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## 2.4 Relationship of Risk and Return

Valuing financial assets under conditions of certainty is a breeze. The challenge is to value assets in the real world of uncertainty -- of risk. If we can relate risk and returns, such as by discounting returns depending on their risk, we can value them!

This section considers some basic methods. It sets the stage for our study of more sophisticated methods -- namely, the Capital Asset Pricing Model and the Arbitrage Pricing Theory.

2.4.1 - Valuing probability distributions

How does one value a distribution of possible returns? One method would be to estimate the relative probability of different future possibilities and then discount them to present value. For example, if we believed it was equally likely that an investment after one year would produce either \$5 or \$12 or \$20, and the current rate for a risk-free one-year investment were 6.3%, we could compute the investment's present value as follows. (More 2.4.1>>)

2.4.2 - Valuing certainty equivalents

Another method to value a range of future results is to find the present value of their "certainty equivalents." Return to our example of an investment that will return either \$5 or \$12 or \$20 after one year, with an assumed current rate of 6.3% for a risk-free one-year investment. Perhaps we could determine the expected value of this investment, and then determine the equivalent certain amount this investment is worth, given the variability of its returns. Once we determine this "certainty equivalent" we could then compute its present value -- thus. the investment's value. (More 2.4.2>>)

2.4.3 - Adjusting discount rates

Another method for valuing future returns is to focus on the volatility of the expected return and adjust the discount rate to account for this volatility. (In this way the discount rate compensates for two financial elements -- volatility risk and time value of money.) (More 2.4.3>>)

 Chapter Subsections 2.4.1 Valuing probability distributions 2.4.2 Valuing certainty equivalents 2.4.3 Adjusting discount rates

 2.3 Risk of Multiple Assets (Portfolio Risk) 2.5 Capital Asset Pricing Model (CAPM)
 This page was last updated on: March 16, 2004