Session 4: Defining and Measuring Risk

Session 4: Risk and Return Models in Finance

In this session, we will define risk as a central measure in any financial decision. We will look at conventional definitions of risk and how financial theory measures it. We will also start a discussion of hurdle rates and set up the estimation questions that will be coming up in the next few sessions.

Defining Risk

• A benchmark is needed to break even on an investment.

• The hurdle rate for an investment has two components: the riskless rate and a risk premium.

• Risk is equal to danger plus opportunity.

• Corporate finance measures the danger in an investment and asks how much opportunity is needed to compensate for taking that danger.

Risk and Return Models

• The first two steps in deriving risk and return models are exactly the same for every model.

• Define risk as the deviation of actual returns around an expected return.

• Use this definition to calculate variance, standard deviation, beta, or any other measure of risk.

Conclusion

In this session, we defined risk as a central measure in any financial decision. We looked at conventional definitions of risk and how financial theory measures it. We also started a discussion of hurdle rates and set up the estimation questions that will be coming up in the next few sessions. Finally, we discussed how to derive risk and return models using a common framework.

The Tradeoff Between Risk and Return

In this section, the speaker discusses the concept of risk in investments and how it affects returns. He explains that all risk is in the future and defines risk as the deviation of actual returns around an expected return.

Defining Risk

• The answer is always going to be half a percent for a truly riskless investment.

• A ten-year T-bond is not risk-free if you're looking at a one-year time horizon.

• Stocks are very risky investments because you can never be sure what return you will make.

Types of Risks

• All risks are in the future, and there is no risk in the past.

• There are two types of risks: firm-specific risks that affect only a few companies, and market risks that affect most or all companies.

• Market risks cannot be diversified away, while firm-specific risks tend to average out across your portfolio.

CAPM Model

• The Capital Asset Pricing Model (CAPM) assumes there are no transaction costs and nobody knows which stocks are cheap or expensive.

• The CAPM model uses beta to capture an investment's risk added to the market portfolio.

Measuring Market Risk

In this section, the speaker discusses different models for measuring market risk and their limitations.

Arbitrage Pricing Model

• The arbitrage pricing model allows for multiple sources of market risk to be measured against each other separately.

• The model uses multiple unnamed economic factors and betas against each one to come up with a hurdle rate.

• The factors remain unspecified, making it difficult to have an intuitive feel for the model.

Multi-Factor Models

• Multi-factor models try to attach macroeconomic names such as interest rates, term structure, inflation, GDP growth to those factors.

• These models do better in explaining the past but are limited by the instability of the macroeconomic factors that drive stock prices.

Proxy Models

• Eugene Fama and Ken French developed proxy models that let the market tell us what risk is by looking at a long period of stock price history to see what kinds of companies had earned high returns.

• They made a leap of faith that small market cap companies are riskier than large market cap companies and low price-to-book companies are riskier than high price-to-book companies.

• These models effectively give up on measuring risk and let something else stand in.

Critiques of CAPM

In this section, the speaker discusses critiques of CAPM (Capital Asset Pricing Model).

Unrealistic Assumptions

• The first critique is that CAPM makes unrealistic assumptions. However, having unrealistic assumptions doesn't bother the speaker because he would rather have a model with unrealistic assumptions that he can use rather than one that makes realistic assumptions that nobody can use.

Parameter Errors

• The second critique is that the speaker's parameters might be wrong, his data might be wrong, his risk rate might be wrong, or his risk premium might be wrong. However, anytime you're estimating the future, you are going to be wrong.

Model Doesn't Work Well

• The third critique is that the model doesn't work very well. Beta should explain most of the differences in returns across stocks over very long time periods but it doesn't.

• Fama-French proxy models were developed as a response to this critique and try to find something that does better than beta.

The CAPM Model

In this section, the speaker discusses the flaws of the CAPM model and why it is still used despite its limitations.

Flaws of the CAPM Model

• The alternatives to the CAPM model are just as flawed.

• Other models might do better at explaining the past, but they are not much better at explaining the future.

• The speaker prefers a flawed hurdle rate with one beta over a multi-factor model or proxy model with five betas.

• The speaker sees the CAPM as a tool that does at least as good a job as any other model out there.

Using Models to Estimate Hurdle Rates

• Before using any models, it is important to determine whether the marginal investor in your company is well-diversified.

• Institutional investors are often diversified and trade shares in large-market companies around the globe with high trading volume.

• Assuming that the marginal investor is diversified allows for focusing on risk that cannot be diversified away and bringing it into hurdle rates.

Conclusion

• If a more pragmatic or better model for measuring risk and coming up with hurdle rates becomes available, then using it would be preferred over using CAPM.

• Focusing only on risks that cannot be diversified away and bringing them into hurdle rates is an important first step.