QFIP-155: Fundamentals of Efficient Factor Investing

Question 1

State the Treynor-Black Rule

Answer 1

The Treynor-Black Rule states that “the maximum possible unconstrained Sharpe
ratio squared is equal to the market portfolio Sharpe ratio squared plus the sum of
the squared information ratios of the other factors”

In equation form, this can be stated as:
SR2P
SR2M
􀀀
¸K
j2
IR2

Question 2

State the Sharpe Ratio Improvement Capture.

Answer 2

Sharpe Ratio Capture
SR SRM
SRP SRM
Notation:

SR is the Sharpe ratio of the portfolio being measured

SRP is the unconstrained optimal Sharpe ratio

SRM is the Sharpe ratio of the market portfolio

Question 3

State how to compute the market plus one factor asset weights.

Answer 3

wA
M IRA
SRM A
wA 􀀀 wM 100%

Question 4

The expected reduction in Sharpe ratio from imposing the long-only constraint
increases with which quantities?

Answer 4

1. Number of nonmarket factors
2. Magnitude of factor information ratios
3. Lower levels of nonmarket factor risk
4. Negative correlations between nonmarket factor returns/exposures

Question 5

State how idiosyncratic risk accumulates across homogeneous assets in an equally
weighted portfolio.

Answer 5

If idiosyncratic risk is homogeneous, then the impact of portfolio’s idiosyncratic risk in
an equally weighted portfolio is given by:
,P

?
N
In other words, the idiosyncratic risk is reduced by a square-root-of-N factor.