Fundamental Law & Portfolio Optimization

Question 1

Write the equation that describes the Fundamental Law of Active Management. Define each term.

Answer 1

IR = IC x sqrt(BR)

IR = Information Ratio
-“Performance”

IC = Information Coefficient

• Correlation of forecasts to returns
• Range of 0-1, 0 = no correlation, 1 = correlation
• “How good of an investor are you?” aka “Skill”

BR = Breadth
-Number of trading opportunities per year

Question 2

Calculate the expected return of a single coin-flipping bet:

• .51 for heads
• 1000 tokens
• $1 each token

Answer 2

= (.51 * 1000) + (.49 - 1000)
= (510) + (-490)
= $20

Question 3

Calculate the expected return of 1000 coin-flipping bets:

• .51 heads
• $1 each token

Answer 3

=1000 x (.51*1 + .49-1)
=1000 x (.51 + -.49)
=1000 x (.02)
-$20

Question 4

Simons vs Buffet

• Both have same IR
• Simon’s algo is 1/1000 as smart as Buffet
• Buffet trades 120/year

How many trades must Simons execute?

Answer 4

IR is the same.
IC(Buffet) * sqrt(120) = IC(Simon) * sqrt(X)
IC(Buffet) * sqrt(120) = IC(Simon)/1000 * sqrt(X)
1000 * sqrt(120) = sqrt(X)
1000^2 * 120 = X
X = 120,000,000

Question 5

In terms of the fundamental law, when aiming for high performance, you can make up for low skill with ___.

A) low breadth
B) low sharpe ratio
C) high breadth
D) high volatility

Answer 5

C

Question 6

Which statement is true regarding the Fundamental Law of Portfolio Management?

A) IR = IC * sqrt(BR)
B) IC = IR * sqrt(BR)
C) BR = IC * IR
D) IR = IC + sqrt(BR)

Answer 6

A

Question 7

To assess weights for portfolio that minimizes risk using Mean Variance Optimization technique, what are the inputs required?

A) Expected Return, Volatility, Covariance, Target return
B) Expected Return, Volatility, Standard Deviation, Target return
C) Momentum, Volatility, Standard Deviation, Mean
D) Bollinger bands, Volatility, Standard Deviation, Target return

Answer 7

A