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In: Finance

An equity portfolio is worth $100 million with the benchmark of the Dow jones Industrial Average....

An equity portfolio is worth $100 million with the benchmark of the Dow jones Industrial Average. The Dow is currently at 10,000 and the corresponding portfolio beta is 1.2. The multiplier for the Dow is 10.

1) Please compute the number of contracts needed to double the portfolio beta.

2) Please compute the number of contracts needed to cut the beta in half.

Solutions

Expert Solution

We have following formula to calculate the number of contracts required

Number of contracts = {Total value of indexed equity portfolio / (Index value * multiplier for index)} *beta

Where,

Total value of indexed equity portfolio = $100 million

Index value (Dow jones Industrial Average) = 10,000

Multiplier for index = 10

Portfolio beta = 1.2

Therefore,

Number of contracts = {$100,000,000 / (10,000 * $10)}*1.2

= {$100,000,000 / $100,000}*1.2

= 1,200

1) Please compute the number of contracts needed to double the portfolio beta.

Number of contracts needed to double the portfolio beta = {Total value of indexed equity portfolio / (Index value * multiplier for index)} *beta

Where,

Total value of indexed equity portfolio = $100 million

Index value (Dow jones Industrial Average) = 10,000

Multiplier for index = 10

Portfolio beta = 1.2 *2 = 2.4

Therefore,

Number of contracts = {$100,000,000 / (10,000 * $10)}*2.4

= {$100,000,000 / $100,000}*2.4

= 2,400

2) Please compute the number of contracts needed to cut the beta in half.

Number of contracts needed to cut the beta in half = {Total value of indexed equity portfolio / (Index value * multiplier for index)} *beta

Where,

Total value of indexed equity portfolio = $100 million

Index value (Dow jones Industrial Average) = 10,000

Multiplier for index = 10

Portfolio beta = 1.2/2 = 0.6

Therefore,

Number of contracts = {$100,000,000 / (10,000 * $10)}*2.4

= {$100,000,000 / $100,000}*0.6

= 600

jeff jeffy answered 1 year ago
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