Capm Flashcards
What is the cml?
The capital market line is the line that is tangent to the efficient frontier, the line consist of a mix of risky securities and a risk free security. Remember the efficient frontier only holds risky assets. But the CFL holds risky assets and a risk free asset. The cml shows the different trade offs between the expected return and risk (SD).
Where the Cml line is tangent to the efficient frontier it creates an optimal point. The optimal point is where there is the biggest return for a unit of risk. It is assumed that most rational investors would invest at this point. The investor can move along this line to his tolerable risk. If a risky investor wanted to borrow money to then invest it he would be at the top end of the cml past the optimal portfolio.
What is portfolio theory?
Modern portfolio theory (MPT) is a theory of finance that attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets.
What is the efficient frontier?
The efficient frontier is the bullet shape curve that is created when 2 risky assets are differently weighted. It gives the expected risk/return trade off given a combination of weightings
What is sml? Security market line
The security market line is the line that contains the risk/return trade-off only a singular security. The sml uses beta as the measurement of risk. We know that the market beta is equal to one if we plot that one the graph going towards the sml then it will give us the market risk/return trade off this is used as a benchmark.
If the point is above/below the sml then the stock is either overvalued or undervalued. If it is above the line then it is undervalued because the expected return is greater than the return available on the sml even though the risk(beta) is the same. If the stock is below the line then it is overvalued as you could earn a greater return on the sml even though the risk(beta) is the same. See image on Google.
What is the CAPM equation
R = Rf + B(Rm-Rf)
optimal point
This optimal point is also known as the market portfolio because this is where every rational investor would invest at this is the optimum. The capital allocation line is also the capital market line.
Why do all investors hold the market portfolio?
When we consider all the elements of the portfolios of all the investors, lending and borrowing will cancel each other out because to everyone person that lend there is a person that borrows. And the value of all the elements considered within the risky portfolio will equal the entire wealth of the economy. All the people who borrow and lend make up the economy.
The risk premium of the market
THE EXPECTED RETURN ON THE MARKET MINUS THE RISK FREE RATE IS THE ADDITION RISK THAT YOU ARE TAKEN ON, SO WHAT ADDITIONAL RETURN SHOULD YOU EXPECT FOR THAT.
Risk and return
A less risky investment is a US treasury bill, since the return on it is fixed. It will be affected by changes in the economy. As it has no risk it has a beta of zero. A more risky investment usually has an average beta around 1.
Market portfolio
The market portfolio contains all risky assets in the world.
An investor would expect a higher return from a market portfolio than what they would from a risk free asset. The difference between the return on the market and the return of a risk free asset is called the MARKET PREMIUM = (Rm – Rf)
market beta is equal to 1 and the beta for the risk free security is 0.
which can be diversified away systematic risk or unsystematic risk
Un- systematic risk is diversifiable this is also known as specific or diversifiable risk.
Systematic risk - this is risk that cannot be diversified away.
what is systematic risk and unsystematic risk
systematic risk is the risk that is associated with the whole economy such as a recession. there is no kind of diversification that can reduce or eliminate this.
unsystematic risk - is the risk that is associated specifically to a company or an industry. just think like a workers strike would only affect them and businesses related to them not the whole economy.
difference between SML and CML
The CML is a line that is used to show the rates of return, which depends on risk-free rates of return and levels of risk for a specific portfolio. SML, which is also called a Characteristic Line, is a graphical representation of the market’s risk and return at a given time.
One of the differences between CML and SML, is how the risk factors are measured. While standard deviation is the measure of risk for CML, Beta coefficient determines the risk factors of the SML.
two fund separation theorem - it is the portfolio that has the highest Sharpe ratio
Sharpe ratio = E(Rp) - Rf / SDp
How to do the Macaulay equation?
suppose you have a 3 year bond, with a coupon rate of 11%, FV = 2000, YTM or required rate of return is 7%
the first step that you need to take its to work out the present value each year. take the value of the bond and multiply it by the coupon rate
2000*0.11 = 220
we now need to take the Cash flow value and discount it by the yield to maturity 7% remember on the last year you need to add the face value.
220/1.07 (power of 1) = 205.61
220/1.07 (power of 2) = 192.16
2200/1.07 (power of 3) = 1795.85
not we need to total these answers up! = 2,193.62
now we have this value we can do the equation.
