Corporate Finance Flashcards
Week 1 Risk Return - What has the highest return if invested $1 in 1900 and valued in 2007?
Portfolio of Treasury Bills
Portfolio of U.S government Bonds
Portfolio of U.S common stock
Portfolio of Treasury Bills: $71
Portfolio of U.S government Bonds: $242
Portfolio of U.S common stock: $14,276
Week 1 Risk Return - Given the following portfolios:
Portfolio of Treasury Bills
Portfolio of U.S government Bonds
Portfolio of U.S common stock
What is can be said about the attributes of each?
Treasury Bills: No default risk and relatively stable prices.
U.S government Bonds: Prices fluctuate with interest rates to remain competitive (bond price down when interest rate up). Newly realeased bonds may have different coupon payments so the existing bonds adjust to remain competitive.
Portfolio of U.S common stock: Risk subject to interest rate changes and the volatile of the stocks.
The higher the risk, the higher the expected return required by investors.
Week 1 Risk Return - r|p|?
The Expected Return from a portfolio of N securities, being the weighted average of expect returns from the single securities in the portfolio.
Week 1 Risk Return - r|p| equation?
w|1| r|1| + w|2| r|2| + … + w|N| r|N|
= Σ w|i| r|i|
where w|i| is the weight of the security in the portfolio and will be the percentage (in decimal terms)
equally be 0.XX, where xx is the expected return.
Week 1 Risk Return - What is the rate of return of a stock? (formula) - CHECK THIS
r = [ { p(t) - p(t - 1) } / p(t-1)] * 100
Week 1 Risk Return - Aside from expected return, what are two possibly equivalent measures of risk?
Variance and Standard Deviation.
Week 1 Risk Return - Variance Formula and interpretation?
σ² = 1/N [Σ (x|i| - μ)²]
The mean of the squared deviations from the mean.
It is a measure of volatility.
If 0, the portfolio is riskless.
Week 1 Risk Return - When talking about the risk of a portfolio, what are we really talking about?
- Idiosyncratic Risk (Stock specific or unsystematic): The risk associated with each individual security.
Systematic Risk (Macro Risk): The degree to which the securities covary, being the covariance between securities.
Week 1 Risk Return - Covariance In terms of the standard deviation and correlation coefficient of two stocks?
σ|12| = ρ|12| σ|1| σ|2|
σ|12|: the Covariance of the two securities.
σ|i|: the variance of security i.
ρ|12|: The correlation coefficient between security 1 and 2.
Week 1 Risk Return - Given the covariance definition “ σ|12| = ρ|12| σ|1| σ|2| “, write the formula for risk (variance) of a portfolio.
σ|p|² =
Σ|i=1| Σ|j=1| w|i| w|j| σ|ij|
= Σ|i=1| Σ|j=1| w|i| w|j| ρ|ij| σ|i| σ|j|
σ|ij|: the Covariance of the two securities.
σ|i|: the variance of security i.
ρ|12|: The correlation coefficient between security 1 and 2.
Week 1 Risk Return -What will the portfolio volatility of a two stock portfolio be?
BA 1.
σ|p|² =
Σ|i=1| Σ|j=1| w|i| w|j| σ|ij|
σ|p|² = w|1|²σ|1|² + w|2|²σ|2|² + 2w|1| w|2| σ|12|
where σ|12| = ρ|12| σ|1| σ|2|
The following equation is therefore equivalent:
σ|p|² = w|1|²σ|1|² + w|2|²σ|2|² + 2w|1| w|2| ρ|12| σ|1| σ|2|
Week 1 Risk Return - Given the two security portfolio variance equation:
σ|p|² = w|1|²σ|1|² + w|2|²σ|2|² + 2w|1| w|2| σ|12|,
What is the interpretation of each part?
w|1|²σ|1|²: Component due variance (idiosyncratic risk) of security 1.
w|2|²σ|2|²: Component due variance (idiosyncratic risk) of security 2.
2w|1| w|2| σ|12|: Component due to the covariance between security 1 and security 2 (systematic risk).
Each security contributes w|1| w|2| σ|12| worth of systematic risk.
Week 2 Risk Return - Consider a portfolio of securities with expected return r|p| = 20% and standard deviation σ|p| = 50%. Suppose the composition of the portfolio is changed, such that the standard deviation reduces. What is this an example of?
Diversification.
Week 2 Risk Return - What iii diversification with a portfolio?
To get at least the same return with lower risk, or lower risk and a lower return.
It is not diversification if the expected return falls though and the risk remains the same.
We need the expected return to stay the same (or improve) AND the portfolio risk to fall (So the standard deviation to fall.
