Risk Management in Turbulent Times

By Gilles Bénéplanc; Jean-Charles Rochet | Go to book overview

7
Risk Neutral Valuation

Risk neutral valuation (RNV) is a very elegant method for pricing risky securities. It was elaborated for the pricing of options and other derivatives, but it can be applied to many other questions such as determining the profitability of a risky investment or assessing the value of complex securities. The reasons for the popularity of RNV are its simplicity and, more importantly, the fact that it allows determination of risk premiums (how much financial markets require to bear different risks) without any knowledge of economic fundamentals. But this is too good to be true. The method relies on two assumptions that are completely unrealistic: all risks are traded on active markets (market completeness) and trade is efficient (no frictions nor transaction costs).

This chapter explores the magic of perfect markets and shows that these two assumptions imply that the RNV method is indeed valid. However, it also shows the mirages of the perfect markets world: putting too much faith into these assumptions leads to some crude fallacies: “maturity transformation is not risky,” “leverage does not matter,” and “risk management is useless!”


7.1 THE EXPECTED PRESENT VALUE CRITERION

The simplest tool used in finance to evaluate an investment is to compute the expectation of the net present value of future cash flows generated by this investment—for example, a project that needs an investment of I = 100 and provides expected cash flows of 60 in each of the next 2 years. Its expected (net) present value is:

When the interest rate, r, used to discount future cash flows is 5%, we obtain a positive value:

This suggests that the investment should be undertaken. However this computation does not take into account the risk of future cash flows, because a random cash flow

is valued identically to a certain cash flow with the same mean

In practice, investors usually require a higher rate of return on risky investments. For example, stocks, which are more volatile than bonds, typically have higher returns (on average, over a long period). The difference is called a risk premium. Similarly, corporate bonds, which are subject to default risk, have higher nominal returns than government bonds, which are normally immune to default.1 The difference in returns is called the corporate spread: it is usually bigger than what a simple estimation of the probability of default would imply.

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