1 X 220/1.07P1 divided by 2193.62 +
2 X 220/1.07P2 divided by 2193.62 +
3 X 2220/1.07P3 divided by 2193.62 = 2.72
see lecture 3 page 19
what is the Macaulay equation for?
is a measure of a bond’s sensitivity to interest rate changes. Technically, duration is the weighed average number of years the investor must hold a bond until the present value of the bond’s cash flows equals the amount paid for the bond.
High/Low cyclicality of revenues
revenues are generally higher in periods of economic prosperity and expansion, and lower in periods of economic downturn and contraction.
High/Low Operating leverage
A measurement of the degree to which a firm or project incurs a combination of fixed and variable costs.
- A business that makes few sales, with each sale providing a very high gross margin, is said to be highly leveraged. A business that makes many sales, with each sale contributing a very slight margin, is said to be less leveraged. As the volume of sales in a business increases, each new sale contributes less to fixed costs and more to profitability.
- A business that has a higher proportion of fixed costs and a lower proportion of variable costs is said to have used more operating leverage. Those businesses with lower fixed costs and higher variable costs are said to employ less operating leverage.
weighted average cost of capital
if a company needs to raise money then they can either issue bonds which is a form of debt or they can issue stocks which I a form of equity. this is essentially the average rate of raising money. the company wants to know how much it will cost to raise money. they will look at both compnents and see what the cost is to raise debt through and what the cost is to raise equity through equity.
the cost of equity can either be through common stocks or preferred stocks (they have no voting rights but they get there money first)
WACC formula - Wd * Rd(1-T) + We * Re Wd - weight of debt Rd - the cost of debt (1-T) - the cost of debt after tax We - weight of equity Re - return of equity
if we have a referred stock then the formula is the same with a little added on to it.
Wd * Rd(1-T) + We * Re + Wp * Rp
A company wants to raise money, the company will sell $10m of common stock, the expected return is 15%. moreover, the company will issue $5m of debt, the cost of debt is $5m and the tax rate is 30%. find the WACC
first we need to figure out the weight of debt and the weight of equity $10 + $5 = $15m
so the
weight of debt is 5/15 = 0.33%
weight of equity is 10/15 = 0.67%
both of these added together needs to give me a weight of 100%.
so Wd = 0.33 Rd - 0.12 (1-T) - 0.30 We - 0.67 Re - 0.15
WACC = 0.33 * 0.12 (1-0.30) + 0.67*0.15 = 0.1282
Modified Duration
Modified duration provides a good indication of a bond’s sensitivity to a change in interest rates. The more your duration changes with a 1% increase in interest rates, the more volatility your bond will exhibit. The bonds with lower coupons and longer maturities tend to have greater price volatility than bonds with higher coupon rates and shorter maturities.
Macaulay/modified
in order to find the modified duration, first of all you have to find the macualay duration. see the slide above for explanation.
Taken from the sample in these slides, if the bond is 3 years, FV = £2000, CR = 11%, and the required rate of return is 7% and the Macaulay duration is 2.72
then you use this figure to find the modified duration by dividing it by its required rate of return.
2.72/1.07 = 2.54
your modified duration is 2.54
Basic bond duration
Similar to finding the price of the bond.
instead you are multiplying the results by the amount of years there are.
1 * ((220/1.011P1)/2000)) + 2 * ((220/1.011P2)/2000) +3 * ((2220/1.011P3)/2000) = 2.71
the duration of the bond is 2.71
On this equation you use the coupon rate
Yield to maturity
Yield to maturity (YTM) measures the annual return an investor would receive if he or she held a particular bond until maturity.
what beta does a risk free asset have
A less risky investment is a US treasury bill, since the return on it is fixed. It will be affected by changes in the economy. As it has no risk it has a beta of zero. A more risky investment usually has an average beta around 1.
what assets are contained in a market portfolio?
The market portfolio contains all risky assets in the world.
what is the market premium
The difference between the return on the market and the return of a risk free asset is called the MARKET PREMIUM = (Rm – Rf)
what is the market risk premium?
beta(Rm-Rf)
capital asset pricing models depends on what two things?
(1) the compensation for the time value of money (risk free rate) and (2) a risk premium, which depends on the beta and market risk premium.
the capm assumes that the stock market is dominated by ?
The CAPM assumes that the stock market is dominated by well- diversified investors who are concerned only with market risk.
what happens if X lies below/above the SML?
this means that X is overpriced and will eventually come back to sml (equilibrium) if the stock is overpriced no one will buy it and it will therefore decrease in price.
if X lies above the line it means that the stock is undervalued, investors will all rush to this, which will push up prices.
