We previously discussed implied dividend yield and how to extract it from traded financial instruments. Given that dividend is considered a cash payment the shareholder receives when holding a stock, naturally one would think that dividend yield can only be zero or positive. We recently, however, worked with a client whose implied dividend yield is negative. What does this mean?
In most of the equity derivative pricing models, the number of outstanding shares is treated as a constant. Reference , however, incorporated the number of shares as a variable within the context of dilution and stock buyback. It pointed out that stock buyback is viewed as providing a synthetic positive dividend yield, whereas dilution provides a synthetic negative dividend yield.
Our paper is one of the first to provide a theoretical link between payout policy and the pricing of listed derivatives. We have seen that dilutions can be viewed as synthetic negative dividends and buybacks as synthetic positive dividends. Options on equity are dilution protected, and for highly levered firms, they may be more valuable than equity itself. We have seen that dilutions and buybacks can cause the stock price distribution to dramatically depart from the shape of the equity distribution, and that prices of stock-based claims can, therefore, differ from prices of claims based on total equity.
That explains why we obtained an implied negative dividend for our client. They are an airline that suffered economic losses during the pandemic and needed to raise working capital by issuing a convertible bond through a private placement. The conversion of the convertible bond would dilute the outstanding shares up to 13%, which is a large number.
The article also established a relationship between the dilution effect and leverage of a firm. Dilution has a smaller effect in low-leverage firms than in high-leverage ones.
For low leverage, there are few dilutions and the percentage differences are very small, except at very low strikes. The difference increases with leverage, as large coupon payments cause more dilution, making call stock options cheaper and put stock options more expensive relative to their equity counterparts.
 Backwell, Alex and McWalter, Thomas and Ritchken, Peter H., On Buybacks, Dilutions, Dividends, and the Pricing of Stock-Based Claims (2019). https://ssrn.com/abstract=3422692