Alpha = abnormal return -> the difference between the actual return and the Security Market
Lline
E(r) = alpha + (rf + (beta* (Rm -Rf))
Alpha = E(r) - (Rf + (beta * (Rm - Rf))
If one has a positive alpha, one has identified underpriced stocks
Alpha = forecast return - required rate of return
E(r) = rf + beta ( E(rm) - rf)
Sharpe ratio: a measure of return to compare the performance by adjusting for risk:
(R - Rf) / std
buy call option = when you buy a call, you pay a premium for the right to buy shares at a
fixed price on or before a specific date. -> so, profits when price increases
buy put option = when you buy a put, you pay a premium for the right to sell a specified
amount of an underlying security at a predetermined price on or before a specific date. -> so,
profits when price decreases.
writing a put option = you sell someone the right to sell back their asset to you at a
predetermined price -> you make a profit if stock price remains high
,Writing a call option = you sell someone the right to buy an underlying stock at an exercise
price which is specified. -> you make a profit if stock price decreases
future = futures are derivative financial contracts which obligate the parties to transact an
asset at a predetermined price and date, regardless of the market price at the predetermined
date for that asset
Week 1: Empirical asset pricing I
If market interest rates go down, (government) bond prices go up. This is because if the
market interest rate goes down, the demand for bonds goes up as their coupon rate is fixed.
Therefore, their prices go up as well. They co-move negatively. Triple B rated bonds are not
so much affected by interest rates. For these lower credit company bonds, one has the
concern whether they are going to repay their debt (bond price decreases), while the
government will always be able to repay. The lower the creditworthiness, the less they co-
move with interest rates. What determines the bond prices is the creditworthiness of the
firm.
For a bond, you receive coupons (interest rate), so you do not only need to look at bond
prices.
Total return stocks = interest return + dividend
Total return bonds = price return + coupons
,Real rate of return is already corrected for inflation (the rising price level) relative to the
nominal rate of return.
If a company defaults, who receives its money?
Tax authority -> bond holders -> other credit people -> then, the stockholders
Stockholders therefore have more risks than bond holders, in addition to the fact that
dividends are more risky than coupons. Therefore, they get compensated. If you take a look
at the history, the compensation for risk is actually higher than for the risk you run. That is
what we call the equity premium puzzle. The excess returns on risky assets are too high to
be consistent with theory and reasonable levels or risk aversion.
Risk premium = the difference between the return on a risky investment and the return on a
risk free investment (government bonds).
How can the equity premium puzzle be explained?
- selection bias
- survivorship bias: think of e.g. stocks, if you analyze a bunch of stocks, you look at
the stocks which currently exist. If you only take a look at the stocks which are
existing today, you actually ignore a lot of stocks in the past, which went default. By
only basing your findings on existing stocks, you ignore defaulting companies and
therefore you overstate the actual return.
- limitations of asset pricing framework: e.g. people may be exposed to more risks than
systematic risk, and thus require a higher return than we think we do.
Empirical asset pricing II
Capital Asset Pricing Model is built on several assumptions:
1. individual behaviour
a. investors are rational, mean-variance optimizers -> they try to optimize the
average return for the risk they run
b. their common planning horizon is a single period -> they look forward for one
period
c. investors use all identical input lists, an assumption often term homogeneous
expectations. Homogeneous expectations are consistent with the assumption
that all relevant information is publicly available.
2. Market structure
a. All assets are publicly held and trade on public exchanges -> short positions
are allowed
b. investors can borrow or lend at a common risk-free rate, and they can take
short positions on traded securities
c. No taxes
d. No transaction costs
e. It assumes normally distributed security returns
If all assumptions are satisfied, everyone holds the same portfolio (= market portfolio).
Hence, the portfolios are fully diversified (all tradable assets are included in everyone’s
portfolio) and are only exposed to systematic risk (only to market risk, not firm-specific risk)
as investors have diversified their portfolios. All firm-specific risks therefore cancel out to
each other.
, The one with higher risk, also earns higher E(r) -> expected return. Does not perse mean
they also receive this return, as unexpected things can happen.
If the stocks are perfectly correlated, you get a line like the black line.
If you invest everything in the stock A, you will have the risk and return combination on the
red dot. If you have 50% in the one and 50% in the other, you will have around the orange
dot combination.
Not all stocks are perfectly correlated. The lower the correlation, the more of these firm
specific risks you can diversify by combining them in a portfolio. By going a little bit from
asset 1 to asset 2, your E(r) goes down and risk goes down as you are diversifying. We call
this line the opportunity set of risky assets, this is the blue line. As of the green point
upwards, we call the blue line the efficient frontier. This is only from this point as under this
line the combinations are not efficient as they can get a higher E(R) for the same risk rate
more upwards.
What will be the most optimal portfolio to invest in on this line?
The minimum variance portfolio is the green dot, it is the portfolio which gives you the lowest
amount of risk, but it is not the most optimal portfolio.
You want to get the highest level of return, for the lowest risk however. People typically
combine a risky portfolio with a risk free portfolio. What matters is the Risk free rate.
