Finance Risk and Risk Premiums Quiz

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Questions and Answers

What does value at risk (VaR) primarily measure?

Average market return

Worst loss with a given probability (correct)

Expected gain on investment

Potential overall profit

Which of the following best describes a risk-free rate?

The expected return above all investments

The average return of all market securities

The rate with a high probability of loss

The rate of return that can be earned with certainty (correct)

What is the formula for calculating the Sharpe ratio?

Portfolio risk premium divided by standard deviation of excess returns (correct)

Risk premium divided by the average return

Expected return divided by variance

Standard deviation of excess returns divided by expected return

What is meant by risk aversion?

Reluctance to accept risk (A) Signup and view all the answers

What is the price of risk a measure of?

Risk premium to variance ratio (D) Signup and view all the answers

In mean-variance analysis, what is considered a better portfolio when comparing Sharpe ratios?

A higher Sharpe ratio (B) Signup and view all the answers

Which term refers to the expected return in excess of that on risk-free securities?

Risk premium (D) Signup and view all the answers

How is excess return defined?

Rate of return in excess of risk-free rate (A) Signup and view all the answers

What does the Holding-Period Return (HPR) formula calculate?

Discrete rate of return over a specific investment period (A) Signup and view all the answers

How is the HPR for an investment calculated?

HPR adds the net price change to the dividends received and divides by the initial price. (B) Signup and view all the answers

What is the result of calculating the HPR for a stock bought at $25, sold for $27, with $1.25 in dividends?

13% (C) Signup and view all the answers

What does the geometric average return provide?

A single per-period return representing cumulative performance (B) Signup and view all the answers

Which return calculation method gives the internal rate of return on an investment?

Dollar/SAR-weighted average return (A) Signup and view all the answers

What is the formula for the arithmetic average return?

Total returns in each period divided by the number of periods (B) Signup and view all the answers

When considering multiple periods of return, what does the geometric average differ from in terms of performance measurement?

Total return over the entire investment duration (A) Signup and view all the answers

In investment analysis, which of the following statements is true regarding a Holding-Period Return of 13%?

It indicates the investment's performance over the entire holding period. (A) Signup and view all the answers

What is the formula for the Effective Annual Rate (EAR) when compounding is continuous?

EAR = e^{APR} - 1 (A) Signup and view all the answers

How is the Annual Percentage Rate (APR) calculated when using continuous compounding?

APR = ln(EAR + 1) (C) Signup and view all the answers

What does the term 'rReal' represent in the nominal and real interest rates relationship?

Real Interest Rate (C) Signup and view all the answers

If an investment has a nominal interest rate of 10% and inflation is 5%, what is the real rate of return?

4.8% (D) Signup and view all the answers

Which equation correctly relates nominal interest rate, real interest rate, and inflation?

1 + rNom = (1 + rReal)(1 + i) (B) Signup and view all the answers

What does an increase in nominal interest rates typically correspond with, based on historical trends since the 1950s?

Increase in inflation rates (A) Signup and view all the answers

In the case of volatile inflation in the 1930s/1940s, how did it affect real rates of return?

Led to fluctuations in real rates of return (C) Signup and view all the answers

When calculating APR using compounded interest, what variable represents the number of compounding periods?

n (B) Signup and view all the answers

What is the arithmetic average of the returns 10%, 25%, -20%, and 20%?

8.75% (C) Signup and view all the answers

What does the geometric average represent in terms of investment performance?

The single period return equivalent to cumulative performance (A) Signup and view all the answers

Which formula is used to calculate the geometric average of returns?

$[(1 + r1) imes (1 + r2) imes ... imes (1 + rn)]^{1/n} - 1$ (D) Signup and view all the answers

How is the annual percentage rate (APR) calculated?

Per-period rate multiplied by periods per year (A) Signup and view all the answers

What is the primary difference between the effective annual rate (EAR) and the annual percentage rate (APR)?

EAR includes compounding, while APR does not (D) Signup and view all the answers

What type of average return is known as the internal rate of return on an investment?

Dollar-weighted average return (B) Signup and view all the answers

Which of the following is true about the geometric average compared to the arithmetic average?

Geometric average is more applicable for volatile returns (C) Signup and view all the answers

In calculating rates of return, when is it appropriate to use the dollar-weighted average?