Week 2 Risk Return - Given the portfolio risk equation for two stocks:
σ|p|² = w|1|²σ|1|² + w|2|²σ|2|² + 2w|1| w|2| σ|12|,
What additions would be made if there were three stocks.
We would add
w|3|²σ|3|² + 2w|1| w|3| σ|23| + 2w|2| w|3| σ|23|
So the idiosyncratic risk associated with the additional stock and the systematic risk due to the covariance with the third stock with the other two stocks.
Week 2 Risk Return - If you have calculated the portfolio variance of two stocks and want to calculate the standard deviation when adding a further stock, what would the process be?
You could start from scratch and calculate using the equation, or, given the knowledge of the first portfolio variance, use this to get the standard deviation and use the equation counting the portfolio as a solitary security.
Week 2 Risk Return - When N securities are uncorrelated, what is the portfolio S.D?
σ|p| = [w|1|²σ|1|² + w|2|²σ|2|² + … + w|N|²σ|N|²]^1/2
SO the second part of the equation is removed (the systematic risk) leaving only the stock specific idiosyncratic risk.
Week 2 Risk Return - How do we get to the risk pooling result in which variance is equal to 0 when N approaches infinity and what other axioms are required?
We assume stocks are uncorrelated (strong and unrealistic assumption) so
σ|p| = [w|1|²σ|1|² + w|2|²σ|2|² + … + w|N|²σ|N|²]^1/2
We then assume each share has the same variance and weighting, so w|I| become 1/N
The whole equation simplifies to:
(N * 1/N² σ²) ^1/2 =
(1/N σ²) ^1/2
As N approaches infinity, σ|p| approaches 0 (as this is what we were using the equation to find).
As more and more uncorrelated risks are pooled together, total risk is reduced.
Week 2 Risk Return - Market Risk?
Graph?
The risk that cannot be eliminated through optimal diversifying the investment portfolio.
It is the risk driven by the economy as a whole.
See BA 2 for graph.
Week 2 Risk Return - Total Risk?
Total Risk = Diversifiable risk + market risk.
It is the contribution of an individual security to the risk of a portfolio.
Diversifiable risk contributed to unique risk and can be eliminated through diversification.
Only market risk contributes towards risk of a well diversified portfolio.
Week 2 Risk Return - What does risk pooling show?
That there is one type of risk that cannot be diversified away from, being market risk,
Week 2 Risk Return - Beta (β)?
A measure of sensitivity of the stock, being how much the stock fluctuates given a change in the market (Purely Theoretical)
The market is made up of all stocks, so has a β=1 (this is an assumption)
Securities that move in the same direction but tend to amplify the movement of the market have β > 1.
Those that move in the same direction as the market but tend to reduce the movement have 0 < β < 1.
They will move up or down with the market.
Stocks that move opposite the market are very rare.
Week 2 Risk Return - Beta (β)?
The systematic risk part.
The covariance of the asset with the market portfolio return divided by the variance of the market portfolio
A measure of sensitivity of the stock, being how much the stock fluctuates given a change in the market (Purely Theoretical)
The market is made up of all stocks, so has a β=1 (this is an assumption)
Securities that move in the same direction but tend to amplify the movement of the market have β > 1.
Those that move in the same direction as the market but tend to reduce the movement have 0 < β < 1.
They will move up or down with the market.
Stocks that move opposite the market are very rare.
Week 2 Risk Return - How do we calculate β?
r|i| = α + β|i| r|m| + error|i|
r|m| : Return of market portfolio.
r|i| : Return on security
We use linear regression to calculate the slope of the line.
β|i| = σ|im| / σ|m|²
The beta is the covariance between stock and the market scaled by the variance of the market.
Week 2 Risk Return - What is a well diversified portfolio?
A portfolio that has low unique risk and mainly consists of market risk.
Week 2 Risk Return - Markowitz Portfolio Risk - Efficient Portfolios?
The combination of securities that create the OPTIMAL combination of expected returns and standard deviations.
Optimal means diversifying away specific risk.
On a graph showing risk and returns, these will be the points to the far left of the possible combination and then all the way to the greatest standard deviation in attainable.
The point will be dependent on the risk averseness/ love of the investor, but an point should be selected along the efficient frontier.
Week 2 Risk Return - See BA 3. What is this function representative of and when should it be used?
See BA 3.
Week 2 Risk Return - If the daily returns are distributed approximately by the normal distribution, what does this lead us to say?
The expected value and variance (or standard deviation) of a portfolio are the only measures an investor needs to consider.
This is because the normal distribution can be calculated using only these two, as shown in BA 3.
Week 2 Risk Return - When evaluating a two security portfolio, how would the variance and expected return vary with different weighting?
