Investment Expected Value and Probabilities

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Questions and Answers

What represents the expected value of an investment?

The highest possible outcome

The most probable outcome (correct)

The average of the outcomes (correct)

The sum of all possible outcomes

How do you calculate the expected value for the $1,000 investment scenario?

0.1 × $100 + 0.4 × $700 + 0.4 × $1,400 + 0.1 × $2,000 (correct)

0.2 × $1,000 + 0.3 × $1,400 + 0.2 × $700 + 0.3 × $2,000

0.1 × $2,000 + 0.4 × $1,400 + 0.4 × $700 + 0.1 × $100

0.1 × $100 + 0.4 × $1,400 + 0.4 × $700 + 0.1 × $1,000

What indicates that one investment is riskier than another?

Lower probabilities of payoffs

Wider range of outcomes (correct)

Higher expected value

More potential for loss

What is a risk-free asset?

An investment with a guaranteed return Signup and view all the answers

What is the first step in calculating variance?

Compute the expected value Signup and view all the answers

In the context of investment, what does variability refer to?

The range of possible outcomes Signup and view all the answers

What is the formula for calculating expected value based on probabilities and payoffs?

Weighted average of outcomes based on probabilities Signup and view all the answers

Which of the following describes how risk is assessed in investments?

By determining the potential payoffs and their probabilities Signup and view all the answers

What is the primary purpose of calculating the internal rate of return when considering the purchase of the machine?

To compare the present value of revenues to the cost of the machine Signup and view all the answers

What would be the outcome if the interest rate for borrowing is equal to or greater than 8.14%?

You should not purchase the machine Signup and view all the answers

What does the internal rate of return represent in the context of the machine investment?

The discount rate that makes the present value of cash inflows equal to investment cost Signup and view all the answers

What is a coupon bond primarily characterized by?

It mandates annual interest payments known as coupon payments Signup and view all the answers

In the context of a preventable future disaster, what factor is essential for assessing expected losses?

Discount rates and scale of future losses Signup and view all the answers

What is the maturity date of a bond?

The date on which the final repayment of the loan occurs Signup and view all the answers

What impact does certainty about revenue have on the decision to purchase the machine?

It simplifies the calculation of the internal rate of return Signup and view all the answers

If the machine generates $150,000 per year for ten years, what is the total revenue generated over its lifespan?

$1.5 million Signup and view all the answers

What is the present value (PV)?

The amount that must be invested today to achieve a specific future value. Signup and view all the answers

How does increasing the future value affect present value?

It increases present value. Signup and view all the answers

What happens to present value if the interest rate increases?

Present value decreases. Signup and view all the answers

If no changes are made to the payment amount or interest rate, what is the effect of changing the time period until payment?

Longer time periods reduce present value. Signup and view all the answers

What is the compound annual rate if an investment grows at 0.5% per month?

6.17% Signup and view all the answers

What is one factor that leads to a higher present value?

A shorter time until payment. Signup and view all the answers

What equation expresses the relationship between future value (FV) and present value (PV)?

FV = PV × (1+i) Signup and view all the answers

In the context of present value, what effect does doubling the future value have on present value if all other factors remain constant?

It doubles the present value. Signup and view all the answers

What is the expected value computed based on the given scenario?

$1,050 Signup and view all the answers

What is the result of subtracting the expected value from the higher payoff?

$350 Signup and view all the answers

What does the standard deviation measure in the context of investments?

Risk of an investment Signup and view all the answers

How is variance related to standard deviation?

Variance is the square of standard deviation. Signup and view all the answers

What is Value at Risk (VaR) focused on?

The worst possible loss at a given probability. Signup and view all the answers

What does a higher standard deviation indicate in an investment scenario?

Higher risk Signup and view all the answers

In terms of investment, why is standard deviation preferred over variance?

It is expressed in normal units. Signup and view all the answers

What aspect does VaR ignore when assessing risk?

The average loss over time Signup and view all the answers

What is the primary reason why risk-averse investors avoid certain investments?

They dislike the uncertainty associated with riskier investments. Signup and view all the answers

What is a defining characteristic of systematic risk?

It affects the entire economy. Signup and view all the answers

Which of the following best describes idiosyncratic risk?

Risk that impacts only a single sector or individual. Signup and view all the answers

What happens when an investor fails to diversify their investments?

They become more exposed to idiosyncratic risks. Signup and view all the answers

What is meant by the term 'risk premium'?

The additional return required by investors to hold a risky asset. Signup and view all the answers

Why might a rise in oil prices be considered both an idiosyncratic risk and a systemic event?

It can produce varied effects on different sectors of the economy. Signup and view all the answers

What strategy can help reduce idiosyncratic risk for an investor?

Diversifying investments across various assets. Signup and view all the answers

What risk do traders refer to when they mention 'blowing up'?

Facing a total loss due to high-risk trading. Signup and view all the answers

Study Notes

Expected Value

Expected value represents the mean outcome of an investment, calculated as the sum of probabilities multiplied by payoffs.
Example calculation: Expected Value = 0.5 × $700 + 0.5 × $1,400 = $1,050.
Investment scenarios can include various outcomes with specified probabilities, allowing a calculated expected value.

Investment Scenarios

An investment of $1,000 may have various outcomes and probabilities:
- Rise to $2,000 (0.1 probability)
- Rise to $1,400 (0.4 probability)
- Fall to $700 (0.4 probability)
- Fall to $100 (0.1 probability)
Overall expected value: 0.1 × $100 + 0.4 × $700 + 0.4 × $1,400 + 0.1 × $2,000 = $1,050.

Risk Measurement and Variability

Higher variability in returns signifies increased risk, making comparison between investment options essential.
A risk-free asset guarantees a known future value and a fixed rate of return.
Understand risk by measuring the spread of outcomes through variance and standard deviation calculations.

Variance and Standard Deviation

Variance measures the average of squared deviations of possible outcomes from their expected value, weighted by their probabilities.
Steps to compute variance:
- Calculate expected value.
- Find deviation from expected value for each outcome and square it.
- Multiply the squared result by the respective probability and sum them.
Standard deviation, the positive square root of variance, is more applicable in practical financial analysis.

Present Value

Present value (PV) refers to the current worth of an amount to be received in the future, discounted at a specific interest rate.
Formula: PV = FV / (1 + i)^n where FV is future value, i is interest rate, and n is the number of periods.
Influenced by:
- Higher future value increases present value.
- Shorter time periods until payment raise present value.
- Lower interest rates elevate present value.

Internal Rate of Return (IRR)

For projects, IRR is the interest rate that makes the present value of future cash flows equal to the initial investment.
Example: Machine costing $1 million generates $150,000 annually for ten years.
IRR calculated through cash flow analysis, crucial for investment decision-making.

Value at Risk (VaR)

VaR assesses the potential loss in an investment under worst-case scenarios over a specified time frame at a defined probability.
Useful for evaluating risks like mortgages, focusing on maximum losses instead of averages.

Risk Types and Aversion

Risks categorized as idiosyncratic (unique to specific individuals or sectors) or systematic (affecting the entire economy).
Risk-averse individuals prefer certain returns over uncertain ones, incurring a risk premium on risky investments.

Diversification as a Risk Management Strategy

Diversification mitigates idiosyncratic risks through broader exposure across various investments.
Protects against severe losses from individual investments, reducing overall portfolio risk.

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Description

This quiz covers the concepts of expected value in finance, including how to calculate the average outcome based on probabilities and payoffs. You'll learn to apply these principles to real investment scenarios and understand their implications. Test your knowledge on the formulas and practical applications of expected value.