When cash flows vary unevenly over time (C) Signup and view all the answers

What does 'Asset Allocation' refer to in investment management?

Portfolio choice among broad investment classes (C) Signup and view all the answers

Which equation represents the Expected Return of the complete portfolio?

E(rC) = y * E(rp) + (1 - y) * rf (B) Signup and view all the answers

What is meant by 'Capital Allocation' in investment terms?

Choice between risky and risk-free assets (C) Signup and view all the answers

Which of the following is considered a risk-free asset?

Treasury bonds (B) Signup and view all the answers

What does the standard deviation of the complete portfolio represent?

The variability of returns related to risky assets (B) Signup and view all the answers

In the formula $\sigma_C = y × \sigma_P$, what does $\sigma_P$ represent?

Standard deviation of the risky portfolio (A) Signup and view all the answers

What is the relationship between the percentage of assets in a risky portfolio and its expected return?

Higher percentage leads to higher expected return (C) Signup and view all the answers

Which of the following statements about money market instruments is accurate?

They are considered effectively risk-free (C) Signup and view all the answers

Study Notes

Risk and Risk Premiums

Value at Risk (VaR): Measures downside risk. It represents the worst possible loss for a given probability (usually 1% or 5%).

Risk Premiums and Risk Aversion

Risk-Free Rate: The return earned with absolute certainty.
Risk Premium: Expected return exceeding the risk-free rate.
Excess Return: Return exceeding the risk-free rate.
Risk Aversion: Reluctance to take on risk.
Price of Risk: Ratio of risk premium to variance.

Mean-Variance Analysis

Uses Sharpe Ratio (reward-to-volatility ratio) to rank portfolios.
Higher Sharpe ratio indicates a more favorable portfolio.
Sharpe Ratio Formula:
- Portfolio Risk Premium / Standard Deviation of Excess Returns

Measuring Returns Over Multiple Periods

Arithmetic Average: Sum of returns divided by the number of periods, used for averaging returns.
Geometric Average: Single per-period return that gives the same cumulative performance as the sequence of actual returns, useful for showing compounding effects.
Dollar-Weighted Average Return: Internal rate of return on an investment, considers the timing and amount of cash flows.

Inflation and Real Interest Rates

Nominal Interest Rate: The stated interest rate without considering inflation.
Real Interest Rate: The nominal interest rate adjusted for inflation.
Real Interest Rate Formula: (1 + Nominal Interest Rate)/(1 + Inflation Rate) - 1
Historical US data shows that nominal rates have increased roughly in tandem with inflation.

Annualizing Rates of Return

Annual Percentage Rate (APR): Per-period rate multiplied by the periods per year, does not account for compounding.
Effective Annual Rate (EAR): The actual rate at which an investment grows, considering compounding.
EAR Formula (n Periods of Compounding): (1 + APR/n)^n - 1
EAR Formula (Continuous Compounding): e^(APR) - 1

Asset Allocation

Asset Allocation: Portfolio choice among broad investment classes (stocks, bonds, Treasury bills, etc.).
Complete Portfolio: Total portfolio, including risky and risk-free assets.
Capital Allocation: Decision between risky and risk-free investments.

The Risk-Free Asset

Treasury bonds are generally considered risk-free, although they are still subject to inflation risk.
Price-indexed government bonds and money market instruments are considered essentially risk-free.
CDs and commercial paper are considered low-risk compared to other asset classes.

Portfolio Asset Allocation: Expected Return and Risk

Expected Return of Complete Portfolio Formula: y * E(rp) + (1 - y) * rf
- y: Percentage of assets in the risky portfolio
- E(rp): Expected return of the risky portfolio
- rf: Return of the risk-free asset
Standard Deviation of Complete Portfolio Formula: y * σp
- σp: Standard deviation of the risky portfolio

Investment Opportunity Set

This represents the range of possible portfolio combinations, the relationship between expected return and risk for different portfolio allocations.

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Description

Test your knowledge on concepts of risk, risk premiums, and portfolio analysis. This quiz covers key topics such as Value at Risk (VaR), risk aversion, and the Sharpe Ratio. Get ready to challenge yourself with questions that will deepen your understanding of financial risk assessment.