#### GoPro Inc (GPRO) Valuation: The Options Tell the Story by Bradford Cornell and Andrew Cornell

The stock performance of GoPro Inc (NASDAQ:GPRO) has been stunning. Rising from an IPO price of \$24 earlier in the year to over \$80. All this based on the production of action cameras, a market in which there are few barriers to entry. It seems like a screaming short, but not so fast. There is a problem and it can be seen by looking at the option market.

As part of his research on options, Nobel Prize winner Robert Merton derived what has come to be called the put-call parity relation. Merton showed that in properly functioning markets the current option price S, the put price, P, the call price, C, the option strike price K (for puts and calls with the same strike price), and the interest rate, r, are tied together by an arbitrage relation which can be written as,

C + K*exp(-r*T) = P +S,

where T is the time to maturity for the options.

Because put-call parity requires no more than the proper functioning of the market for the relevant securities, it tends to hold within tight bounds. Rarely are discrepancies of 10% or more observed between the price of an option and the price implied by put-call parity.

### GoPro’s  put options exceeded their put-call parity price

But not so for GoPro Inc (NASDAQ:GPRO). The figure below plots the percentage by which the price of January 17, 2015 put options exceeded their put-call parity price during the period from August 1, 2014 through September 25, 2014. The results are dramatic. On August 1, the market price exceeded by 28% and the discrepancy rises from there to a maximum of 243% on September 25. Such massive discrepancies are virtually unprecedented.

Given the massive discrepancies, Merton’s work implies that investors can make risk-free returns on the order of 100%. But there is a catch. The arbitrage position required to exploit the discrepancy requires shorting the stock. As the current authors discovered, borrowing the stock proved to be extraordinarily expensive. Demand for shares to short was so great that security firms were charging a fee of 100% per year to borrow the stock. This fee essentially eliminates the possibility of pure arbitrage. Such massive fees are also further evidence that the market for the stock is not functioning properly.

The bottom line is that the option market is flashing warning lights that say investors should approach the stock with great caution. The combination of a sky high price relative to earnings and the dramatic rise in the cost of put options compared to put-call parity suggest that a sharp drop in the stock price is a distinct possibility.