CFA论坛 - Powered by Discuz! Board

LOS d: Demonstrate how the geometric return of an actively managed commodity basket can be positive, whereas the underlying average commodity has a geometric return near zero.

The least likely condition for an actively managed commodity basket to yield a positive geometric return is when:

A)	the average geometric return of each underlying commodity is zero.

B)	the portfolio prohibits tactical deviations from its stated policy statement but requires annual rebalancing to the portfolio’s strategic asset allocation.

C)	the prices of commodities with a negative return in the basket are perfectly correlated.

The geometric return of an actively managed basket of commodities will be positive if each commodity in the basket has a positive return, regardless of their correlation with each other. The basket can still produce a positive return if the individual commodity returns are close to zero, assuming commodity returns are not perfectly correlated and the portfolio is rebalanced periodically (e.g. annually) to its strategic asset allocation.

A portfolio with an initial value of $100,000 contains two commodities: sugar and corn with a 60/40 percent strategic allocation in the two commodities, respectively. The portfolio is rebalanced at the end of each year to its strategic asset allocation. Corn prices remain unchanged over the next two years, with a 0% return in each of the periods. Sugar experiences significant swings in its price, returning 60% the first year while dropping 37.5% the second year.

The value of sugar at the end of the second year and the portfolio’s geometric average return over the two years, respectively, are closest to:

The following table shows the portfolio values:

T=0 T=1 Rebalanced to
strategic
allocation T=2

Sugar $60,000 $96,000 $81,600 $51,000

Corn $40,000 $40,000 $54,400 $54,400

Portfolio $100,000 $136,000 $136,000 $105,400

The portfolio’s geometric average return is:

Gains from rebalancing a portfolio of commodities to its strategic asset allocation when the average return on the underlying commodities is zero may occur under:

A)	passive but not active portfolio management.

B)	either active or passive portfolio management.

C)	active but not passive portfolio management.

Commodities in a passively managed portfolio are not rebalanced periodically and are allowed to deviate from their initial allocation. A passively managed portfolio would thus yield a zero return when the underlying commodities average a zero return. Commodities in an actively managed portfolio, on the other hand, are rebalanced periodically to their initial strategic asset allocation. This ensures that even when the average commodity gain is zero, the overall portfolio may yield a positive return.

	T=0	T=1	Rebalanced to strategic allocation	T=2
Sugar	$60,000	$96,000	$81,600	$51,000
Corn	$40,000	$40,000	$54,400	$54,400
Portfolio	$100,000	$136,000	$136,000	$105,400