at 22.8, each June $19 VIX call will be worth $380 ($3.80 x $100 contract multiplier).
  • 10% of the fund manager’s portfolio is worth $100,000.
  • Number of VIX calls required to protect 10% of the portfolio is therefore: $100,000/$380 = 264
  • Total cost of purchasing the 264 VIX June $19 calls at $0.40 each = 264 x $0.40 x $100 = $10,560
  • Premium received for selling 264 June $12.50 VIX puts at $0.25 each = 264 x $0.25 x $100 = $6,600
  • Total investment required to construct the hedge = $10,560 – $6,600 = $3,960
S&P 500 Index VIX Call Options Value Put Options Value Net Premium Received Unhedged Portfolio Hedged Portfolio
1210
(-15%)
26.08
(+60%)
$186,912 $0 $182,952 $850,000 $1,032,952
1280
(-10%)
22.80
(+40%)
$100,320 $0 $96,360 $900,000 $996,360
1352
(-5%)
19.56
(+20%)
$14,784 $0 $10,824 $950,000 $960,824
1423 16.30 $0 $0 -$3,960 $1,000,000 $996,040
1494
(+5%)
13.04
(-20%)
$0 $0 -$3,960 $1,050,000 $1,046,040
1565
(+10%)
9.78
(-40%)
$0 $71,808 -$75,768 $1,100,000 $1,024,232
1636
(+15%)
9.78**
(-40%)
$0 $71,808 -$75,768 $1,150,000 $1,074,232

** – Based on historical data, the VIX does not stay below 10 and we assume the same for this example.

As can be seen from the table above, should the market retreat, as represented by the declining S&P 500 index, the negatively correlated VIX move upwards at a much faster rate. The VIX puts sold short will expire worthless while the value of the VIX call options rise to offset the loss of value in the portfolio.

Conversely, should the market appreciate, the rise in his holding’s value is offset by the rise in the value of the VIX put options sold short. Notably, because the VIX has traditionally never gone below 10 for long, the put options sold short should not appreciate too much to cause significant damage to the portfolio. Hence, it is more favorable to implement this hedging strategy when the VIX is low.

In the event that the VIX spiked sharply (not impossible, given that the trading range of the VIX is 10 to 50), the rise in value of the VIX calls can even exceed the losses taken by the portfolio, resulting in a net overall gain.

Note: For the above example, transaction costs are not included in the calculations. Additionally, the following assumptions are made:

  • Full correlation (beta of 1.0) between the portfolio and the S&P 500 index.
  • The rise/fall of the market occurred on option expiration date.

Things to remember

Unless very near expiration, VIX option prices reflect the forward VIX rather than the spot VIX. To discover the forward VIX, one can refer to the VIX futures price.

Historically, the VIX only move opposite the SPX 88% of the time. So this means there is still a 12% chance that the negative correlation will not materialise. So, unlike hedging with index puts, the protection is not 100% guaranteed.

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Writing Puts to Purchase Stocks

If you are very bullish on a particular stock for the long term and is looking to purchase the stock but feels that it is slightly overvalued at the moment, then you may want to consider writing put options on the stock as a means to acquire it at a discount. [Read on. ]

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Effect of Dividends on Option Pricing

Cash dividends issued by stocks have big impact on their option prices. This is because the underlying stock price is expected to drop by the dividend amount on the ex-dividend date. [Read on. ]

Bull Call Spread: An Alternative to the Covered Call

As an alternative to writing covered calls, one can enter a bull call spread for a similar profit potential but with significantly less capital requirement. In place of holding the underlying stock in the covered call strategy, the alternative. [Read on. ]

Dividend Capture using Covered Calls

Some stocks pay generous dividends every quarter. You qualify for the dividend if you are holding on the shares before the ex-dividend date. [Read on. ]

Leverage using Calls, Not Margin Calls

To achieve higher returns in the stock market, besides doing more homework on the companies you wish to buy, it is often necessary to take on higher risk. A most common way to do that is to buy stocks on margin. [Read on. ]

