L11 - CAPM Flashcards
What is the CAPM model?
- Equilibrium model that
- – predicts optimal portfolio choices
- – predicts the relationship between risk and expected return
- – underlies much of modern finance theory
- y – underlies most of real-world financial decision making
- ■ Derived using Markowitz’s principles of portfolio theory, with additional simplifying assumptions
- . ■ Sharpe, Lintner and Mossin are researchers credited with its development.
- ■ William Sharpe won the Nobel Prize in 1990.
What are the CAPM assumptions?
- Stylized Assumptions:
- The market is in a competitive equilibrium;
- Single-period investment horizon;
- All assets are tradable;
- No frictions;
- Investors are rational mean-variance optimizers with
- homogeneous expectations
- ■ Some assumptions can be relaxed, and CAPM still holds.
- ■ An important approximation of reality in any case.
- ■ If many assumptions are relaxed, generalized versions of CAPM applies. (Topic of ongoing research.)
What does assumption 1, the market is in a competitive equilibrium mean?
Equilibrium:
- – Supply = Demand
- – Supply of securities is fixed (in the short-run).
- – If Demand > Supply for a particular security, the excess demand drives up the price and reduces expected return.
- – (Reverse if Demand < Supply)
■ Competitive market:
- – Investors take prices as given
- – No investor can manipulate the market.
- – No monopolist
What does assumption 2, single-period horizon mean?
All investors agree on a horizon.
■ Ensures that all investors are facing the same investment problem.
Doesnt really hold in the real world –> pension funds vs day traders
What does assumption 3,All assets are tradable mean?
- This includes in principle:
- – All financial assets (including international stocks)
- – Real estate
- – Human capital
- ■ This ensures that every investor has the same assets to invest in:
- – all the assets in the world, the “market portfolio
What does assumption 4, No frictions mean?
No taxes
■ No transaction costs (no bid-ask spread)
Same interest rate for lending and borrowing
■ All investors can borrow or lend unlimited amounts. (No margin requirements.)
What does assumption 5/6, Investors are rational mean-variance optimisers with homogeneous expectations mean?
Investors choose efficient portfolios consistent with their risk-return preferences
■ Investors have the same views about expected returns, variances, and covariances (and hence correlations).
What is the mathematical interpretation of the market portfolio?
What is the equilibrium tangency portfolio under CAPM?
Recall from portfolio theory:
- – All investors should have a (positive or negative) fraction of their wealth invested in the risk-free security, and
- – The rest of their wealth is invested in the tangency portfolio.
- – The tangency portfolio is the same for all investors (homogeneous expectations).
■ In equilibrium, supply=demand so:
– the tangency portfolio must be the portfolio of all existing risky assets, the “market portfolio” !!
What is the CML?
What does the E(R)-SD Frontier and the CML look like on a graph?
- investors who are risk tolerance are to the right of the tangency portfolio
- risk-averse investors are the opposite.
What is the required Return on an individual stock under CAPM?
b > 1 –> more risk than the market
b = 1 –> has the same systemic risk as the market
b < 1 –> less systemic risk than the market, thus the stock has a lower return
How can you derive the CAPM from the market tangency portfolio?
- Bottom equation can be simplified to the CAPM
Security market line on a graph?
- slope is the excess return on the market
How are CML and SML related?
- Market portfolio has the same expected return on the SML with a beta of 1
- stocks of lower expected returns –> have a beta less than one
- stocks with higher expected returns –> have a beta > 1
How can you mathematically write the total risk of a security?
What risk must investors be compensated for?
- For each beta in stock, we need to compensate the market risk premium –>excess return on the market
- the equilibrium risk premium in increasing in:
- the variance of the market portfolio
- the degree of risk aversion of the average investor
- if people become more risk-averse –> premiums increase
How can we estimate Beta by using OLS?
- This is called the Security Characteristic Line(SCL)
- according to CAPM alpha is equal to zero
- To estimate you regress the excess return on the asset on the excess return on the market
How can CAPM be used for stock selection and Active Management?
- One possible benchmark for stock selection is to find assets that are cheap relative to CAPM (or more advanced models).
- Alpha is defined as the difference between the excess return on the stock compared to the beta weighted excess return on the market
- Some fund managers try to buy positive-alpha stocks (underpriced and above the SML) and sell negative-alpha stocks (overpriced and below the SML)
- CAPM predicts that all alpha’s are zero.
