L7 - CAPM I

Question 1

What do we need to consider if we sell some risk-free assets to invest in asset I, in order to raise our portfolios Sharpe ratio?

Answer 1

• Consider Required Rate of Return/ internal Rate of return
• The re-write variance of Rp by subbing into the Covariance formula with Correlation

The volatility of the portfolio is not just based on the standard deviation of the security but all how it is scaled by the correlation between itself and the current portfolio

Question 2

How do you derive the volatility of portfolio P when you add security i to it?

Answer 2

Question 3

What is the decision rule of whether we keep investing in security i?

Answer 3

• First line
  
  • sharpe ratio of asset i is greater than Sharpe ratio of asset p scaled by the correlation between the two (the risk you are adding to the portfolio)
  • times through by the standard deviation to get the second line
• Get bottom equation for subbing in for correlation between the two
  
  • stuff in green is a separate equation
  • to get from the last green line the the line in the slide sub for covariance and cancel out the SD(Rp)

Question 4

What should expected returns be under an efficient portfolio?

Answer 4

• efficient portfolio –> one that offers the highest Sharpe ratio ( tangency portfolio)

Expected new portfolio return = Expected return on original fund + weight borrowed to invest( Expected return of new fund - borrowing rate)

Question 5

What is the Capital Asset Pricing Model?

Answer 5

• What’s the relationship between the efficient portfolio and the market portfolio?
• We now turn to the implications of the collective investment decisions of all investors.
• Equation (2) –> the required rate of return for efficient portfolio formula –> implies that we can compute the expected return of any security based on its beta with the efficient portfolio.
• But for this, we need to compute the efficiency portfolio which is difficult.
• CAPM uses the optimal choices investors make to identify the efficient portfolio as the market portfolio, the portfolio of all stocks and securities in the market.

Question 6

What are the assumptions of CAPM?`

Answer 6

Three main assumptions:

• 1. Investors can buy and sell all securities at competitive market prices and can borrow and lend at a risk-free interest rate.
• .2. Investors hold only efficient portfolios of traded securities, portfolios that yield the maximum expected return for a given level of volatility.
• 3. Investors have homogeneous expectations regarding the volatilities, correlations, and expected returns of securities.
     * All have the same information about the stocks

This means that :

• If investors have homogeneous expectations, they will all hold the tangent portfolio (of risky securities).
• All investors demand an efficient portfolio, and the supply of securities is the market portfolio; hence the two must coincide.
• What if security were not part of the efficient portfolio?
  
  • Prices in the market will adjust so that the efficient portfolio and the market portfolio coincide, and demand equals supply (price drop, expected return will rise and thus people will start demanding it again)

Question 7

What is the Capital Market Line?

Answer 7

Question 8

What does beta mean under CAPM?

Answer 8

• The beta of security measures its volatility due to market risk relative to the market as a whole, and thus captures the security’s sensitivity to market risk
• Following the Law of One Price, in the competitive market, investments with similar risk should have the same expected return
• . The right measure of risk here is the non-diversifiable risk, market risk.

Question 9

What is the Security Market Line?

Answer 9

Question 10

What happens when a security is above the SML?

Answer 10

• positive alpha –> undervalued and should be bought
• equally if below –> it is overvalued and should be sold

if zero it is fairly priced under CAPM theory

Question 11

How do you calculate the expected return, variance and the Sharpe Ratio of a new portfolio after adding asset i?

Answer 11

*** :LOOK UP EQUATIONS

Expected new portfolio return = Expected return on original fund + weight borrowed to invest( Expected return of new fund - borrowing rate)