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Day trading options can be a successful, profitable strategy but there are a couple of things you need to know before you use start using options for day trading. [Read on. ]

What is the Put Call Ratio and How to Use It

Learn about the put call ratio, the way it is derived and how it can be used as a contrarian indicator. [Read on. ]

Understanding Put-Call Parity

Put-call parity is an important principle in options pricing first identified by Hans Stoll in his paper, The Relation Between Put and Call Prices, in 1969. It states that the premium of a call option implies a certain fair price for the corresponding put option having the same strike price and expiration date, and vice versa. [Read on. ]

Understanding the Greeks

In options trading, you may notice the use of certain greek alphabets like delta or gamma when describing risks associated with various positions. They are known as “the greeks”. [Read on. ]

Valuing Common Stock using Discounted Cash Flow Analysis

Since the value of stock options depends on the price of the underlying stock, it is useful to calculate the fair value of the stock by using a technique known as discounted cash flow. [Read on. ]

Using Options as a Hedging Strategy

Hedging strategies are used by investors to reduce their exposure to risk in the event that an asset in their portfolio is subject to a sudden price decline. When properly done, hedging strategies reduce uncertainty and limit losses without significantly reducing the potential rate of return.

Usually, investors purchase securities inversely correlated with a vulnerable asset in their portfolio. In the event of an adverse price movement in the vulnerable asset, the inversely correlated security should move in the opposite direction, acting as a hedge against any losses. Some investors also purchase financial instruments called derivatives. When used in a strategic fashion, derivatives can limit investors’ losses to a fixed amount. A put option on a stock or index is a classic hedging instrument.

How Put Options Work

With a put option, you can sell a stock at a specified price within a given time frame. For example, an investor named Sarah buys stock at $14 per share. Sarah assumes that the price will go up, but in the event that the stock value plummets, Sarah can pay a small fee ($7) to guarantee she can exercise her put option and sell the stock at $10 within a one-year time frame.

If in six months the value of the stock she purchased has increased to $16, Sarah will not exercise her put option and will have lost $7. However, if in six months the value of the stock decreases to $8, Sarah can sell the stock she bought (at $14 per share) for $10 per share. With the put option, Sarah limited her losses to $4 per share. Without the put option, Sarah would have lost $6 per share.

Key Takeaways

  • A hedge is an investment that protects your portfolio from adverse price movements.
  • Put options give investors the right to sell an asset at a specified price within a predetermined time frame.
  • The pricing of options is determined by their downside risk, which is the likelihood that the stock or index that they are hedging will lose value if there is a change in market conditions.

Option Pricing Determined by Downside Risk

The pricing of derivatives is related to the downside risk in the underlying security. Downside risk is an estimate of the likeliness that the value of a stock will drop if market conditions change. An investor would consider this measure to understand how much they stand to lose as the result of a decline and decide if they are going to use a hedging strategy like a put option.

By purchasing a put option, an investor is transferring the downside risk to the seller. In general, the more downside risk the purchaser of the hedge seeks to transfer to the seller, the more expensive the hedge will be.

Downside risk is based on time and volatility. If a security is capable of significant price movements on a daily basis, then an option on that security that expires weeks, months or years in the future would be considered risky and would thus would be more expensive. Conversely, if a security is relatively stable on a daily basis, there is less downside risk, and the option will be less expensive.

Call options give investors the right to buy the underlying security; put options give investors the right to sell the underlying security.

Consider Expiration Date and Strike Price

Once an investor has determined on which stock they’d like to make an options trade, there are two key considerations: the time frame until the option expires and the strike price. The strike price is the price at which the option can be exercised. It is also sometimes known as the exercise price.

Options with higher strike prices are more expensive because the seller is taking on more risk. However, options with higher strike prices provide more price protection for the purchaser.

