REAL-WORLD AND RISK-NEUTRAL EXPECTATIONS OF MARKETS

The expectations for the future evolution of market risk factors are a fundamental concept in financial market analysis. All values and expected liquidity build on the expected future performance of the underlying market risk factors.

The view of the real-world expectations of economic probability is looking at the future by taking into account the past and/or by deterministically or stochastically defining future scenarios to figure out the possible future outcomes of value and liquidity. In fact, real- world expectations are considering real-world probabilities, which can be determined through empirical studies. We can model them with economic scenario generator models, for example. Naturally, such models include future uncertainties of the market risk factors within the time evolution. These risk factors adjust their values according to market conditions.

Deterministic economic scenarios should be based ideally on nonbiased and more or less realistic assumptions that consider quantitative variables such as money supply, unemployment rate but also qualitative idiosyncratic factors of market behavior. Stochastic economic scenarios are mathematically driven and simulate the evolution and uncertainties of market risk factors.

Risk-neutral probabilities assume the absence of arbitrage. Based on the risk-neutral pricing approach, we can price an asset based on its expected payoff. With this, we can calculate the correct net present value (NPV) by discounting it with the risk-free interest rate. In the risk-neutral world, the present value V of a cash flow occurring at a future date t is given by the relatively straightforward formula (6.1)

where

r(t) is the compounded risk-free interest rate,

E is the risk-neutral expectation with respect to the risk-neutral probabilities, and

CF is the expected cash flow.

In risk-neutral valuations, the economic expectations of asset returns, or the probabilities of realistic economic scenarios, are irrelevant. Only the risk-neutral probabilities matter.

In summary, we can arrive at a valuation by using the following expectations:

■Risk-neutral expectations for cash flows and risk-free rates for discounting

■Real-world expectations for cash flows and risk-adjusted interest rates for discounting.

Risk-neutral valuation is mostly used by the analysts who are confident about the elegance of strictly mathematical approaches in an arbitrage-free “ideal little happy world.” Practically speaking, it is easier not to bother with the probabilities and real-world expectations and uncertainties. In normal and liquid markets, this works quite well. However, the ugly truth is that markets can be illiquid. Uncertainties may occur in the future, even in markets that were stable throughout history. For this reason, real-world expectations and risk adjustments will always drive future expected cash flows and values.

6.2