Optimal Portfolio Choice and the CAPM Flashcards
What are portfolio weights?
-The fraction of the total investment in the portfolio held by each individual investment
-xi = Value of Investment i/ Total value of portfolio
-Portfolio weights sum to 1
What is the expected return of a portfolio?
-The weighted average of the expected returns of the investments within it using portfolio weights
=-Sigmaixi[Ri]
What is an inefficient portfolio (2 stocks)?
This is when it is possible to find another portfolio that is better in terms of both expected return and volatility
What is an efficient portfolio (2 stocks)
There is no other portfolio of the two stocks that offers a higher expected return with lower volatility
What is the effect of correlation on a portfolio?
-Correlation has no effect on the expected return of a portfolio
-Correlation does affect the volatility of a portfolio
How do you find the efficient portfolio?
-Multivariate optimisation using variance of stocks, solve using Lagrange method
What is a long position?
A positive investment in a security
What is a short position?
A negative investment in a security
What is a short sale or transaction?
This is when you sell stock that is not your own, with the obligation to buy it back in the future
How can a short position be included in a portfolio?
Assign the relevant stock a negative weight
When is short selling profitable?
It is profitable when a stock’s price is expected to decline in the future (big short lol)
What is the efficient frontier?
The locus of portfolios that offer the highest possible expected return for a given level of volatility
How do you calculate expected return if some money is invested in risk free assets?
(1-x)rf+xE[lRp]= rf+ x([Rp]-rf)
What is buying on the margin?
-Money is borrowed to buy stocks
-Short selling is an example of this
What is the Sharpe Ratio?
Sharpe Ratio= Portfolio Excess Return/ Portfolio Volatility = (E[Rp]-rf)/SD(Rp)
What is the tangent portfolio?
-Optimal portfolio
-This is the portfolio with the highest Sharpe Ratio
-Every investor should invest in the tangent portfolio
-Efficient portfolio = tangent portfolio
What happens if the risk free investments are sold and the proceeds invested in investment i
- Expected return increases by i’s excess return E[Ri}-rf
-Volatility i has in common with the portfolio is added SD(ri)Corr(Ri,Rp)
-Beta = [SDRi)*Corr(Ri,Rp)]/ SD(Rp)
What is the required return?
The expected return that is necessary to compensate for the risk investment i will contribute to the portfolio, after selling the risk free assets
What is the relationship between expected returns and the efficient portfolio?
A portfolio is efficient IFF the expected return of every available security equals its required returns
What are the key assumptions of the CAPM?
-Investors can buy and sell all securities at competitive market prices
-Investors can borrow and lend at the risk-free interest rate
-Investors only hold efficient portfolios of traded securities
-Investors have homogenous expectations regarding volatilities, correlations and the expected returns of securities
Based on CAPM assumptions, what is the reasoning behind assuming all investors will hold the efficient portfolio?
-All investors will identify the same portfolio as being the efficient portfolio
-All investors will therefore demand the same portfolio
-The combined portfolio of risky securities of all investors must also equal the tangent portfolio
-The sum of all investors’ portfolios must equal to portfolio of all risky securities in the market
What is the Capital Market Line?
The tangent line of the market portfolio
What does the beta of a security measure?
-A security’s market risk relative to the market as a whole
-Captures the security’s sensitivity to market risk
What is the security market line?
The line along which all individual securities should lie when plotted according to their expected return and beta
What is the beta of a portfolio?
The weighted average beta of the securities in the portfolio
