Delta Hedging

[00:00:00.22] - Speaker 1
Investing using options, if done the right way, has many advantages. Options allows you to take profit in any market conditions. If the price rises or falls, as well as if the price stays within a price range and moves sideways, we can invest by looking at the direction of the price. In other cases, we may be interested in time or volatility. Whatever our strategy is, the first thing we need to think about when we decide to put our capital into action is risk management risk.

[00:00:26.03] - Speaker 1
There are different ways of hedging our exposure of our option positions. The delta becomes fundamental because it can help us create what we know as the hedge ratio. The hedge ratio is a coefficient used to quantify the amount of underlying required to hedge risk of another asset. It is mainly used in hedging the risk of one asset against another. The hedge ratio specifies the amount of underlying asset required to hedge one unit of risk of the hedged asset.

[00:00:51.29] - Speaker 1
In our case, we try to hedge the exposure of our option with another option or by buying or selling the underlying asset. Now, let's try to understand this concept by looking at a more practical example. The first thing we want to figure out is the formula for creating our hedge ratio. We know that an in the Money option has a delta of 100 and moves as if we were long the underlying. So if we were long an underlying asset, that is like being long 100 delta.

[00:01:17.19] - Speaker 1
For this reason, the first thing we want to do to calculate our hedge ratio is to divide 100 which represents our exposure to the underlying by the delta value of our option. Let's take a real example of an at the Money call option. We know that the at the Money call has a delta of 50. For this reason, finding our hedge ratio is simple. Just divide 100 by 50.

[00:01:37.09] - Speaker 1
Our ratio is therefore 2 to 1. This means that if we want to hedge based on the hedge ratio, for every two options we buy, we have to sell one unit of underlying or 100 shares. If we do this, our position becomes delta neutral. Also remember that call option always have positive delta from 0 to 100. The same formula also applies to hedging of a put option.

[00:01:58.29] - Speaker 1
To find the hedge ratio of an at the money put, we divide 100 by 50 which always gives the same hedge ratio of 2 to 1. Now unlike a call option though, if we buy a put, we are long put to hedge. We need to buy the underlying and not sell. In this case, for every two put option we buy, we have to buy one unit of underlying or 100 shares. This happens because unlike calls, puts have negative delta.

[00:02:22.04] - Speaker 1
In this slide we present the delta of a call and how it moves based on the price of the underlying. As you can see, the delta is positive. Finally, the delta movement of a put when the price of the underlying changes. Until now, when we introduced the concept of hedge ratios, we have talked about hedging with options or being long or short underlying. In order to be delta neutral, traders can hedge by using options, buying or selling underlying or a combination of the two.

[00:02:47.27] - Speaker 1
The important thing is not what asset to use, but that the delta will be covered. Let's try another example to better understand this concept. We have two positions, two long calls with a delta of 50 and five long puts with a delta of minus 20. If we use the calculation we have studied so far, we can calculate the exposure of both positions. First, we take the two calls and multiply them by the delta.

[00:03:09.11] - Speaker 1
We do the same thing with the five puts. As we can see here, calls have an exposure of 100 while puts have an exposure of minus 100. This means that our position is effectively delta neutral because the difference in exposure of both positions equals to zero. This is a very simple example. Of course, in many cases, a retail professional or investor portfolio is composed of different underlying positions, calls or puts options with different strike price and maturities.

[00:03:36.20] - Speaker 1
But what is important to remember is that when we try to hedge, what matters is the overall delta of our portfolio. And that has to be equal to zero. In that case, we will be delta neutral. To recap, the underlying asset always has a delta of 100. An option with a delta of 100 is the equivalent of having a long or short position in the underlying asset.

[00:03:55.10] - Speaker 1
An investor who is long and at the money call has a delta of 50. This means that is instead long half a contract of the underlying shares or 50 shares. And finally, a position of 200 Delta is equal to being long 2 units of underlying. These are important points to remember, especially if you manage your portfolio actively or work at a desk where you are constantly delta hedging through the day. These are other important points to remember.

[00:04:19.25] - Speaker 1
The delta of a call option ranges from 0 to 100. A delta of 0 is out of the money, a delta of 50 is at the money and a delta of 100 is in the money. Call options have positive delta and put options have negative delta. To beat delta hedged, we need to understand how to create the edge ratio of our position. We are delta H'd when our net delta is zero.

[00:04:41.12] - Speaker 1
Finally, the more time passes, the more our expectations on volatility decrease. This means that the delta of our calls moves away from 50 while the delta of our puts moves away from minus 50. The reverse happens if the volatility expectations rise. Now let's look at some other examples. Let's look at the delta hedging of a long call position.

[00:05:00.25] - Speaker 1
In this example, the price of the SPX index is 3800 and our call has a debt of 50. This means that our call is at the money. Now, thanks to the delta, we can establish how much underlying is needed to remain covered. When we looked at the edge ratio, we know that the delta of being long, one unit of underlying always equals to 100. If the delta of our option is 50, we know that we will need 50 shares of underlying to be delta neutral.

[00:05:25.17] - Speaker 1
Since we are long a call, we need to short the underlying. So we will use the negative sign in front of our hedge. What you can see is that we are in effect subtracting the underlying from the delta value. In this case, we have subtracted 50 underlying units from 50 Deltas. This will become clearer when we rebalance our position is executed and we are delta neutral.

[00:05:45.20] - Speaker 1
At this point, let's assume that the spot price of the index has moved up from 3,800 to 3,900. In this case, the delta of our call is no longer 50, but 70. This means that the position is no longer delta neutral. With the increase in the spot price, our net Delta has become 20, which is nothing more than the 70 delta of our new position minus the 50 delta of RH. We would then need to add an additional minus 20 short to the initial minus 50 to be delta neutral.

[00:06:15.13] - Speaker 1
The trade to rebalance is then to sell 20 shares. So the net delta column helps us understand whether to be delta H, we have to buy or sell the underlying. It all depends on the sign. When the net delta is negative, we buy. When is positive, we sell.

[00:06:29.03] - Speaker 1
To remain delta neutral. We have covered a lot up to this point. In the last few lessons we talked about delta and about delta hedging. The concept of delta hedging will be a recurring concept throughout the course. Our goal is to identify the reason why the market maker is forced to hedge during the day.

[00:06:45.01] - Speaker 1
Because, as we explained in the previous section, this activity affects liquidity and price movements. And it is that activity that our Q models track every morning. The delta is conditioned not only by the spot price. It is important to remember that the Greeks are not linear, but in addition to the spot, they follow speed, volatility, the passage of time and interest rates. Understanding what these variables are and how they interact with the data is essential if we want to become better traders.

[00:07:11.12] - Speaker 1
In the next lesson, we will talk about the Greek Gamma. We will try to understand how it interacts with other Greeks and how it affects market makers. Delta hedging activity.