ABSTRACT When raising new equity capital managers have historically rejected the direct offer method favoring instead the seemingly more expensive underwritten public issue. This paper provides a resolution for this equity financing paradox by demonstrating empirically that firms which engage in direct offers enjoy a comparative cost advantage that is more than sufficient to account for the absolute reported cost differences between the two methods of equity financing.

ABSTRACT Asset prices contain information about the probability distribution of future states and the stochastic discounting of those states as used by investors. To better understand the challenge in distinguishing investors' beliefs from risk‐adjusted discounting, we use Perron–Frobenius Theory to isolate a positive martingale component of the stochastic discount factor process. This component recovers a probability measure that absorbs long‐term risk adjustments. When the martingale is not degenerate, surmising that this recovered probability captures investors' beliefs distorts inference about risk‐return tradeoffs. Stochastic discount factors in many structural models of asset prices have empirically relevant martingale components.