Capital Asset Pricing Model Flashcards
Week 4
What are the two questions that must be asked about how much wealth should be invested into each security?
- What portfolio which can be made up of what risky assets
- How best to distribute risky and risk-free assets
How can you eliminate specific risks? What does that mean if it can be eliminated?
- Systemic risk can be eliminated through diversification
- There is thus no reward for bearing systemic risk if it can be eliminated
- Therefore, only market risk provides a risk premium
How can we tell how much systematic risk an asset has relative to the Portfolio?
- Beta (β) values
What is β? How accurate is β?
- An index of responsiveness of the changes in returns of securities relative to changes in the market (β>0)
- β is an average of risk or a line of best fit
What is the formula for β?
- Covariance (Rx, Rm) / σ²m
- This can be rewritten (because σm cancel) as:
[ρxy * σx] / σm - Where Rx is the return of security x and Rm is the return of the market
What does it mean if β>1?
- Stock carries more systematic risk, so the expected return would be higher
What does it mean if 0<β<1?
- Stocks move in the same direction of the market
- If the market becomes more risky, so does the security
What is the β of the market? Why is it this way
- βm = 1
- This is because the Cov of (Rm,Rm) =σ²m
- This would then equal σ²m / σ²m = 1
What does the Capital Asset Pricing Model try to answer?
- Developed by Markowitz, Sharpe and Miller in 1990 as an attempt to predict how capital markets behave under risk condition
What are some of the assumptions with the Capital Asset Pricing Model?
- Financial Markets are competitive, so investors are price-takers
- Perfect information and homogenous beliefs in returns
- Returns are normally distributed
- All investors are looking over the same timeframe and have equal opportunities
- No taxes/transactional costs
- Investors can borrow and lend at one rate
- Investors can hold a fraction of an asset
What is the risk-free rate of return?
- Effectively makes a ‘floor’ under all risky assets
- Therefore, all risky assets must pay more than a risk free rate
- Rf = Return on SR treasury bills
What is the efficiency frontier?
- Shows the highest expected return for any level of risk, denoted by a solid curved line
- It is possible to be within the efficient frontier line, but you cannot go above the line
- More assets gives a wider selection of risk and return
What does having an ‘efficient portfolio’ mean?
- An efficient portfolio yields the best possible expected level of return for its risk level
How do you find the most efficient portfolio using the efficiency frontier?
- Draw a tangent to the curve from point Rf
- If you borrow at Rf, you can extend beyond point S*
- If you lend at Rf, you end up between Rf and S*
What are market portfolios? How can the claim be tested?
- The market portfolio represents the optimal combination of risky assets given a risk-free asset
- This can be tested using the Sharpe Ratio
What is the Sharpe Ratio? How can this be calculated?
- The Sharpe Ratio is the ratio of risk premium to standard deviation
- E(Rp) - Rf / σ
What are some properties of portfolio selection?
- Portfolios that offer the highest expected return at a given standard deviation are efficient
- If investors can lend/borrow at a risk-free rate, then there can be an optimal portfolio
- Each investor should hold the same portfolio
- β measures marginal contribution of a stock to market risk
What does this mean if an efficient portfolio can be reached?
- Investors must select the best portfolio of common stocks
- Then, they can subsequently borrow/lend to achieve their personal level of risk
What is the formula for Reward-to-Risk ratio?
- [E(Rα) - Rf]/βα = [E(Rβ) - Rf]/ββ
What is the premise of the Security Market Line?
- Because all assets in the market must have the same risk-to-reward ratio, they must plot on the same line (SML)
What are some properties of SML?
- X-Axis: Asset β
- Y-Axis: Expected Return
- If any point is above the SML, investors will buy until the price goes up and expected return falls
- Same with the inverse
- The slope is: E(Rm)-Rf / βm so just E(Rm)-Rf
How does the CAPM link to the SML?
- (E(Rx) - Rf) / βx = E(Rm) - Rf
- This can be rearranged to give:
- E(Rx) = Rf + β(E(Rm)-Rf)
What is the CAPM dependant on?
- Time Value of Money (Rf): Reward for waiting for money with 0 money
- Reward for Bearing Risk (E(Rm)-Rf): Reward market offers
- Amount of systematic risk (βx): Amount of risk present in Asset x relative to average asset
What other method can be used to estimate SML and CAPM?
- You can estimate SML and CAPM with OLS (econometric)
- Rx - Rf = α + β[E(Rm)-Rf] + εt
- Theory suggests that α = 0, but if α>0, the asset is underpriced so the asset should be bought
