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Questions and Answers
What does value at risk (VaR) primarily measure?
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?
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?
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?
What is meant by risk aversion?
What is the price of risk a measure of?
What is the price of risk a measure of?
In mean-variance analysis, what is considered a better portfolio when comparing Sharpe ratios?
In mean-variance analysis, what is considered a better portfolio when comparing Sharpe ratios?
Which term refers to the expected return in excess of that on risk-free securities?
Which term refers to the expected return in excess of that on risk-free securities?
How is excess return defined?
How is excess return defined?
What does the Holding-Period Return (HPR) formula calculate?
What does the Holding-Period Return (HPR) formula calculate?
How is the HPR for an investment calculated?
How is the HPR for an investment calculated?
What is the result of calculating the HPR for a stock bought at $25, sold for $27, with $1.25 in dividends?
What is the result of calculating the HPR for a stock bought at $25, sold for $27, with $1.25 in dividends?
What does the geometric average return provide?
What does the geometric average return provide?
Which return calculation method gives the internal rate of return on an investment?
Which return calculation method gives the internal rate of return on an investment?
What is the formula for the arithmetic average return?
What is the formula for the arithmetic average return?
When considering multiple periods of return, what does the geometric average differ from in terms of performance measurement?
When considering multiple periods of return, what does the geometric average differ from in terms of performance measurement?
In investment analysis, which of the following statements is true regarding a Holding-Period Return of 13%?
In investment analysis, which of the following statements is true regarding a Holding-Period Return of 13%?
What is the formula for the Effective Annual Rate (EAR) when compounding is continuous?
What is the formula for the Effective Annual Rate (EAR) when compounding is continuous?
How is the Annual Percentage Rate (APR) calculated when using continuous compounding?
How is the Annual Percentage Rate (APR) calculated when using continuous compounding?
What does the term 'rReal' represent in the nominal and real interest rates relationship?
What does the term 'rReal' represent in the nominal and real interest rates relationship?
If an investment has a nominal interest rate of 10% and inflation is 5%, what is the real rate of return?
If an investment has a nominal interest rate of 10% and inflation is 5%, what is the real rate of return?
Which equation correctly relates nominal interest rate, real interest rate, and inflation?
Which equation correctly relates nominal interest rate, real interest rate, and inflation?
What does an increase in nominal interest rates typically correspond with, based on historical trends since the 1950s?
What does an increase in nominal interest rates typically correspond with, based on historical trends since the 1950s?
In the case of volatile inflation in the 1930s/1940s, how did it affect real rates of return?
In the case of volatile inflation in the 1930s/1940s, how did it affect real rates of return?
When calculating APR using compounded interest, what variable represents the number of compounding periods?
When calculating APR using compounded interest, what variable represents the number of compounding periods?
What is the arithmetic average of the returns 10%, 25%, -20%, and 20%?
What is the arithmetic average of the returns 10%, 25%, -20%, and 20%?
What does the geometric average represent in terms of investment performance?
What does the geometric average represent in terms of investment performance?
Which formula is used to calculate the geometric average of returns?
Which formula is used to calculate the geometric average of returns?
How is the annual percentage rate (APR) calculated?
How is the annual percentage rate (APR) calculated?
What is the primary difference between the effective annual rate (EAR) and the annual percentage rate (APR)?
What is the primary difference between the effective annual rate (EAR) and the annual percentage rate (APR)?
What type of average return is known as the internal rate of return on an investment?
What type of average return is known as the internal rate of return on an investment?
Which of the following is true about the geometric average compared to the arithmetic average?
Which of the following is true about the geometric average compared to the arithmetic average?
In calculating rates of return, when is it appropriate to use the dollar-weighted average?
In calculating rates of return, when is it appropriate to use the dollar-weighted average?
What does 'Asset Allocation' refer to in investment management?
What does 'Asset Allocation' refer to in investment management?
Which equation represents the Expected Return of the complete portfolio?
Which equation represents the Expected Return of the complete portfolio?
What is meant by 'Capital Allocation' in investment terms?
What is meant by 'Capital Allocation' in investment terms?
Which of the following is considered a risk-free asset?
Which of the following is considered a risk-free asset?
What does the standard deviation of the complete portfolio represent?
What does the standard deviation of the complete portfolio represent?
In the formula $\sigma_C = y × \sigma_P$, what does $\sigma_P$ represent?
In the formula $\sigma_C = y × \sigma_P$, what does $\sigma_P$ represent?
What is the relationship between the percentage of assets in a risky portfolio and its expected return?
What is the relationship between the percentage of assets in a risky portfolio and its expected return?
Which of the following statements about money market instruments is accurate?
Which of the following statements about money market instruments is accurate?
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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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