Lline
E(r) = alpha + (rf + (beta* (Rm -Rf))
Alpha = E(r) - (Rf + (beta * (Rm - Rf))
If one has a positive alpha, one has identified underpriced stocks
Alpha = forecast return - required rate of return
E(r) = rf + beta ( E(rm) - rf)
Sharpe ratio: a measure of return to compare the performance by adjusting for risk:
(R - Rf) / std
buy call option = when you buy a call, you pay a premium for the right to buy shares at a
fixed price on or before a specific date. -> so, profits when price increases
buy put option = when you buy a put, you pay a premium for the right to sell a specified
amount of an underlying security at a predetermined price on or before a specific date. -> so,
profits when price decreases.
writing a put option = you sell someone the right to sell back their asset to you at a
predetermined price -> you make a profit if stock price remains high
,Writing a call option = you sell someone the right to buy an underlying stock at an exercise
price which is specified. -> you make a profit if stock price decreases
future = futures are derivative financial contracts which obligate the parties to transact an
asset at a predetermined price and date, regardless of the market price at the predetermined
date for that asset
Week 1: Empirical asset pricing I
If market interest rates go down, (government) bond prices go up. This is because if the
market interest rate goes down, the demand for bonds goes up as their coupon rate is fixed.
Therefore, their prices go up as well. They co-move negatively. Triple B rated bonds are not
so much affected by interest rates. For these lower credit company bonds, one has the
concern whether they are going to repay their debt (bond price decreases), while the
government will always be able to repay. The lower the creditworthiness, the less they co-
move with interest rates. What determines the bond prices is the creditworthiness of the
firm.
For a bond, you receive coupons (interest rate), so you do not only need to look at bond
prices.
Total return stocks = interest return + dividend
Total return bonds = price return + coupons
,Real rate of return is already corrected for inflation (the rising price level) relative to the
nominal rate of return.
If a company defaults, who receives its money?
Tax authority -> bond holders -> other credit people -> then, the stockholders
Stockholders therefore have more risks than bond holders, in addition to the fact that
dividends are more risky than coupons. Therefore, they get compensated. If you take a look
at the history, the compensation for risk is actually higher than for the risk you run. That is
what we call the equity premium puzzle. The excess returns on risky assets are too high to
be consistent with theory and reasonable levels or risk aversion.
Risk premium = the difference between the return on a risky investment and the return on a
risk free investment (government bonds).
How can the equity premium puzzle be explained?
- selection bias
- survivorship bias: think of e.g. stocks, if you analyze a bunch of stocks, you look at
the stocks which currently exist. If you only take a look at the stocks which are
existing today, you actually ignore a lot of stocks in the past, which went default. By
only basing your findings on existing stocks, you ignore defaulting companies and
therefore you overstate the actual return.
- limitations of asset pricing framework: e.g. people may be exposed to more risks than
systematic risk, and thus require a higher return than we think we do.
Empirical asset pricing II
Capital Asset Pricing Model is built on several assumptions:
1. individual behaviour
a. investors are rational, mean-variance optimizers -> they try to optimize the
average return for the risk they run
b. their common planning horizon is a single period -> they look forward for one
period
c. investors use all identical input lists, an assumption often term homogeneous
expectations. Homogeneous expectations are consistent with the assumption
that all relevant information is publicly available.
2. Market structure
a. All assets are publicly held and trade on public exchanges -> short positions
are allowed
b. investors can borrow or lend at a common risk-free rate, and they can take
short positions on traded securities
c. No taxes
d. No transaction costs
e. It assumes normally distributed security returns
If all assumptions are satisfied, everyone holds the same portfolio (= market portfolio).
Hence, the portfolios are fully diversified (all tradable assets are included in everyone’s
portfolio) and are only exposed to systematic risk (only to market risk, not firm-specific risk)
as investors have diversified their portfolios. All firm-specific risks therefore cancel out to
each other.
, The one with higher risk, also earns higher E(r) -> expected return. Does not perse mean
they also receive this return, as unexpected things can happen.
If the stocks are perfectly correlated, you get a line like the black line.
If you invest everything in the stock A, you will have the risk and return combination on the
red dot. If you have 50% in the one and 50% in the other, you will have around the orange
dot combination.
Not all stocks are perfectly correlated. The lower the correlation, the more of these firm
specific risks you can diversify by combining them in a portfolio. By going a little bit from
asset 1 to asset 2, your E(r) goes down and risk goes down as you are diversifying. We call
this line the opportunity set of risky assets, this is the blue line. As of the green point
upwards, we call the blue line the efficient frontier. This is only from this point as under this
line the combinations are not efficient as they can get a higher E(R) for the same risk rate
more upwards.
What will be the most optimal portfolio to invest in on this line?
The minimum variance portfolio is the green dot, it is the portfolio which gives you the lowest
amount of risk, but it is not the most optimal portfolio.
You want to get the highest level of return, for the lowest risk however. People typically
combine a risky portfolio with a risk free portfolio. What matters is the Risk free rate.
