Hello and welcome to this week's installment of "Derivatives Demystified."

The topic on today's menu is "Delta."

I'm not talking Greek alphabet or clay deposits at river mouths. I'm also not talking brain waves or radiotelephone phonetics.

In my first post, I wrote how derivatives are paper contracts with prices that reference an underlying asset's price.

Delta in a sentence: How your trade value will change when the underlying asset's price changes by 1%.

__Example 1: 100% Delta__

Say I bought 100,000 Sasol Shares on 25 May 2020 at R75 per share for a total spend of R7,500,000.

The Sasol Share price went up by 1% (from R75.00 to R75.75) on the same day.

So the full value of my investment went to R7,575,000, and I had a profit of R75,000*. As the underlying price changed by 1%, my investment value changed by 1%. So we would say this investment is delta one or has 100% delta. Simply, a 1% change in underlying relates to a 1%x100% change in investment value.

*100,000 shares x R75.75 share price

**R7,575,000 - R7,500,000

***R75,000 / R7,500,000

Let's stop with the delta one example before reliving the Sasol share price, eventually trading to R483.00 per share, or 644% profit for delta one holders.

What if something is not delta one? What if my investment value does not have a 100% or 1:1 correlation with the underlying asset's price?

Then, we have either GEARING or a NON.LINEAR.DERIVATIVE. Boom. A derivative like an option.

__Example 2: 50% Delta__

Say I'm exporting Faf Undies to Perth and will receive a payment of AUD100,000 at the end of 1 month. I will then need to sell the AUD as I need ZAR to keep my Landcruiser running and to add another solar panel to my roof.

I could sell a 1-month AUDZAR forward contract, ensuring a rate of 11.1500. At the end of 1-month, I sell AUD100,000 at 11.1500 and receive ZAR1,115,000.

Alternatively, I could buy an AUD put option with a strike at 11.1500.

**Possible Outcome 1:** If AUDZAR trades below 11.1500 at the end of the month, I sell AUD100,000 at 11.1500 and receive ZAR1,115,000.

**Possible Outcome 2:** If AUDZAR trades at 11.2500 (above my strike) at the end of the month, I sell AUD100,000 at 11.2500 and receive ZAR1,125,000.

I will pay a premium of ZAR17,500 for this option.

Why ZAR17,500?

The premium should be positive because we are protected against ZAR strength and can participate in ZAR weakness. Similarly to having to pay an insurance premium. We use a Black-Scholes option-pricing formula to calculate the premium amount. Luckily, many brainiacs have built these pricers, they are available for free online, and we need not disturb our Delta Waves over understanding the math. What we need to know is the formula has the following inputs:

· Spot & Forward Price (underlying asset)

· Implied Volatility

· Deposit rates of AUD and ZAR

· Term

Delta measures by how much my put option premium will change if AUDZAR forward prices change. Because the strike of the option is at the forward price or "at the money," it is a 50% delta option. A loose interpretation for the 50% is that the ATM option is equally likely to be exercised or not.

Let's say AUDZAR trades from 11.1500 to 11.0385 (1% lower). Since the option's delta is 50% and my nominal is AUD100,000, the option premium price will change as if I'd sold AUD50,000* of the underlying outright. The option premium will change from ZAR17,500 to ZAR23,075**.

*AUD100,000 x 50% (delta)

**ZAR17,500 + 50,000 x (11.1500 - 11.0385)

__Example 3: 25% & 10% Delta__

Just to drive the point home: if a USD1mio option has a 25% delta, the price of the option will move as if you are running a USD250,000 outright spot/forward position. And if a USD1mio option has a 10% delta, the price of the option will move as if you are running a USD100,000 spot/foward outright position.

Finally, we get to delta hedging - this is something options traders do. Unlike the exporter in our last example, vol traders want exposure to other inputs of the Black-Scholes formula (like volatility). They may not have a view on whether the underlying will trade up or down, but they may think that volatility will increase. They don't want the value of their option position to change when the underlying forward price changes, so they would simultaneously buy a AUD100,000 put option and buy AUD50,000 outright. They are then delta neutral or delta hedged.

Thanks for reading!

Remember, "Love your neighbour, but pull not down your hedge.”

– George Herbert (1633), poet, orator, priest and now “Derivatives Demystified” quotee