Only the idiosyncratic risk will be altered, being the first two additions in the equation.
The portfolio SD and r are functions of the amount invested in each company, when there is no perfect correlation (+ or -)
Function of meaning?
Something (such as a quality or measurement) that is related to and changes with (something else) Height is a function of age in children. It increases as their age increases.
So part of the equation that make sure the y.
Week 2 Risk Return - Explain the graph in BA 4.
A graph showing the resulting portfolio r and σ given different combination of w in a two stock portfolio.
The blue line represents that risk reward payoff.
Week 2 Risk Return - Efficient Portfolios?
Lie on the efficient frontier and offer the highest expected return for a given level of risk, or the lowest level of risk for a given expected return.
Week 2 Risk Return - r|f|?
The investors can borrow at the risk free rate, r|f|.
Week 2 Risk Return - With the introduction of lending money, how would this effect the S.D and expected returns ?
The expected returns would just the proportion of money in each tool multiplied by the expected return.
When lending, the S.D is 0. Therefore, the S.D of a combination of a portfolio and lending would just be the weighting of S that is in the portfolio multiplied by the S.D of the portfolio.
Week 2 Risk Return - With the introduction of borrowing money, how would this effect the S.D and expected returns ?
Expected returns: The amount of wealth compared to initial wealth due to borrowing * expected return of S minus the amount of wealth borrowed * interest rate
S.D: The amount of wealth compared to initial wealth due to borrowing * Standard deviation of S minus the amount of wealth borrowed * interest rate
Week 2 Risk Return - Looking at BA 5, Explain the graph.
BA 5.
Week 2 Risk Return - If you have a graph of efficient portfolios, and know the risk free rate r|f|, how would you add the borrowing and lending line?
Start at r|f| and draw the steepest line that touches the efficient frontier.
Week 2 Risk Return - Sharpe Ratio?
The ratio of risk premium to standard deviation:
Sharpe Ratio =
Risk Premium/ S.D =
(r - r|f|) / σ
Week 2 Risk Return - What are the shortcomings of the Markowitz Approach?
Zero taxes and transaction costs false.
Fractional securities are not available.
Credit limits constrain investors
Investors seem to have an influence on the market (large institutional investors)
Correlations between assets are never stable and fixed.
Past performance is not a good indicator of future performance.
Week 3 Asset Pricing - Why do Treasury Bills have a Beta value of 0?
Return is flex, so they are unaffected by the market, giving them a Beta value of 0.
Week 3 Asset Pricing - How do we get from Markowitz to the CAPM model?
Previously we looked at a market portfolio with Beta = 1 and treasury bills beta = 0/
What about when the Beta of the portfolio is not 1?
Week 3 Asset Pricing - What underpinning of the CAPM model?
In a Competitive Market, the expected risk premium varies in direct proportion to beta.
The risk premium is r|p| - r|f|, as at the risk free rate, the risk is 0.
This leads all investments to lie on the SECURITY MARKET LINE, being the line that is drawn from the r|f| on the y axis to the market portfolio r|m| and associated beta = 1.
e.g. the expected risk premium of an investment with beta of .4, will have .4 * the expected market risk premium.
Week 3 Asset Pricing - How do we get from Markowitz to the CAPM model?
Previously we looked at a market portfolio with Beta = 1 and treasury bills beta = 0.
What about when the Beta of the portfolio is not 1?
Week 3 Asset Pricing - What underpinning of the CAPM model?
In a Competitive Market, the expected risk premium varies in direct proportion to beta.
The risk premium is r|p| - r|f|, as at the risk free rate, the risk is 0.
This leads all investments to lie on the SECURITY MARKET LINE, being the line that is drawn from the r|f| on the y axis to the market portfolio r|m| and associated beta = 1.
e.g. the expected risk premium of an investment with beta of .4, will have .4 * the expected market risk premium.
CAPM assumed that investors are only concerned about the expected return and the risk of an investment strategy.
Week 3 Asset Pricing - CAPM - Expected risk premium on stock formula?
Expected risk premium on stock =
beta x expected risk premium on market
r - r|f| = β(r|m| - r|f|)
Week 3 Asset Pricing - What are the 5 basic principle of the CAPM model?
- Investors like high expected return and low standard deviation. Common stock
portfolios that offer the highest expected return for a given standard deviation are
known as efficient portfolios. - If the investor can lend or borrow at the risk-free rate of interest, one efficient
portfolio is better than all the others: the portfolio that offers the highest ratio of risk
premium to standard deviation.
A risk-averse investor will put part of his money in this efficient portfolio and part in the risk-free asset.
