# Collar (finance)

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Collar (finance)

In finance, a collar is an option strategy that limits the range of possible positive or negative returns on an underlying to a specific range.

## Equity Collar

### Structure

A collar is created by an investor being:[1]

These latter two are a short Risk reversal position. So:

Underlying - Risk reversal = Collar

The premium income from selling the call reduces the cost of purchasing the put. The amount saved depends on the strike price of the two options. If the premium of the long call is exactly equal to the cost of the put, the strategy is known as a "zero cost collar". [Strictly speaking the name should be "zero premium collar" as the cost of holding the position can be potentially high if the price of the underlying rises above the strike level of the call.]

At expiration the value (but not the profit) of the collar will be:

• zero if the price of the underlying is below X
• positive if the price of the underlying is between X and (X + a)

The maximum value occurs for any price of the underlying above X+a.

### Example

Consider an investor who owns one hundred shares of a stock with a current share price of \$5. An investor could construct a collar by buying one put with a strike price of \$3 and selling one call with a strike price of \$7. The collar would ensure that the gain on the portfolio will be no higher than \$2 and the loss will be no worse than \$2 (before deducting the net cost of the put option, i.e., the cost of the put option less what is received for selling the call option).

There are three possible scenarios when the options expire:

• If the stock price is above the \$7 strike price on the call he wrote, the person who bought the call from the investor will exercise the purchased call; the investor effectively sells the shares at the \$7 strike price. This would lock in a \$2 profit for the investor. He only makes a \$2 profit (minus fees), no matter how high the share price goes. For example, if the stock price goes up to \$9, the buyer of the call will exercise the option and the investor will sell the shares that he bought at \$5 for \$9, for a \$4 profit, but must then pay out \$9-\$7=\$2, making his profit only \$2.
• If the stock price drops below the \$3 strike price on the put then the investor may exercise the put and the person who sold it is forced to buy the investor's 100 shares at \$3. The investor loses \$2 on the stock, but can only lose \$2 (plus fees), no matter how low the price of the stock goes. For example, if the stock price falls to \$1, then the investor exercises the put and has a \$2 gain. The value of the investor's stock has fallen by \$5-\$1 = \$4. The call expires worthless (since the buyer does not exercise it), and the total net loss is \$2-\$4= -\$2.
• If the stock price is between the two strike prices at the expiration date, both options expire unexercised, and the investor is left with the 100 shares whose value is that stock price (x100), plus the cash gained from selling the call option, minus the price paid to buy the put option, minus fees.

One source of risk is counterparty risk. If the stock price expires below the \$3 floor then the counterparty may default on the put contract, thus creating the potential for losses up to the full value of the stock (plus fees).

## Interest Rate Collar

### Structure

In an interest rate collar, the investor seeks to limit exposure to changing interest rates and at the same time lower its net premium obligations. Hence, the investor goes long on the cap (floor) that will save it money for a strike of X +(-) S1 but at the same time shorts a floor (cap) for a strike of X +(-) S2 so that the premium of one at least partially offsets the premium of the other. Here S1 is the maximum tolerable unfavorable change in payable interest rate and S2 is the maximum benefit of a favorable move in interest rates.[2]

### Example

Consider an investor A who has an obligation to pay floating 6 month LIBOR annually on a notional N and which (when invested) earns 6%. A rise in LIBOR above 6% will hurt the investor while a drop will benefit her. Thus it is desirable for her to purchase an interest rate cap which will pay her back if the LIBOR rises above her level of comfort. Figuring that she is comfortable paying upto 7%, she enters into an Interest Rate Cap with counterparty B wherein B will pay her the difference between 6 mo LIBOR and 7% when the LIBOR exceeds 7% for a premium of 0.08*N. To offset this premium, she sells an Interest Rate Floor to counterparty C wherein she will pay them the difference between 6 mo LIBOR and 5% when the LIBOR falls below 5%. For this she receives 0.075*N premium, thus offsetting what she paid for the Cap.[3]

Now she can face 3 scenarios:

1. Rising interest rates - she will pay a maximum of 7% on her original obligation. Anything over and above that will be offset by the payments she will receive from party B under the Cap agreement. Hence A is not exposed to interest rate rises of more than 1%.
2. Stationary interest rates - as long as the LIBOR stays around 6%, A is not affected.
3. Falling interest rates - she will benefit from a fall in interest rates upto a limit of 5% as per the floor agreement. If it falls further, A will make payments to C under the Floor agreement while saving the same amount on the original obligation. Hence A cannot benefit from a fall of more than 1%.

## Why do this?

In times of high volatility, or in bear markets, it can be useful to limit the downside risk to a portfolio. One obvious way to do this is to sell the stock. In the above example, if an investor just sold the stock, the investor would get \$5. This may be fine, but it poses additional questions. Does the investor have an acceptable investment available to put the money from the sale into? What are the transaction costs associated with liquidating the portfolio? Would the investor rather just hold onto the stock? What are the tax consequences?

If it makes more sense to hold onto the stock (or other underlying asset), the investor can limit that downside risk that lies below the strike price on the put in exchange for giving up the upside above the strike price on the call. Another advantage is that the cost of setting up a collar is (usually) free or nearly free.The price received for selling the call is used to buy the put—one pays for the other.

Finally, using a collar strategy takes the return from the probable to the definite. That is, when an investor owns a stock (or another underlying asset) and has an expected return, that expected return is only the mean of the distribution of possible returns, weighted by their probability. The investor may get a higher or lower return. When an investor who owns a stock (or other underlying asset) uses a collar strategy, the investor knows that the return can be no higher than the return defined by strike price on the call, and no lower than the return that results from the strike price of the put.

## References

• Hull, John (2005). Fundamentals of Futures and Options Markets, 5th ed. Upper Saddle River, NJ: Prentice Hall. ISBN 0-13-144565-0.
1. ^ "Statement 133 Implementation Issue No. E18". Retrieved July 8, 2011.
2. ^ HM Revenues and Customs. "CFM13350 - Understanding corporate finance: derivative contracts: interest rate collars: Using interest rate collars". Retrieved July 8, 2011.
3. ^ "Interest Rate Collars". Investopedia. Retrieved July 8, 2011.

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