cityboy Wrote: ------------------------------------------------------- > > Many pricing models (e.g. Black Scholes) actually > suppose that investors are risk neutral. absolutely no model ever makes such outrageously flawed assumption! risk-neutrality comes into being for other reasons as bchad mentioned
Mobius Striptease Wrote: > absolutely no model ever makes such outrageously > flawed assumption! risk-neutrality comes into > being for other reasons as bchad mentioned You are wrong. Google “risk neutral model” and you’ll find lots of models which assume risk-neutrality. In fact, the Black Scholes model doesn’t directly assume risk-neutrality, but you use risk neutral pricing to solve the Black Scholes equation.
MattLikesAnalysis Wrote: > isn’t this because BS is only useful for a limited > time period (less than a year or two). in the > short-term, its impossible to assess with high > probability, the return of a specific asset class. > thus why the risk premium on equity can only > really be captured with a certain level of > certainty in the long-run and why day and swing > trading is assumed to be a zero-sum game… The main reason is that risk-neutral pricing makes solving the equation easier. Of course, it’s just an assumption; it’s pretty clear that equities outperform bonds in the long run, which means that the assumption of risk-neutrality is not valid in the real world.
cityboy, dont confuse “using risk-neutrality principle in order to price derivatives” with “making the assumption that investors are risk-neutral”. the former is a lot deeper concept grounded in theory, the latter is layman’s explanation of why the cost of equity doesn’t show up in Black Scholes and is completed wrong
The model prices options “as if” investors are risk neutral. That doesn’t mean that the model assumes that investors are risk neutral. It’s just a short cut to a longer argument that results in the same thing. The key to arbitrage pricing is that - as long as markets are liquid and transaction costs are negligible - arbitrage pricing trumps ordinary supply/demand type pricing. You can create a replicating portfolio for an option by dynamic hedging. The price of that portfolio is what determines the price of an option, no matter how risk averse the market is. Why? Because if you see an option at a different price, you buy it or sell it, and then create the appropriate replicating portfolio. The result is free money. So pick up free money until the price of the option equals the price of the replicating portfolio. The value of [(option) - (replicating portfolio)] has zero risk to it, as long as the assumptions above hold. That’s why it’s priced “as if” investors are risk neutral. That doesn’t mean we think investors actually are risk neutral. It just means that if an investor insists on an option price that reflects risk aversion, someone else will offer that option to them and make money on it. This is why selling options is (usually) such a profitable business. Many buyers actually are risk averse and therefore prone to want them at a price that is profitable for a risk-neutral (because they can create the replicating portfolio and take no risk) hedger to provide. It all falls apart, however, when markets start to gap and become illiquid and transaction costs rise. At this point, it becomes expensive or impossible to create the replicating portfolio and the fund, bank, or whoever blows up, often quite spectacularly.
Mobius Striptease Wrote: ------------------------------------------------------- > cityboy, dont confuse “using risk-neutrality > principle in order to price derivatives” with > “making the assumption that investors are > risk-neutral”. the former is a lot deeper concept > grounded in theory, the latter is layman’s > explanation of why the cost of equity doesn’t show > up in Black Scholes and is completed wrong I already corrected myself.
The comments regarding utility are all true, and likely the primary driver behind investors choosing the less risky option among choices with equal expected returns. However, a secondary driver is that over multiple periods, an investment with lower volatility provides a higher return. For example, a guaranteed 10% annual return will increase in value by 46.4% over 4 years, but an investment that returns 20%, 0%, 20%, 0% (in any sequence) will only return 44.0%, despite having the same mean. In addition to the behavioral responses to capital loss, it’s mathematically a better option to minimize risk.
Since their conception, risk and return have immatured into a jocuserious fanzine-journal-orphanage based on true stories deeply concerned with art-design-music-language-literature-architecture and uptight optipessimistic stoppy/revelatory ghostwriting by friendly spirits mapping b-sides and out-takes pushing for a resolution in bleak midwinter through late summer with local and general aesthetics wound on an ever tightening coil.
Bchad you are a maestro with words sir.
Thank you.
tkpk, excellent point, never thought that way