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What does Covariance measure?
How two random variables move with one another
What is the formula for Covariance?
Cov(X,Y) = E(XY) - E(X) E(Y)
What is the covariance if X and Y are independent?
0
What does it mean if the covariance is positive?
The variables move in the same direction
What does it mean if the covariance is negative?
The variables move in opposite directions
What is the formula for the variance of a portfolio?
Var(aX + bY) = a2Var(X) + b2Var(Y) + 2abCov(X,Y)
What is the formula for Correlation?
Corr(X,Y) = Cov(X,Y)/StDev(X)*StDev(Y)
What sign will correlation always take?
The same sign as the covariance
What is standard deviation always in correlation?
Positive
What is correlation between?
-1 and 1
What is risk aversion?
Investor’s reluctance to accept risk
How is the aversion to accept risk overcome?
By offering investors a risk premium
What is a risk premium?
Compensation above what an investor would receive if he/she took on no risk
What do risk averse investors reject?
Fair games (a risky investment with a risk premium of zero)
What is the formula for the Risk Premium?
RP = E(r ) - r(f)
What is the risk-free rate?
The rate investors can receive on a riskless investment
How are risk premia related to risk aversion?
The risk premium that an individual investor demands for holding a portfolio should be increasing in both his risk aversion and the risk of the portfolio
What is the variance of a riskless asset?
0 because it doesn’t move
What is the covariance between a riskless asset and a risky asset?
Always 0
What is the formula for the Utility Function?
U = E(r ) - 1/2*A*σ2
If expected return increases, what happens to utility?
It increases
If the variance of the return increases, what happens to utility?
It decreases
If the coefficient of risk aversion increases, what happens to utility?
It decreases
What is the formula for weight?
w = (E(Ra) - rf)/Aσa2
What does the Sharpe Ratio measure?
Compensation relative to unit of risk
What is the formula for the Sharpe Ratio?
S = (Portfolio Risk Premium)/(σ of Portfolio Excess Return) = (E(Rp) - rf)/σp
Where does the Sharpe Ratio show up in our graph?
As the slope of the CAL
Are high or low Sharpe Ratios good?
High ratios
