Portfolio management

Question 1

Calculate the sharpe ratio of a active managed portfolio compared to a benchmark.

Answer 1

Sharpe ratio of portfolio ^ 2 = Sharpe ratio of benchmark ^ 2 + Transfer coefficient ^ 2 * active return / active risk ^ 2

Question 2

Calculate the Information ratio based on number of active trade made in the year.

Answer 2

IR = IC * SQRT(number of active trade per year)

Question 3

Calculate correlation using covariance.

Answer 3

Correlation = Covariance / (standard deviation A + standard deviation B)

Question 4

Calculate standard deviation from variance

Answer 4

standard deviation = sqrt( variance)

Question 5

Three assumptios of arbitrage pricing theory (APT)?

Answer 5

Asset returns are descibed by linear relationship to a set of factors.

Investor can elimate specific risk with well diversified portfolio.

Asset price are set there is no arbirage opportunties.

Question 6

What are the 4 factors in the Carhart model?

Answer 6

4 factors are:

Small minus big (size)
High minus low book value to price
winner minus loser (mometum)
Sensivity to market index

Question 7

How to calculate return in Fama-French Model ?

Answer 7

FF return = risk free return + beta * market risk premium + beta * small minus big factor + beta * high minus low book value

Question 8

How to calculate return in Pastor-Stambaugh Model?

Question 9

What is the Taylor rule that predict policy interest rates?

Answer 9

The Taylor rule states that:

Policy interest rate = I + i + 0.5(i-i) + 0.5(Y-Y)

(i-i*) is the difference between the inflation rate and the target inflation rate

(Y-Y*) is the output gap measured in percentage terms

Long term equilibrium interest rate is I + i (i.e. the real equilibrium interest rate + level of inflation)