The notion of “arbitrage-free” pricing is important not only in Finance 4366, but also in your other finance studies. In Finance 4366, we take it as given that investors are *risk averse*. However, it turns out that we don’t need to invoke the assumption of risk aversion in order to price risky securities such as options, futures, and other derivatives; all we need to assume is that investors are “greedy” in the sense that they prefer more return to less return, other things equal. Through a variety of trading strategies, we can *synthetically *replicate any security we want, and do so in such a way that we (in theory anyway) are able to take no risk, incur zero net cost of investment, and yet earn positive returns.

Without question, the notion of arbitrage-free pricing is THE key concept in Finance 4366. However, it is also important in corporate finance. For example, the famous Modigliani-Miller Capital Structure Theorem; i.e., that the value of a firm’s shares is unaffected by how that firm is financed, is based upon this principle. For your personal enjoyment and intellectual edification, I attach a copy of a short (3 page) teaching note which provides a “no-arbitrage” proof based upon a simple numerical example:

The Modigliani-Miller Capital Structure Theorem – A “No-Arbitrage” Proof

*Related*