Pricing Kernels Defined in Relation to Asset Pricing

Pricing Kernels Defined in Relation to Asset Pricing The asset pricing kernel,  also known as the stochastic discount factor (SDF), is the random  variable that satisfies the function used in computing the price of an asset. Pricing Kernel and Asset Pricing   The pricing kernel, or stochastic discount factor, is an important concept in mathematical finance and financial economics. The term  kernel  is a common mathematical term used to represent an operator, whereas the term stochastic discount factor  has roots in financial economics and extends the concept of the kernel to include adjustments for risk. The fundamental theorem of asset pricing in finance suggests that the price of any asset is its discounted expected value of future payoff specifically under risk-neutral measure or valuation. Risk-neutral  valuation can only exist  if the market is free of arbitrage opportunities, or opportunities to exploit price differences between two markets and profit from the difference. This relationship between an assets price and its expected payoff is considered the underlying  concept behind all asset pricing. This expected payoff is discounted by a unique factor that depends upon the framework set forth by the market.  In theory, risk-neutral valuation (in which there is an absence of arbitrage opportunities in the market) implies the existence of some positive random variable or the stochastic discount factor. In risk-neutral  measure, this positive stochastic discount factor would theoretically be used to discount the payoff of any asset. Additionally, the existence of such a pricing kernel or stochastic discount factor is equivalent to the law of one price, which presumes that an asset must sell for the same price in all locales or, in other words, an asset will have the same price when exchange rates are taken into consideration. Real-Life Applications Pricing kernels have numerous uses in mathematical finance and economics. For instance, pricing kernels can be used to produce contingent claim prices. If we were to know the current prices of a set of securities in addition to the future payoffs of those securities, then a positive pricing kernel or stochastic discount factor would provide an efficient means of producing  contingent claim prices assuming an arbitrage-free market. This valuation technique is particularly helpful in an incomplete market, or a market in which total supply is not sufficient to meet the demand. Stochastic Discount Factors Apart from asset pricing, another use of the stochastic discount factor is in the evaluation of the performance of hedge funds managers. In this application, however, the stochastic discount factor would not strictly be considered the equivalent to a pricing kernel.

Blue-sky still appeals - Emphasis

Blue-sky still appeals Blue-sky still appeals Corporate jargon and management buzzwords are persistent pests. We train around two thousand people a year in business-writing skills. But weve yet to meet anyone who likes phrases like paradigm shift or blue-sky thinking. Raising the bar and low hanging fruit sound more like some kind of tropical limbo challenge than anything to do with the business world. And still the corporate world continues to embrace such phrases. Nor is the public sector immune: phrases such as step change and going forward seem as common there as in the commercial world (if not more so). Maybe its a confidence issue. These impressively meaningless words and phrases give people and organisations a misplaced sense of professionalism or belonging. Organisations even adopt their own personalised brand of corporate jargon as some kind of employee bonding tool. Unfortunately, it often has the opposite effect when people start to use the jargon to get one over on their bemused colleagues, who lack the courage to ask what these phrases actually mean. Management consultants may be partly to blame too, especially where they influence language at board level, which then trickles down to managers. One civil service manager we spoke to said that its almost a hopeless case in some instances: he couldnt see his department ever letting go of stakeholder, for example, even though he believed people used such jargon as a substitute for thinking. But there is a growing contempt for this kind of language, underlined by a strong suspicion that it is often used to mask inexperience and a lack of expertise. So well continue to campaign for people to turn their backs on corporate buzzwords and replace them with clear, direct and concise language that actually means something.