Chap 7 Flashcards
How do you calculate a risk premium?
nominal - real = premium or
nominal return on stocks - nominal return on bills
What is the arithmetic average rate of return?
an arithmetic average means all values were added together then divided by “n”
-good measure of opportunity C.O.C regardless of the timing of the cash flow
How is the reliability of an estimate of the average measured?
The standard error = the standard deviation divided by the square root of the number of observations (n)
How is the compound (geometric) annual return measured?
=(products of possible value of stock as a percentage)^1/n
Or for log normally distributed returns,
the annual compound (geometric) return = the arithmetic average return minus half the variance
When are arithmetic vs compound/geometric return measures used?
If the cost of capital is estimated from historical returns or risk premiums, use arithmetic averages
If not, use compound annual rates of return.
Is the market portfolio risk, rm, stable over time? Why?
not likely
- because rm=rf + normal risk premium
- we know that the risk free rate, rf, rate on T-Bills, varies
- we assume a normal, stable, risk premium on the market portfolio
What are the two reasons that history may over- state the risk premium that investors demand today?
- By focus- ing on equity returns in the United States, we may obtain a biased view of what investors expected.
- Stock prices in the United States have for some years outpaced the growth in company dividends or earnings.
What does the high risk premium earned in the market seems to imply?
that investors are extremely risk-averse (want low risk)
How does a change in expected market risk premium affect realized rates of return?
A decrease in the expected market risk premium can lead to an increase in realized rates of return.
How do you calculate the real risk premium?
real risk premium = (rm – rf)/(1 + i)
where i= inflation
What happens to the ratio of price to dividends when dividend yields fall?
When dividend yields fall, the ratio of price to dividends increases
-the returns realized by investors also increase
All else remaining equal, what happens if the growth in price-dividend ratio stalls?
If the growth in the price-dividend ratio stalls,
then average returns and risk premiums will be lower in the future than in the past.
Do low dividend yields forecast high dividend growth?
No, low dividend yields do not seem to forecast high dividend growth
Should firms ignore yr-yr fluctuations in the dividend yield?
It seems that, when estimating the discount rate for longer term investments, a firm can safely ignore year-to-year fluctuations in the dividend yield
How do we calculate variance of market return?
=expected value(rm(with bar) - rm)^2
first rm, with bar, is actual return
second rm is expected return
note: divide by N-1 if sample size
What are the two standard statistical measures of spread?
- variance
- standard deviation
What can you say about the variability of T-bills, Stocks, and Gov. bonds?
Treasury bills are the least variable security, and common stocks are the most variable. Government bonds hold the middle ground.
Is the nominal return on a long term government bond certain?
Yes, the nominal return on a long-term government bond is absolutely certain to an investor who holds on until maturity; in other words, it is risk-free if you forget about inflation
What is more variable, individual stocks or market indexes? Why?
individual stocks for the most part are more variable, because market indexes have diversification benefits
How does a graph with standard deviation on the y axis, and # of stocks on the x axis look?
Downward sloping, this is because average risk is reduced by diversification
NOTE: diversification reduces risk rapidly at first, then more slowly…
Do you get the most benefit or diversity with a few stocks or a lot?
Notice also that you can get most of this benefit with relatively few stocks: The improvement is much smaller when the number of securities is increased beyond, say, 20 or 30.
What kind of risk does diversification eliminate?
Diversification eliminates specific risk: stems from the fact that many of the perils that surround an individual company are peculiar to that company and perhaps its immediate competitors
What risk can never be eliminated?
Market risk : Market risk stems from the fact that there are other economywide perils that threaten all businesses. That is why stocks have a tendency to move together
What are other names for specific risk?
- unsystematic risk
- residual risk
- unique risk
- diversifiable risk.
What are other names for market risk?
systematic risk or undiversifiable risk.
How do you calculate expected portfolio return?
Expected Return = (% in one portfolio x return NOT IN PERCENT) + (% in another portfolio x return NOT IN PERCENT)
How do we calculate standard deviation of a portfolio if covariance is 0?
the standard deviation of the portfolio is a weighted average of the standard deviations of the two stocks IF covariance is 0, meaning they move in perfect lock step
How do you calculate the covariance between 2 stocks?
Covariance between stocks 1 and 2 = σ12 = ρ12 σ1σ2
How do you calculate portfolio variance?
Portfolio variance = x1^2σ1^2 + x2^2σ2^2 + 2(x1x2ρ12σ1σ2)
or expected value of (̃r1 − r1) × (̃r2 − r2)
What is any security’s covariance with itself?
is just its variance
What kind of portfolio correlation is ideal?
perfect negative correlation
What is an index fund?
You can “buy the market” by purchasing shares in an index fund
examples: a mutual fund or exchange traded fund (ETF) that invests in the market index that you want to track
What does the risk of a well diversified portfolio depend on?
The market risk of the securities included in the portfolio.
What is beta, its calculation, and what does it measure?
Beta measures an individual stocks market risk, and that boils down to measuring how sensitive it is to market movements…. This sensitivity is called beta.
Beta tells us for a 1% change in market return, how much the individual stock will change
β i = σ i m / σ 2m
- the covariance between the stock and market
- over the variance of the market
What can you say about Beta’s >1, and Beta’s between 0 and 1?
Betas greater than 1.0 tend to amplify the overall movements of the market
Stocks with betas between 0 and 1.0 tend to move in the same direction as the market, but not as far
What is the market beta?
1
What risk accounts for most of the risk in a well diversified portfolio?
Market risk
As your # of securities in portfolio increases, what happens to the risk?
with better diversification, portfolio risk declines until all specific risk is eliminated and only the bedrock of market risk remains.
Where is the “bedrock” of market risk?
It depends on the average beta of the securities selected
How is portfolio risk driven by security beta’s?
The risk of a well-diversified portfolio is proportional to the port- folio beta, which equals the average beta of the securities included in the portfolio
What does the formula for Beta measure, other than stock sensitivity to market?
This ratio of covariance to variance measures a stock’s contribution to portfolio risk.
Does diversification add to a firms value?
No , diversification does not add or subtract from it
Firm’s aren’t more attractive if they are diversified. If investors can diversify on their own account, they will not pay any extra for firms that diversify
