Decision Making: Expected Value

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Questions and Answers

What is the concept of expected value in the context of decision making, and how is it used by risk-neutral individuals?

Expected value is a concept borrowed from statistics, representing the average amount one would earn by playing a lottery many times. It is used as a benchmark for deciding when to play a lottery instead of choosing a safe option, and it is based on the object itself, not the person choosing. Risk-neutral individuals use expected value to make decisions based solely on calculation.

What does the certainty equivalent (w) represent in the context of decision making under uncertainty, and how does it relate to risk preferences?

The certainty equivalent (w) represents the maximum willingness to pay for a lottery, and it is used to determine an individual's risk preference. If w < EV, the individual is risk-averse; if w = EV, they are risk-neutral; and if w > EV, they are risk-seeking.

What is the risk premium, and how does it relate to an individual's risk aversion?

The risk premium is the difference between the expected value (EV) and the certainty equivalent (w), and it is a quantitative expression of an individual's risk aversion. It represents how much an individual would need to be paid to choose a risky option over a safe one.

What is the purpose of insurance in the context of decision making under uncertainty, and who is more likely to purchase it?

Insurance allows individuals to pay a third entity to take on some risk, reducing their exposure to uncertainty. Individuals who are highly risk-averse are more likely to purchase insurance, as it provides a sense of security and reduces their risk exposure. Signup and view all the answers

What is diversification, and how does it reduce risk exposure?

Diversification is the practice of splitting risk over two or more independent and identically distributed lotteries, reducing the overall risk exposure. This is achieved by multiplying the probabilities of an event occurring, resulting in a lower risk with the same expected value. Signup and view all the answers

What is the effect of diversification on the possible outcomes of an event?

Diversification moves the possible outcomes of the event from the extremes to the center, reducing the risk. Signup and view all the answers

How does pooling protect a community from risk?

Pooling, where two or more people put their earnings in one single pool and equally divide it, protects the whole community from risk by providing a sort of social insurance. Signup and view all the answers

What is an example of aggregate risk?

Unemployment is an example of aggregate risk, as it affects the whole market and cannot be diversified or pooled. Signup and view all the answers

Why is diversifiable risk essentially irrelevant in the valuation of securities?

Diversifiable risk is essentially irrelevant in the valuation of securities because investors can almost eliminate it by constructing portfolios that contain a large number of assets, each of which has a very small weight. Signup and view all the answers

What is the difference between systematic risk and diversifiable risk?

Systematic risk arises from shocks that affect large classes of securities simultaneously and cannot be diversified, whereas diversifiable risk can be eliminated by constructing a diversified portfolio. Signup and view all the answers

Study Notes

Uncertainty and Decision Making

Expected value (EV) represents the average amount earned by playing a lottery many times, used as a benchmark for deciding between a lottery and a safe option.
EV has nothing to do with personal preferences, but rather the object itself.
People can be risk-neutral, risk-averse, or risk-seeking, with different preferences influencing their decision-making.

Risk and Preferences

Certainty equivalent (w) represents the maximum willingness to pay for a lottery.
If w < EV, the person is risk-averse.
If w = EV, the person is risk-neutral.
If w > EV, the person is risk-seeking.
Risk premium is the difference between EV and w, quantifying a person's risk aversion.

Managing Risk

Insurance: paying a third entity to take on some risk, usually expensive and only beneficial for highly risk-averse individuals.
Diversification: "splitting the risk" by investing in multiple independent and identically distributed events, reducing risk and variance.
Pooling: combining earnings with others to protect the community from risk, similar to social insurance.

Types of Risk

Aggregate risk: affects everyone at the same time, such as unemployment, and cannot be diversified or insured.
Idiosyncratic risk: specific to an individual or firm, such as a successful drug trial, and can be diversified.
Systemic risk: threatens the entire financial system, such as a global economic crisis.

Assessing Risk

Diversifiable risk is essentially irrelevant in valuing securities, as investors can eliminate it by constructing diverse portfolios.
Systematic risk, affecting large classes of securities, cannot be diversified and is a significant concern.

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Description

Learn about the concept of expected value, borrowed from statistics, and its application in decision making. Understand how it's used to decide between taking a risk or playing it safe.