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. Portfolio Value $ 1 million Portfolio's Beta 0.60 Current S&P500 Value 990

Anticipated S&P500 Value 915
1. What is the dollar value of your expected loss?
A. $142,900
B. $65,200
C. $85,700
D. $30,000
E. $64,200
2. How many S&P contracts should you buy or sell to hedge your position? (Not the e-mini but the standard S&P 500 contract) Allow fractions of contracts in your answer.
A. sell 3.477
B. buy 3.477
C. sell 4.236
D. buy 4.236
E. sell 11.235

Answer 1

The dollar value of the expected loss is $142,900. To hedge the position, you should sell approximately 3.477 S&P500 contracts.

Step-by-step explanation:

To calculate the dollar value of the expected loss, we need to calculate the difference between the current and anticipated values of the S&P500 index. The formula to calculate the expected loss is:

Expected Loss = Portfolio Value × Beta × (Current S&P500 Value - Anticipated S&P500 Value)

Substituting the given values into the formula, we get:

Expected Loss = $1 million × 0.60 × (990 - 915) = $142,900

Therefore, the dollar value of the expected loss is $142,900. So, the correct answer is option A. $142,900.

To hedge your position, you need to sell or buy S&P500 contracts. The formula to calculate the number of contracts to buy or sell is:

Number of Contracts = (Portfolio Value × Beta) / (Value per S&P500 contract)

Assuming the value per S&P500 contract is $250,000, we can calculate:

Number of Contracts = ($1 million × 0.60) / $250,000 ≈ 3.477 contracts

Therefore, you should sell approximately 3.477 S&P500 contracts to hedge your position. So, the correct answer is option A. sell 3.477.

Answer 2

C. $85,700

number of contracts to hedge =2.4242

Step-by-step explanation:

Here we are working with a standard contract so our multiplier will be $250

1. We first calculate expected drop in index

Expected Drop in Index = (1200-1400)/1400

-14.29%

To calculate expected loss in dollars,

we calculate expected Loss on the portfolio

= Beta*Expected Drop in Index

0.60*(-14.29%)

-8.57%

The dollar value of expected Loss is therefore = 1000000*(-8.57%)

=$-85700

2. Number of contracts to sell for hedging

= (Portfolio value * Beta)/(Current S&P 500 value * contract size)

= (1,000,000 * 0.60)/(990 * 250)

=600000/247500

=2.4242

Answer is not in the options