Ideally, the purchase price of the put option would be exactly equal to the expected downside risk of the underlying security. This would be a perfectly-priced hedge. However, if this were the case, there would be little reason not to hedge every investment.

Why Do Most Options Have Negative Average Payouts?

Of course, the market is nowhere near that efficient, precise or generous. For most securities, put options have negative average payouts. There are three reasons for this:

  1. Volatility Premium: Implied volatility is usually higher than realized volatility for most securities. The reason for this is open to debate, but the result is that investors regularly overpay for downside protection.
  2. Index Drift: Equity indexes and associated stock prices have a tendency to move upward over time. When the value of the underlying security gradually increases, the value of the put option gradually declines.
  3. Time Decay: Like all long option positions, every day that an option moves closer to its expiration date, it loses some of its value. The rate of decay increases as the time left on the option decreases.

Because the expected payout of a put option is less than the cost, the challenge for investors is to only buy as much protection as they need. This generally means purchasing put options at lower strike prices and thus, assuming more of the security’s downside risk.

Long Term Put Options

Investors are often more concerned with hedging against moderate price declines than severe declines, as these types of price drops are both very unpredictable and relatively common. For these investors, a bear put spread can be a cost-effective hedging strategy.

In a bear put spread, the investor buys a put with a higher strike price and also sells one with a lower strike price with the same expiration date. This only provides limited protection because the maximum payout is the difference between the two strike prices. However, this is often enough protection to handle either a mild or moderate downturn.

Another way to get the most value out of a hedge is to purchase a long-term put option, or the put option with the longest expiration date. A six-month put option is not always twice the price of a three-month put option. When purchasing an option, the marginal cost of each additional month is lower than the last.

Example of a Long Term Put Option

  • Available put options on iShares Russell 2000 Index ETF (IWM)
  • Trading at $160.26
Strike Days to Expiry Cost Cost/Day
78 57 3.10 0.054
78 157 4.85 0.031
78 248 5.80 0.023
78 540 8.00 0.015

In the above example, the most expensive option also provides an investor with the least expensive protection per day.

This also means that put options can be extended very cost-effectively. If an investor has a six-month put option on a security with a determined strike price, it can be sold and replaced with a 12-month put option with the same strike date. This strategy can be done repeatedly and is referred to as rolling a put option forward.

By rolling a put option forward, while keeping the strike price below (but close to) the market price, an investor can maintain a hedge for many years.

Calendar Spreads

Adding extra months to a put option gets cheaper the more times you extend the expiration date. This hedging strategy also creates an opportunity to use what are called calendar spreads. Calendar spreads are created by purchasing a long-term put option and selling a short-term put option at the same strike price.

However, this practice does not decrease the investor’s downside risk for the moment. If the stock price declines significantly in the coming months, the investor may face some difficult decisions. They must decide if they want to exercise the long-term put option, losing its remaining time value, or if they want to buy back the shorter put option and risk tying up even more money in a losing position.

In favorable circumstances, a calendar spread results in a cheap, long-term hedge that can then be rolled forward indefinitely. However, without adequate research may inadvertently introduce new risks into their investment portfolios with this hedging strategy.

Long Term Put Options Are Cost-Effective

When making the decision to hedge an investment with a put option, it’s important to follow a two-step approach. First, determine what level of risk is acceptable. Then, identify what transactions can cost-effectively mitigate this risk.

As a rule, long-term put options with a low strike price provide the best hedging value. This is because their cost per market day can be very low. Although they are initially expensive, they are useful for long-term investments. Long-term put options can be rolled forward to extend the expiration date, ensuring that an appropriate hedge is always in place.

Keep in mind that some investments are easier to hedge than others. Put options for broad indexes are cheaper than individual stocks because they have lower volatility.

It’s important to note that put options are only intended to help eliminate risk in the event of a sudden price decline. Hedging strategies should always be combined with other portfolio management techniques like diversification, rebalancing, and a rigorous process for analyzing and selecting securities.

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