Briefly speaking, our conclusion is that stochastic volatility does not make a huge difference as far as the pricing is concerned if you get the average volatility right. It makes a big difference as far as hedging is concerned.
Companies typically borrow money at less than their return on equity and therefore compound their return at the expense of lenders.
What happened after publication of our paper was that, for the next 40 years, people said, all right, we now know the answer to the capital structure question under ideal conditions.
The transaction cost approach maintains that some projects are easy to finance by debt and ought to be financed by debt. These are projects for which physical-asset specificity is low to moderate.
There is no such thing as high returns without risk.
The rate of interest acts as a link between income-value and capital-value.
Optimization tells us precisely how to diversify the portfolio, whether I should have 12% in semiconductors or 4% in biotech, etc., and it literally tells me how to diversify not only the industry groups but the stocks.
The chief obstacle to success lies in the stubborn fact that if the favorable prospects of a concern are clearly apparent they are almost always reflected already in the current price of the stock. Buying such an issue is like betting on a topheavy favorite in a horse race. The chances may be on your side, but the real odds are against you.
It's important to understand how people perceive risk, and how that translates into investment behavior.
We next consider the rule that the investor does or should consider expected return a desirable thing and variance of return an undesirable thing.
A financial institution has the task of taking risks, and if it's a well run institution - say, Goldman Sachs - it tries to cover the potential losses to itself, but only to itself.
When rewards go up, people are more inclined to take risks.
Portfolio theory, as used by most financial planners, recommends that you diversify with a balance of stocks and bonds and cash that's suitable to your risk tolerance.
That economic decisions are made without certain knowledge of the consequences is pretty self-evident. But, although many economists were aware of this elementary fact, there was no systematic analysis of economic uncertainty until about 1950.
Our entire approach to the banking and financial services business is risk-adjusted returns. We believe that in most parts of the world, and including pockets in India, banking tends to mis-price risk.
There are some risks we choose to take because the benefits from taking them exceed the possible costs. Optimal behavior takes risks that are worthwhile. This is the central paradigm of finance: we must take risks to achieve rewards, but not all risks are equally rewarded.
Most people have an aversion to risk, my college economics professor told me. Which means they have to be rewarded to take on that risk. The higher the risk, the higher the possible payout has to be for people to jump.
Large credit guarantees also impede optimal allocation of financial resources and increase moral hazard.
Peer-to-peer lenders originally sought to attract retail investors to its loan marketplace, but the lack of high-returning assets elsewhere in the market has made these platforms increasingly attractive to major asset managers and hedge funds.