A risk-tolerant investor may put all her money in this portfolio or she may borrow
and put in even more.
- The composition of this best efficient portfolio depends on the investor’s assessments of expected returns, standard deviations, and correlations. But suppose everybody has the same information and the same assessments. If there is no superior information, each investor should hold the same portfolio as everybody else; in other words,
everyone should hold the market portfolio.
Now let us go back to the risk of individual stocks:
- Do not look at the risk of a stock in isolation but at its contribution to portfolio risk.
This contribution depends on the stock’s sensitivity to changes in the value of the
portfolio. - A stock’s sensitivity to changes in the value of the market portfolio is known as beta.
Beta, therefore, measures the marginal contribution of a stock to the risk of the market
portfolio.
Now if everyone holds the market portfolio, and if beta measures each security’s contribution to the market portfolio risk, then it is no surprise that the risk
Week 3 Asset Pricing - CAPM - What if a stock does not lie on the security market line.
If a stock is below the line, the investor can attain higher return for that level of risk.
The price of A will have to fall until the expected return matches what you could get elsewhere.
Nobody will hold a stock with a lower return than β(r|m| - r|f|)
As no stocks can lie below the line, it must equally be the case that none lie above the line, as the market line is the average of all the securities in the market portfolio.
Week 3 Asset Pricing - What would the expected return be of a portfolio made up of a risk free asset and the market portfolio?
Show how we get the final equation using the expected return.
= w|m| r|m| + (1- w|f|) r|f|
Rearranging:
w|m| = (r|p| - r|f|) /
(r|m| - r|f|)
So the weight dedicated the market portfolio is the premium of the selected portfolio divided by the market premium.
Week 3 Asset Pricing - CAPM meaning?
Capital Asset Pricing Model.
An approach to establishing the reward for baring the systematic risk of a portfolio.
Week 3 Asset Pricing - Week 3 Asset Pricing - What would the S.D be of a portfolio made up of a risk free asset and the market portfolio?
What can this be simplified to?
σ|p| = √(w|m| x σ|m|)²
= w|m| x σ|m|
As the risk free asset has no standard deviation.
We then attain
w|m| = σ|p| / σ|m|
To find the proportion of investment in the market portfolio.
Week 3 Asset Pricing - Derive the Capital Market Line Equation.
From the standard deviation equation we found attained:
w|m| = σ|p| / σ|m|
From the expected return equation we attained:
w|m| = (r|p| - r|f|) /
(r|m| - r|f|)
We now make the above to equal and write in terms of r|p|:
σ|p| / σ|m| = (r|p| - r|f|) /
(r|m| - r|f|)
r|p| = r|f|) +σ|p| / σ|m| (r|m| - r|f|)
See BA 6 for a clearer representation.
Week 3 Asset Pricing - Explain the Capital Market Line Equation:
r|p| = r|f| +[(r|m| - r|f|)/ σ|m|] σ|p|
What will the graph be?
The slope of the line [(r|m| - r|f|)/ σ|m|] shows the rate at which risk σ|p| and return r|p| can be traded against each other on a portfolio as a combination fo the market portfolio and the risk free asset.
It shows how the return of a portfolio increases above the risk free amount and the assorted risk to attain the extra return.
See BA 7 for the graph.
Week 3 Asset Pricing - Given that portfolios on the capital market line are efficient, what can be said about the combinations and the correlation?
Portfolios on the capital market line are efficient portfolios.
This is because they are obtained as a combination of the market portfolio and the risk free asset: therefore, they are perfectly positively correlated with the market portfolio.
Formally, this means
that the correlation coefficient between a portfolio on the capital market line and the market portfolio is equal to ρ|pm| = 1.
Week 3 Asset Pricing - How do we derive the equation for a security market line, given that the capital market line is
r|p| = r|f| +[(r|m| - r|f|)/ σ|m|] σ|p|
We know that ρ|pm| = 1 for the capital market line and the portfolio as the portfolio is made up of a proportion of the market portfolio.
In general, it can be shown that:
r|p| = r|f| +[(r|m| - r|f|)/ σ|m|] σ|p|ρ|pm|
since σ|pm| = ρ|pm| σ|p|σ|m|,
we rewrite the CAPM line to be:
r|p| = r|f| +[(r|m| - r|f|)/ σ|m|] [σ|pm|/
σ|m|]
By analogy, a security:
r|i| = r|f| +[(r|m| - r|f|)/ σ|m|] [σ|im|/
σ|m|]
The β for security I is:
β|i| = σ|im|/
σ|m|²
{from OLS regression]
The Security Market Line is therefore:
r|i| = r|f| + β|i|(r|m| - r|f|)