Question

You combine N risky assets to form an optimal risky asset and achieve a Sharpe Measure S.  If there is now a new asset with a negative Jensen Measure, you could combine the N+1 assets to achieve a Sharpe Measure larger than S.

TRUE or FALSE (briefly explain)

Answer 1

Answer : False

Explanation :

Step 1: Sharpe Measure and Jensen Measure meaning and formula

Sharpe Measure: The Sharpe ratio is measured by subtracting the risk-free return from the average portfolio return i.e. the excess return. This additional/excess return is divided by the standard deviation of the portfolio returns. It is used to evalutate the excess return gained on every additional unit of risk taken.

Jensen Measure:

Jensen's measure is that rate of return which exceeds the return calculated or predicted by the Capital Asset Pricing Model.

Step 2: Relationship between Sharpe Ratio and Jensen Measure

If the Alpha of a stock is negative, combining it with N assets will lead to reduced Sharpe Measure. This is due to the fact that Total Returns of a portfolio will reduce as a result of including a stock with Negative Alpha.

Reduced Total Returns mean lower Risk Premium (Portfolio Returns - Risk Free Rate) used in obtaining the Sharpe Ratio ( in the denominator) .