Chapter 10 Flashcards
Who conducted a key study on historical returns starting in 1926?
Roger Ibbotson and Rex Sinquefield.
What is a risk premium?
The additional return over the risk-free rate for taking on risk.
In a return example, if you buy stock for $5,874, receive $194 in dividends, and sell it for $6,288, what’s your dollar return?
$608 = $6,288 – $5,874 + $194.
What percentage of returns fall within ±2 standard deviations?
Approximately 95.44%.
Why is the geometric average lower than the arithmetic average?
Because it accounts for compounding and volatility over time.
When is the geometric mean overly pessimistic?
Over short time horizons.
What was the average excess return for long-term corporate bonds (1926–2021)?
3.4% = 6.4% – 3.0%.
What statistical measures are commonly used to define risk?
Variance and standard deviation.
What is standard deviation?
The square root of variance; measures total risk or volatility.
What’s one limitation of using historical data to predict returns?
Past performance doesn’t guarantee future results.
What is the arithmetic average return?
The return earned in an average period over multiple periods.
What is the geometric average return?
The average compound return per period over multiple periods.
What does compounding do to investment returns over time?
It increases the growth rate by reinvesting earnings.
How do you calculate geometric average return in Excel?
=GEOMEAN(1+ret1, 1+ret2, …) - 1.
What is the formula for percentage return?
Percentage return = Dollar return / Initial investment.
What does a risk-free rate represent?
The return on an investment with zero risk, often proxied by T-bills.
Why is standard deviation used in finance?
It quantifies the amount of risk or uncertainty in investment returns.
What was the average excess return for small company stocks (1926–2021)?
13.3% = 16.3% – 3.0%.
If T-bill rate is 4.3%, what’s the expected return on small company stocks?
17.6% = 13.3% + 4.3%.
What is the purpose of summarizing return data with a frequency distribution?
To visualize the spread and probability of different return outcomes.
What percentage of returns fall within ±1 standard deviation in a normal distribution?
Approximately 68.26%.
Which is better for long-term projections: arithmetic or geometric mean?
Geometric mean.
What is dividend income?
Earnings distributed to shareholders, typically in cash.
What is the effect of volatility on geometric returns?
Higher volatility reduces the geometric average compared to the arithmetic mean.
If the average return is 12.3% and the standard deviation is 19.6%, what range contains ~68% of annual returns?
Between -7.3% and 31.9%.
What was the average excess return for large company stocks (1926–2021)?
9.3% = 12.3% – 3.0%.
What does a return of -1σ mean in a normal distribution?
The return is one standard deviation below the mean.
What is capital gain?
The profit earned from the increase in the stock’s price.
What’s the probability that a return falls within ±3 standard deviations in a normal distribution?
Approximately 99.74%.
When is the arithmetic mean overly optimistic?
Over long time horizons.
What shape does a normal distribution take?
A bell-shaped curve.
Why do we “add 1” to each return when calculating geometric mean?
To convert returns into growth multipliers.
What does a wider standard deviation indicate?
Greater variability (risk) in returns.
Why are small-cap stocks riskier than large-cap stocks?
They are more volatile and sensitive to market fluctuations.
What does HPR stand for?
Holding Period Return.
What is variance?
A measure of the dispersion of returns from the mean.
What is the formula for Holding Period Return over multiple years?
HPR = (1 + r₁) × (1 + r₂) × … × (1 + rₙ) – 1.
What is the main idea behind using historical returns for investment decisions?
Past performance provides insight into expected risk and return, though not guarantees.
What do we call the additional return for taking on more risk?
Risk premium
What is the formula for dollar return?
Dollar return = Dividend income + Capital gain (or loss).
