An asset is nothing else than the right to future cash flows, whether they are interest payments from bonds, dividend payments from stocks, insurance payments, or capital gains from investments.
To price an asset, all you need to do is figure out the present value of those future cash flows. Why? Because a dollar today is worth more than a dollar tomorrow.
But what happens when you don’t know the value of those future cash flows? Or you have an expected value in mind but are not sure it will be paid?
This is the challenge of asset pricing.
It means those cash flows are risky, as they are uncertain.
For example, interest payments depend on the entity you lent money to being solvent, dividend payments depend on the strength of the company, and gains from investments depend on the success of the project.
The major question in finance is: How do we value a risky cash flow?
When market participants don’t care about risk, you can discount the expected future cash flow at the risk-free rate. But that’s never the case. You must take risk and uncertainty into account, and you can do it in one of four ways:
- Discount the expected cash flow at a rate that is the risk-free rate increased by a risk premium.
- Correct the cash flow itself to decrease it by a certain risk or insurance premium, and discount at the risk-free rate.
- The random cash flows likely follow a normal or binomial distribution. You can distort that distribution of the expected cash flow so it justifies discounting at the risk-free rate.
- Figure out the value of the future cash flow for different states of nature. Attribute a probability to each state of nature, multiply the monetary outcome of each event by its probability (expected value), and sum all expected values together.
These methods depend on theories explaining how to compute risk premiums (1 and 2), how to identify the distorted probability distribution (3), or how to price future dollars state by state (4).
But there’s a more fundamental way of organizing different valuation theories:
The equilibrium approach and the arbitrage approach include all these 4 cases under them.
The equilibrium approach involves analyzing supply, demand, and market structure for the cash flow (asset) in question.
If the market is competitive, you get the equilibrium price by matching supply and demand.
For financial instruments, we assume the supply is fixed. Why? Because companies determine equity and debt, not the market.
This means our analysis will focus on the demand for financial assets—investors’ preferences (utility function) and their attitudes toward risk (risk aversion).
The arbitrage approach values a cash flow based on the values of the many elements that make up that cash flow (asset).
It says the price of an asset must be equal to the sum of the price of all the components that make up the asset, otherwise there’s an arbitrage opportunity.
This approach is a complement to the equilibrium approach, because where else do you get the prices for the components if not through the equilibrium approach?
The two approaches are not mutually exclusive and can be combined.
