#### Introduction

A straddle is a combination of two options, namely a call and a put with the same strike, underlying and expiration date. As such, it is an example of an option strategy. In this node, we will investigate the properties of a straddle, and see how they can be used in investing.

If we buy a straddle, we pay the option premium and get two options, the call and the put. As such, we can say we are long a straddle. Let's assume the currency of the options and the underlying is the euro; you can substitute any currency you want of course, the principle doesn't change. At expiration, a call is worth one euro for each euro the underlying, this is the stock or bond or whatever we want, is over the strike. So, if our strike is 30 euro, and our underlying is 32 euro, we get 2 euro. If it is below 30, we make nothing. A put is worth one currency unit for each currency unit the underlying is below the strike. So, if we have a 35 put, and or underlying is at 32 euro again, we make 3 euro. Above 35, we again make nothing.

The funny thing now is that with a call and put expiring at the same time and having the same strike, we will make one euro for each euro we are above this strike (because of the call), but also make one euro for each euro we are below the strike (because of the put). We only don't make anything if we end up exactly at the strike (something that happens somewhat more often than one would statistically expect). So, in essence, we have now have an exposure to the movement or volatility of the underlying, rather than an outright exposure to the underlying itself. This is something that is very typical of options: a direct investment in the underlying (i.e. buying stocks) would never give you this. As a matter of fact, a straddle is probably the single most easy way in which one could get such an exposure.

Another interesting thing is that the eventual value of a straddle can be quite high. If the underlying is a stock or a stock index, it can in fact be unlimited: the stock can rise to any value, and as such the call can as well. Also, if the company goes bankrupt, the value of the stock will go to 0, and the total payoff is equal to the strike.

People almost always buy the staddle with the strike that is closes to the level of the underlying, or rather, to the level where the underlying is expected to be in the future, if dividend and interest are considered. The reason is that this is the cheapest straddle. Straddles with other strikes are more expensive, because if the stock wouldn't move, apart from the movement caused by going ex-dividend and growth with the risk-free rate, they would already be worth money.

In principle, straddles with an expiry that is further in the future are more expensive. The underlying has more time to move. However, it is interesting to note that the straddle price approximately increases with the square root of the time to expiry; this has something to do with random walk. In practice, this is at best a rule of thumb, because ultimately, supply and demand determine option prices.

Let us elaborate on that last part a bit. As mentioned, a straddle has an expected payoff equal to the expected movement of the underlying. Now, this is of course an unknown number. It is also not easy to guess. Under normal circumstances, most stocks move with about a percent or 2 a day or so, but during a crisis or when the company publishes figures, movements can easily be double-digit. The market price of a straddle as such represents what the market thinks is the expected move. So, simply put, if a straddle that will expire in one year on a stock that is worth 100 is worth 30, the market expects the stock will move 30%, or, more precisely, the expectation value of the movement is 30%. Markets are quite efficient, and as such, when it is known a company has figures or when a stock is more volatile in general, the market price of a straddle will likely be higher.

#### The long straddle in investing

Long straddles are used in investing to get exposure to the movement in the underlying. Now, as mentioned, the price of a straddle depends on the amount of movement the market expects. As such, by buying a straddle, you are betting against the market that the stock will move more than the market expects.

Short-dated straddles can be used if you anticipate for instance that the figures of a company will be quite spectacular, but you don't know in which way. Longer-dated (i.e. multi-year) straddles, on the other hand, can be used to exploit the fact that markets often experience long bull or bear markets, in which a market trend moves the market more than the square root of time behavior of the straddle price suggests.

A long-dated straddle can be combined with shares to hedge the risk shares will go down, while at the same time doubling upward potential. This is useful if you are in principle bullish, but also risk-averse. The price, of course, is the premium you pay for the straddle.

By selling a straddle, we can pocket the premium. This is called being short the straddle. This strategy is popular with very large institutional investors, because in the very long run, it is thought that straddles are overpriced. However, for a private investor, a single bad gamble could bankrupt you, so this is not considered an advisable strategy.

What is done sometimes is to buy the shares and at the same time sell the straddle. At this point, you effectively buy shares at a discount, because of the premium you pocket. However, you won't make (as much) money if the shares rise, because the short call forces you to sell them at the strike price., and if the shares drop, you could be forced to buy more shares. With this strategy, you are betting the market has bottomed. Still, in a crash, options can get very expensive, so if your timing and vision are correct, this can be a very good strategy. Note that the short call is hedged, so you don't have the unlimited loss potential; the maximum loss is the price of the shares, plus the strike of the straddle minus the premium pocketed.

#### Conclusion

A straddle is perhaps the simplest example of a trade based on the expected market volatility, without considering direction. In principle, by buying a straddle, (long straddle) one bets the market will move more than the premium invested. Selling a straddle (short straddle) is the opposite bet. By combining a straddle with shares, different risk profiles can be realized.

Strad"dle (?), v. i. [imp. & p. p. Straddled (?); p. pr. & vb. n. Straddling (?).] [Freq. from the root of stride.]

1.

To part the legs wide; to stand or to walk with the legs far apart.

2.

To stand with the ends staggered; -- said of the spokes of a wagon wheel where they join the hub.

To place one leg on one side and the other on the other side of; to stand or sit astride of; as, to straddle a fence or a horse.

1.

The act of standing, sitting, or walking, with the feet far apart.

2.

The position, or the distance between the feet, of one who straddles; as, a wide straddle.

3.

A stock option giving the holder the double privilege of a "put" and a "call," i. e., securing to the buyer of the option the right either to demand of the seller at a certain price, within a certain time, certain securities, or to require him to take at the same price, and within the same time, the same securities.

[Broker's Cant]