# Golf Options: An exersize in derivatives

In this article, I’ll try to explain derivatives using the price of a season pass to a golf course, the price of a gallon of milk, and from the perspective of a corn farmer.

Red Rocks Golf Club, in Rapid City, SD, sells season golf passes for \$1,450 per adult, plus an additional charge of \$525 for a single seat cart pass. An 18 hole round of golf at Red Rocks costs \$59, excluding tax, with an additional \$21 for a cart. Red Rocks is betting that patrons will golf 24.58 times over the course of the year, (1450/59). They’re also betting that you’ll use the cart 25 times over the year (525/21). By this measure, the cart pass is overvalued. The cart pass should be valued by the same metric as the golf pass; a club member should refuse to pay anything over \$516.18 (plus tax) for the cart pass.

How is this a derivative?

The golf course is selling you the option to golf. Whether you use that option enough times, i.e. golf enough rounds, is completely up to you. I would venture to guess that the price of a golf pass at Red Rocks has outpaced inflation. Why? Perhaps people are golfing more. If the golf course sells the pass, and the golfer gets 40 rounds in throughout the year, Red Rocks loses money on the investment, but the golfer gains. The intrinsic value of the golf pass can be expressed as such:

IV(golf pass) = Price of Pass – (# of Rounds* Price Per Round)

Note: Price of Pass and Price per Round are both constant and known; the only variable is how many rounds of golf the golfer plays.

Black Friday:

The BF price implies the commercially saavy golfer will only play 19.66 rounds of golf. The BF price on a cart pass (\$472.50) implies the golfer will use the pass 22.5 times. Personally, I don’t know many people who like to go to the golf course just for a drive. Why the discrepancy?

I would be curious to see how the rates have changed over time. I wonder if the number of rounds implied has changed over time or if the price is arbitrary. This is the type of problem for an actuary. Under a perfect price discriminatory environment and with perfect information, the club could sell to each patron at a price consistent with their past behavior. A retiree who lives near the golf course and golfs 80 rounds a year is exploiting the system, while someone who can only golf 15 times a year is getting hustled. Looking at a patron’s past should determine their rate, just like insurance.

“Golf is too hard,” some say. And rates of participation are showing it. Red Rock installed a defensive strategy into their rates. College students and millennials get a discount on their passes as a direct result. Supply and demand states that if demand drops so do prices. So instead of keeping a single sticker price on their passes and lowering it to compensate for the drop in participation rates, Red Rock split their pass into several age tenors after identifying who wasn’t buying passes. This is all guess work, but I’m sure this pricing scheme wasn’t conjured out of thin air. (Guardian)

Seniors also get a discount, as they are probably some of Red Rock’s most devout customers. They’re also less likely to tear up the course by duffing their tee shots and taking a ton of mulligans.

Financial options are similar, but instead of number of rounds being variable, it is the underlying spot price’s volatility. Options written on an underlying asset derive their value from the volatility of that asset’s price, for example, the price of a barrel of oil. Oil is a commodity that is highly traded and the price of oil is hotly debated. Big moves in the price of oil are much more likely that a big move in the price of milk; therefore, options on oil are more expensive than options on milk. The price of an option is called premium.

A call option is the right to buy the underlying asset at a certain price. For example, my view is that milk is undervalued, at \$2 bucks a gallon. One option would be to buy 10 gallons of milk and hold onto them until the price rises. However, I’d have to store the milk, keep it cold, and also make sure it doesn’t go bad before I sell it. All these things cost money, and diminish my profits. By buying a call option on milk, I can eliminate these costs. I’m betting that the price of milk will rise. I buy a call on milk at a strike price of \$2. This means I’ve just bought the right to buy milk at \$2, sometime in the future. To buy this right, I will pay the seller premium. If the price of milk goes to \$2.50 like I planned, I’ll exercise the option, buy milk at \$2 then sell it at \$2.50. My profit is:

If the option goes unexercised, meaning the price of milk moves in the opposite direction, say to \$1.50, then my option expires worthless and I’m only out premium. I don’t have an obligation to buy the milk at \$2.00, just the option. Profit in this example would be: