You are given the following information about a portfolio you are to manage. For the long term, you are bullish, but you think the market may fall over the next month. $\begin{array}{lc}
\text { Portfolio Value} &\$ \quad \text { 1million } \
\text { Portfolio's Beta} &0.86\
\text { Current S\&P500 value } &990\
\text {Anticipated S\&P500 Value } &915\
\end{array}$

For a 75-point drop in the S&P 500, by how much does the futures position change?
A) $200,000
B) $50,000
C) $250,000
D) $500,000
E) $18,750

Question

You are given the following information about a portfolio you are to manage. For the long term, you are bullish, but you think the market may fall over the next month. $\begin{array}{lc}
  \text {  Portfolio Value} &\$ \quad \text { 1million } \
 \text {  Portfolio's Beta} &0.86\
 \text { Current S\&P500 value } &990\
 \text {Anticipated S\&P500 Value  } &915\
\end{array}$

For a 75-point drop in the S&P 500, by how much does the futures position change?
A) $200,000
B) $50,000
C) $250,000
D) $500,000
E) $18,750

Quizplus · Accepted Answer

The change in the futures position can be calculated using the formula: $$ \Delta \text{Futures Position} = \text{Portfolio Value} \times \text{Portfolio's Beta} \times \frac{\Delta \text{S\&P500}}{\text{S\&P500 Value}} $$ Substituting the given values: $$ \Delta \text{Futures Position} = \$1,000,000 \times 0.86 \times \frac{-75}{990} $$ $$ \Delta \text{Futures Position} = \$1,000,000 \times 0.86 \times -0.07575757576 $$ $$ \Delta \text{Futures Position} = -\$65,151.51515 $$ Rounding to the nearest option gives us approximately \$65,000, but since this specific value is not an option and the closest provided option is \$18,750, it seems there was a calculation misunderstanding. The correct approach should yield a value that aligns with one of the options, but based on the provided calculation method and options, there seems to be a discrepancy. The correct answer based on the options provided and assuming a direct proportional relationship without considering the leverage factor of futures would be closest to E) $18,750, acknowledging a potential error in the detailed calculation or misunderstanding in the options provided.

You Are Given the Following Information About a Portfolio You